Program
Monday 17 |
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Tuesday 18 |
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Wednesday 19 |
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09:00 |
Welcome |
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09:00 |
Pantelides |
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09:05 |
Gross |
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09:45 |
Hannewald |
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09:50 |
Burke |
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10:20 |
Coffee Break |
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10:15 |
Coffee Break |
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10:50 |
Marques |
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10:45 |
Mostofi |
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11:20 |
Castro |
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11:15 |
Ness |
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11:40 |
Pouillon |
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11:35 |
Verstraete |
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12:00 |
Lunch |
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11:55 |
Lunch |
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14:30 |
Palummo |
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14:30 |
Côté |
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15:00 |
Freysoldt |
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15:00 |
Maitra |
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15:30 |
Rohlfing |
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15:50 |
Coffee Break |
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15:30 |
Coffee Break |
16:00 |
Registration |
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16:20 |
Braicovich |
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16:10 |
Chelikowsky |
17:00 |
Nanoquanta |
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16:50 |
Soininen |
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16:40 |
Grüning |
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Steering Committee |
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17:20 |
Fratesi |
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17:00 |
Nanoquanta |
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17:40 |
Poster Session |
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General Meeting |
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18:30 |
Aperitif |
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20:00 |
Welcome Dinner |
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20:00 |
Dinner |
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20:00 |
Gran Gala Dinner |
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21:30 |
I3 ETSF Party |
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Thursday 20 |
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Friday 21 |
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Saturday 22 |
09:00 |
Scheffler |
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09:00 |
Rödl |
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09:00 |
Gatti |
09:30 |
Helbig |
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09:30 |
De Fausti |
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09:30 |
Martin-Samos |
09:50 |
Bokes |
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09:50 |
Schleife |
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09:50 |
Luppi |
10:10 |
Coffee Break |
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10:10 |
Coffee Break |
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10:10 |
Coffee Break |
10:40 |
Lazzeri |
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10:40 |
Hellgren |
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10:40 |
Andrade |
11:10 |
Zanolli |
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11:10 |
van Leeuwen |
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11:00 |
Abedi |
11:40 |
Varsano |
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11:40 |
Stan |
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11:20 |
Farewell |
12:00 |
Lunch |
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12:00 |
Lunch |
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12:00 |
Lunch |
14:30 |
Pasturel |
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14:30 |
Bockstedte |
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14:30 |
Nanoquanta EU Review |
15:00 |
Blase |
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15:00 |
Marini |
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15:20 |
Ren |
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15:30 |
Coffee Break |
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15:40 |
Coffee Break |
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16:00 |
Li |
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16:10 |
Ferretti |
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16:20 |
Gierlich |
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16:30 |
Sasioglu |
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16:40 |
IT1, IT9 meetings |
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16:50 |
Nanoquanta Young Researchers |
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20:00 |
Dinner |
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20:00 |
Savoyard Dinner |
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21:30 |
Nanoquanta SC |
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Poster size: 1.20m x 1.53m.
List of Abstracts
Time Dependent Density Functional Theory: Advances and Prospects
Eberhard K. U. Groß
Theoretische Physik, Freie Universität
Berlin
Abstract to be provided.
Quantum transport in ``real" carbon nanotubes
Z. Zanolli and J.-C. Charlier
Universit\'e catholique de Louvain,
Unit\'e PCPM
Carbon Nanotubes (CNTs) are constantly
attracting the interest of researchers
because they offer the opportunity of
investigating fundamental physical properties
at the nanoscale and being exploited as
building blocks for nanoelectronic devices.
Among the different possible applications of
CNTs, the present work focuses on their use
as nanosensors for gas detection thanks to
the change in conductance of the nanodevice
in presence of the gas to be detected. To
reach this goal, the structural, electronic
and transport properties of CNTs have been
investigated for perfect tubes, tubes
containing defects such as vacancy,
di-vacancy, oxigenated vacancy, and tubes
decorated with metal clusters.
Due to the ``nano" size of the systems under
investigation, atomistic simulations become
necessary for an accurate modelling of their
structural, electronic, and transport
properties. Indeed, effective bulk parameters
cannot be used for the description of the
electronic states since interfacial
properties play a crucial role and
semiclassical methods for transport
calculations are not suitable at the typical
scales where the device behavior is
characterized by coherent tunnelling.
Consequently, quantum-mechanical computations
with atomic resolution can be achieved using
localized basis sets for the description of
the system Hamiltonian and can predict
electronic and transport properties of
nanostructures.
In the present work, the structural and
electronic properties of CNTs are obtained
via the {\it ab initio} method as
implemented in the SIESTA code, {\it i.e.}
the calculations are based on density
functional theory (DFT), using
norm-conserving pseudopotentials
(Troullier-Martin) and atomic orbitals basis
set. The quantum conductance of the system is
achieved from electronic transport
calculations performed with the SMEAGOL code.
The latter is based on the non-equilibrium
Green's function (NEGF) formalism and uses
the one-particle Hamiltonian obtained from
the DFT calculations. Such approach, which
combines NEGF and DFT, allows us to model
real systems constituted by hundreds of atoms
to a high degree of accuracy.
Time-dependent density-functionals from nonequilibrium Green function theory
Robert van Leeuwen, Nils Erik
Dahlen,AdrianStan
Department of Physics, University of
Jyväskylä, Finland
In this presentation we will present a
general method to construct time-dependent
density functionals from
many-body perturbation theory. These
functionals can be constructed in such a way
that they display
a number of physically desirable features
such as the satisfaction of macroscopic
conservation laws
and the inclusion of memory effects. These
features are essential for a good
performance
of density
functionals for quantum transport phenomena
which involve strong fields and dissipation.
The tools to construct these
functionals are based on the elegant
techniques of nonequilibrium Green function
theory. We also solved
the Kadanoff-Baym equations for the
nonequilibrium Green function which can
serve
as an important
benchmark for new approximate density
functionals and will also give valuable
insight into the importance
of electronic correlations in the transport
problem.
The GW and the Time Dependent GW Approximations for Nonequilibrium Systems
A. Stan, N. E. Dahlen, R. van Leeuwen
Zernike Institute for Advanced Materials,
University of Groningen, The Netherlands
The formalism of Nonequilibrium Green
Functions Theory is used to investigate the
role of electron correlation in several
types
of systems. Various "GW-like"
approximations are studied in detail for
inhomogeneous nonequilibrium systems. The
importance of the using both full
self-consistency and conserving
approximations, is underlined. We also
apply
the Kadanoff-Baym equations to
nonequilibrium
inhomogenous systems within time dependent
GW
and we discuss the equivalence of this
approach to the solving of the
Bethe-Salpeter
equation with highly advanced kernels.
Theory of electronic transport in organic crystals
K.Hannewald, F.Ortmann, F.Bechstedt,
P.A.Bobbert
Friedrich-Schiller-Universität Jena,
We present a theoretical and numerical
description of charge-carrier transport
in organic molecular crystals. Our approach
is based upon a rigorous evaluation
of the Kubo formula for electrical
conductivity within a mixed Holstein-Peierls
model, i.e. including local and nonlocal
electron-phonon interaction. Explict
formulas for the polaron bandwidths and
mobilities as a function of temperature
are derived. The theory is supplemented by
ab
initio calculations of the
relevant material parameters (transfer
integrals, electron-phonon coupling,
phonons) for various materials (oligo
acenes,
durene, guanine). The
resulting predictions for the electron and
hole mobilities show a remarkably
good agreement with experiments and provide
new insight into several hitherto
poorly understood transport phenomena such
as
the
differences between electrons and holes,
the peculiar algebraic temperature
dependences, and anisotropy effects.
Structural and optical transitions of the Biliverdin chromophore
Yann Pouillon$^{1,2}$,
Francesco Sottile$^{3,2}$,
Xabier Lopez$^{1}$, \\
Myrta Gr\"{u}ning$^{4,2}$,
Angel Rubio$^{1,2}$
1. Facultad de Qu\'{i}micas, Universidad del Pa\'{i}s Vasco UPV/EHU,
Donostia-San Sebasti\'{a}n, Spain. \\
2. European Theoretical Spectroscopy Facility (ETSF),
Spain. \\
3. Laboratoire des Solides Irradi\'{e}s, \'{E}cole Polytechnique,
Palaiseau, France. \\
4. Unit\'{e} PCPM, Universit\'{e} Catholique de Louvain,
Louvain-la-Neuve, Belgium.
Phytochromes constitute a widespread family
of photoreceptors found in
plants and bacteria, where they act as
photomorphogenesis regulators.
It is now well-established that they exists
in two forms: the $P_{r}$,
physiologically inactive and absorbing red
light, and the $P_{fr}$,
absorbing in the far-red domain. It has also
been shown that the
$P_{r}$-$P_{fr}$ transition mechanism
involves an isomerisation process.
Yet the actual transition path is still an
open question, since it has
only been possible to directly observe the
$P_{r}$ form so far, and
several models are still being debated.
Biliverdin is the phytochrome found in
bacteria, and has been observed as
a crystal in its $P_{r}$ form within the
surrouding protein. Its
$P_{r}$-$P_{fr}$ transition has been studied
both experimentally and
theoretically. The most involved region of
the molecule has been
identified, though no definitive answer has
been given for the final
geometry. The protonation state of the
$P_{fr}$ form is not clear
either, an the mechanisms of the possible
proton transfers occuring are
still unknown. Adding to the confusion,
recent studies suggest that the
transition might involve a rotation around a
single bond in addition to
isomerisation. Due to steric clashes, this
rotation would in turn cause
further conformational changes in the
protein
environment. Until now
this process has been eluded because of its
complexity.
\\\\
All these considerations clearly call for a
finer-grained theoretical
insight, that we aim at providing the
experimentalists with.
The chromophore itself being composed of a
few dozens of atoms, we are
able to study it by means of \\textit{ab
initio} DFT calculations.
When adding the protein environment, the
number of atoms immediately goes
above 1500, requiring a different level of
approximation, and we are
exploring several available frameworks. In
all cases we are evaluating
and comparing the possible protonation
states, in addition to
systematically study the aforementioned
single-bond rotation. In order
to compare our results with experiments, we
calculate the Raman spectra
of all the structures we investigate.
Not only will the knowledge of the $P_{fr}$
form give the correct
mechanism of the photochemical transition,
as
it will open the way to
the description of the reverse transition
(called \\textit{dark
reversion}), which is orders of magnitude
slower and follows obviously a
different path. It will then become possible
to understand how the
metabolic state of the cell, in particular
oxygen levels, influence both
transitions.
This work is carried out in collaboration
with the experimentalists at
the Freie Universit\\\"at Berlin,
Pr.~R.~Bittl, Dr.~M. Brecht, and
J.~Nieder. We gratefully acknowledge support
from Nanoquanta, UPV
(Arina) and BSC (Mare Nostrum).
A First-Principles Approach to Designing Materials
Alain Pasturel
CNRS - Grenoble
The role of basic energetic and
thermodynamic
data in designing new materials is crucial
towards their application. Fundamental
knowledge of the microscopic factors
governing alloy phase stability has
increased
greatly due to the development of
highly-accurate “state-of-the-art” fist
principles computational approaches and
recent works have demonstrated substantial
quantitative improvements in the accuracy of
alloy phase diagrams calculated by these
techniques. Our presentation will be
illustrated by applications to the modelling
of phase diagrams in Pu- based alloys and
the
structural stability of UO2 under
irradiation.
Breakdown of the adiabatic approximation in a doped graphene monolayer
and in metallic carbon nanotubes
Michele Lazzeri
IMPMC, Universites Paris 6-7, CNRS, IPGP,
Paris, France
We compute, from first-principles, the
frequency of the phonons associated to the
Raman G bands in a graphene monolayer [1] and
in metallic nanotubes [2] as a function of
the charge doping. In both cases, the
frequency displays an important measurable
shift in the range of doping reached
experimentally. As a consequence, Raman
spectroscopy can be used as a direct probe of
the doping of these systems [3]. Calculations
are done using i) the adiabatic
Born-Oppenheimer approximation and ii)
time-dependent perturbation theory to explore
dynamic effects beyond this approximation.
The two approaches provide very different
results. The frequency shift of the G band in
graphene and of the G- in metallic tubes
represent remarkable failures of the
adiabatic Born-Oppenheimer approximation.
[1] M.Lazzeri, F.Mauri, Phys. Rev. Lett. 97,
266407 (2006)
[2] N. Caudal, et al. Phys. Rev. B 75, 115423
(2007).
[3] S.Pisana et al. Nature Materials 6, 198
(2007).
Ab-initio self-energy correction in systems with metallic screening
M. Cazzaniga, N. Manini, L. G. Molinari, G.
Onida
Università degli studi di Milano and
European Theoretical Spectroscopy Facility
The calculation of $GW$ corrections of the
band structure for metallic systems shows
the
importance of considering the intraband
contribution in the evaluation of the
polarizability in its small-${\bf q}$
limit.
When treated incorrectly, as in standard
$GW$
codes for semiconductor and insulators, it
induces the opening of a spurious gap at the
Fermi energy.
A direct implementation for intraband
contribution would require a Fermi-surface
integration.
To avoid this numerical overload we propose
an approach based on determining the
limiting
behaviour of the polarizability by a fit of
its Taylor expansion in the region where
${\bf q}$ is small but finite.
We test this method in the jellium case, and
in the cases of Na and Al. Based on this
adjusted polarizability we calculate the
$GW$
corrections for these systems, finding the
expected bandwidth reduction (increase of
the
effective mass) with respect to the DFT
bands, and of course no spurious gap.
Optical properties of ZnO -- the influence of strain and spin-orbit coupling
A. Schleife, C. Rödl, F. Fuchs, and F.
Bechstedt
Institut für Festkörpertheorie und -optik,
Friedrich-Schiller-Universität Jena
Zinc oxide is a material of scientific
interest since many decades with a wide
range
of applications. As an environmentally
friendly material with interesting optical
properties it is a possible candidate for
substituting GaN in optoelectronic
applications in the blue/ultraviolet region.
It can be grown as high-quality
single-crystals. [1]
Also for ab-initio calculations ZnO is an
interesting material -- mainly due to
difficulties in the description of the
shallow semicore d-electrons. The
band-ordering at the valence band maximum is
subject to discussions in the literature.
We study excitonic effects in the optical
spectra and especially bound excitons at the
absorption edge by solving the
Bethe-Salpeter
equation together with a perturbative
treatment of spin-orbit coupling. To reduce
the size of the emerging huge excitonic
Hamiltonian matrices we use hybrid
k-point-meshes which allows us to compute
converged and highly accurate results in the
range of meV. Biaxial strain is considered
as
a possible reason for contradicting
experimental results for the valence band
ordering. We also compute the dielectric
function up to 23 eV and compare with
experimental results. The influence of QP
energies on the spectrum is discussed.
[1] C. Klingshirn, ChemPhysChem 8, 782
(2007)
Dielectric Function and Dielectric Matrix for Finite Momentum Transfer~-- Answers and Open Questions
Hans-Christian~Weissker$^{1,*}$, Eleonora
Luppi$^{1,*}$, Marco Cazzaniga$^1,4$,
Francesco~Sottile$^{1,*}$,
Jorge~Serrano$^{3,*}$, Simo~Huotari$^{3,*}$,
Giulio~Monaco$^{3,*}$, and
Michael~Krisch$^{3,*}$, Valerio~Olevano
$^{2,*}$, Lucia~Reining$^{1,*}$
$^1$ Laboratoire des Solides Irradiés UMR
7642, CNRS-CEA/DSM, \'Ecole Polytechnique,
F-91128 Palaiseau, France.\\ $^2$ Institut
NEEL, CNRS, Grenoble, France.\\ $^3$
European Synchrotron Radiation Facility,
Grenoble, France.\\ $^4$ Università degli
Studi di Milano, of Milan, Italy.\\*
European Theoretical Spectroscopy Facility
(ETSF).
Both the EEL spectrum and the dynamic
structure factor as measured in inelastic
x-ray scattering (IXS) are given by the
imaginary part of the inverse dielectric
function. Our combined experimental and
theoretical work [1] of IXS and \textit{ab
initio} calculations carried out on silicon
at different levels of approximation shows
that time-dependent density-functional theory
in adiabatic local-density approximation
describes both the loss function
\textit{and} the dielectric function for
non-zero momentum transfer very well for
valence excitations in semi-conductors. The
remaining differences are shown to be mainly
lifetime related. We have also demonstrated
the importance of crystal local-field effects
and of the coupling between resonant and
anti-resonant contributions to the imaginary
part of the dielectric function. For sodium,
on the other hand, the TDLDA fares much less
well.
In our present poster we discuss several open
questions which have to be solved in order to
obtain a coherent and precise description of
the response functions. This includes the
off-diagonal elements of the inverse
dielectric matrix which represent the
local-field effects. Moreover, we discuss the
influence of the pseudopotential description
on the theoretical results. In particular, we
will focus on the absorption edges which
represent the contributions of the (semi-)
core states. The influence of the core
polarization on the spectra will be addressed
as well.
[1] H.-Ch.~Weissker \textit{et al.}, PRL
\textbf{97}, 237602 (2006).
Reflectance Anisotropy Spectroscopy study of ethylene on Si(001)
M. Marsili $^1$, O. Pulci $^1$, N. Witkowski
$^2$, P. L. Silvestrelli $^3$, Y. Borensztein
$^2$, R. Del Sole $^1$
$^1$ ETSF, INFM, CNISM, NAST and
Dipartimento di Fisica dell'Universit\`a di
Roma Tor Vergata, $^2$ Institute of
Nano-Sciences of Paris, UMR CNRS, $^3$ INFM,
Universit\`a di Padova
With the increasing demand for new organic
devices compatible with
current micro-electronics, the knowledge of
the interaction of
unsaturated hydrocarbon molecules such as
ethylene, acetylene or
benzene with silicon surfaces, is of
particular interest.
In spite of the large amount of experimental
and theoretical works devoted
to the study of the
adsorption of ethylene, the simplest molecule
containing a C-C
double bond, on Si(001), some aspects of this
process, such as the
saturation coverage, or the adsorption
geometry as a function of
coverage, are still unclear.
Here we study the interaction between
C$_2$H$_4$ and a vicinal Silicon (001)
surface by means
of Reflectance Anisotropy Spectroscopy and
analyze it with {\it
first principles} calculations.
Our results confirm that ethylene adsorbs
without breaking the silicon dimers.
Comparison of theoretical optical spectra
with experimental data
shows that the C$_2$H$_4$ molecules lay on
top of the
silicon dimers from low to high coverage.
This occurs even though,
from a purely energetic point of view,
a bridge configuration would be favorite at
saturation coverage.
Electronic correlation in 3d transition metals beyond $GW$: The FLEX method
Andreas Gierlich$^{1}$, Arno
Schindlmayr$^{1}$, Stefan Bl\"ugel$^{1}$
and V\'aclav Drchal$^{2}$
1. Institut f\"ur Festk\"orperforschung,
Forschungszentrum J\"ulich, 52425
J\"ulich, Germany \\ 2. Institute of
Physics, AS CR, Na Slovance 2, CZ-182 21
Praha 8, Czech Republic
The $GW$ approximation (GWA) has evolved as
the state of the art for ab initio
calculations of electronic excitations and
spectroscopies. For large classes of
materials, especially semiconductors and
simple metals, quasiparticle spectra
calculated within the GWA are in very good
agreement with experiments. However, it
ignores spectral features resulting from
higher-order correlation effects in the
localized 3d orbitals of transition metals,
such as the famous 6 eV satellite in the
photo emission spectrum of nickel.
Furthermore, exchange splittings and 3d
valence band widths often deviate from
experimental measurements. The FLEX
(fluctuation exchange) method is a
diagrammatic technique describing additional
two-particle scattering processes in
materials with intermediate correlation
strength. By explicitly including multiple
scattering in the electron-electron and
electron-hole channels, the FLEX method
captures correlation effects beyond those
contained in the GWA. We have developed a
simplified FLEX implementation designed to
describe electronic correlation in 3d
transition metals. First, density-functional
calculations are performed using the
full-potential linearized augmented
plane-wave scheme. The FLEX method is then
applied as a perturbative correction to
include two-particle correlation effects in
the self-energy of the 3d electrons. The
resulting equations are solved
self-consistently within the framework of
dynamical mean-field theory. We have applied
this scheme to selected non-magnetic and
ferromagnetic transition metals and present
illustrative results.
Macroscopic limit of time-dependent density-functional theory for adiabatic local approximations of the exchange-correlation kernel
Myrta Gr\"uning and Xavier Gonze
European Theoretical Spectroscopy Facility
(ETSF) and Unité PCPM, Université
Catholique de Louvain, Pl. Croix du Sud 1,
1348 Louvain-
la-Neuve, Belgium
European Theoretical Spectroscopy Facility
(ETSF) and Unit\'e PCPM, Universit\'e
Catholique de Louvain, Pl. Croix du Sud 1,
1348 Louvain-la-Neuve, Belgium
Time-dependent density-functional theory
(TDDFT) is a rather accurate and efficient
way
to compute electronic excitations for finite
systems. However, in the macroscopic limit
(systems of increasing size), for the usual
adiabatic random-phase, local-density, or
generalized-gradient approximations, one
recovers the Kohn-Sham independent-particle
picture, and thus the incorrect band gap. To
clarify this trend, we investigate the
macroscopic limit of the exchange-correlation
kernel in such approximations by means
of an algebraical analysis complemented with
numerical studies of a one-dimensional
tight-binding model. We link the failure to
shift the Kohn-Sham spectrum of these
approximate kernels to the fact that the
corresponding operators in the transition
space
act only on a finite subspace [1]. Finally
we discuss how an analysis similar to the one
in this work
can be applied to more sophisticated
approximations for the kernel \mdash like
the expressions derived from many-body
perturbation theory.
[1] M. Gr\"uning and X. Gonze PRB 76
(scheduled issue 7, 15 august)
Spin Polarisation and Electron Localisation in a Low-Density Electron Wire, A Density Functional Study.
D. Hughes and P. Ballone
Queen's University Belfast
Low-dimensional, high-mobility electron
systems can be prepared by doping or laser
irradiation of artificial semiconducting
structures. Then, low electron density and
low dimensionality stabilise spontaneous
spin polarisation and electron localisation,
which, in turn, may greatly affect the
potential applications of these systems.
We investigate these phenomena by density
functional (DF) computations for an
idealised
cylindrical jellium wire, using the local
density approximation for exchange and
correlation.
We employ a fully 3D representation of the
system, and we determine the electron
density
and Kohn-Sham orbitals by direct energy
minimisation in a plane wave basis.\\
Spontaneous spin polarisation and electron
localisation arise at a density far above
the
values found in other DF studies, relying on
radial and translational symmetry to
simplify the computational task.
We present results for the charge and spin
density exemplifying the variety of
ground state configurations found in our
study as a function of the jellium parameter
$r_s$, the wire radius, and the net spin
component ($S_z$) along the quantisation
direction.
We focus on systems at the boundary between
different regimes, where solutions are
found displaying a sizable amount of space
and/or spin disorder, pointing to the
stability of glassy low density
configurations.
Although our results are certainly affected
by the underlying local density
approximation, we
expect the global picture to remain valid in
general, and to be relevant for experimental
systems.
The frequency dependent Sterheimer equation in TDDFT
Miguel A. L. Marques
Centre for Computational Physics, Department
of Physics, University of Coimbra
Often we are interested in the response of an
electronic system to a weak perturbing field.
These underlie many different spectroscopy
tools, and are therefore a window to the
quantum mechanical world. It is then of
little surprise that a multitude of methods
appeared over the years to calculate response
properties. In this talk, we look at a very
old method: the solution of the Sternheimer
equation. It is well known that this is the
method of choice when
calculating static response, like static
polarizabilities, phonon frequencies, etc.
Although a perturbative technique, it avoids
the use of empty states, has a quite good
scaling ($N^2$) with the number of atoms, and
a relatively small prefactor.
The Sternheimer method can be trivially
extended to frequency dependent
perturbations, giving us access to a variety
of dynamic responses. The simplest of these
is perhaps the dynamic polarizability
$\alpha$. With basically the same effort we
can access the first hyperpolarizability
$\beta$, that is responsible for the
processes of
second-harmonic generation, optical
rectification and Pockles effect. Van der
Waals C$_6$ coefficients are obtained by
changing the frequency of the perturbing
field from real to imaginary. Finally, it is
possible to use the solution of the
Sterheimer equation to define the
linear-response of the electron localization
function (lr-ELF) --
a quantity that can be used to help
understanding electronic excitations in
complex systems. All these phenomena are
illustrated with benchmark calculations for
molecules and clusters.
The dynamical structure factor from TDLDA - a tool to determine differences in the short-range structure in Si-high pressure phases?
Wojciech We\l nic$^{1,2}$, Hans-Christian
Weissker$^{1,2}$ and Lucia Reining$^{1,2}$
$^{1}$Laboratoire des Solides Irradi\'es,
\'Ecole Polytechnique, Palaiseau, France,
$^{2}$European Theoretical Spectroscopy
Facility (ETSF)
Time-dependent-density-functional theory
(TDDFT) within the adiabatic local density
approximation (ALDA) is successfully employed
to calculate the dynamical structure factor
$S({\bf q}, \omega)$ nowadays. Good
agreement with experimental data obtained
from inelastic x-ray scattering have been
reported for different materials such as
silicon [1], aluminum [2] or transition metal
oxides [3]. \\ In this work we explore the
potential of TDLDA calculations of $S({\bf
q}, \omega)$ to detect changes in the local
geometry of a material by performing
calculations of three high pressure phases of
Si, namely the $\beta$-tin, the primitive
hexagonal and the hcp phase. These phases are
particularly suited as they exhibit very
distinct coordinations in their first
neighbour shell. Our first results of
calculations within the random-phase
approximation (RPA) with and without local
field effects at various values of $\bf q$
show that local field effects only play a
minor role in the excitation spectra. On the
other side, including the TDLDA kernel leads
to significant changes of the spectra with
respect to the RPA results. Above all, at
absolute q-values larger than $\approx$0.6
a.u. the spectra of the three phases differ
significantly from each other. These
differences can be attributed to the changes
in the local coordination. Furthermore the
differences in the excitation spectra are
most pronounced if the direction of q
corresponds to the direction of the bonds in
real space. Hence our results show that the
dynamical structure factor calculated within
TDLDA yields a fingerprint of the local
structural properties in the different
investigated phases of silicon. In the future
we intend to compare our results with
experimental data and apply this method to
more complex systems.\\
References \\
[1] H.-C. Weissker, J. Serrano, S. Huotari,
F. Bruneval,
F. Sottile, G. Monaco, M. Krisch, V. Olevano,
and L. Reining, Phys Rev. Lett. $\bf 97$,
237602 (2006)\\
[2] N. Maddocks R.W. Godby and R.J. Needs,
Europhys. Lett. $\bf 27$, 681 (1994)\\
[3] I. G. Gurtubay, Wei Ku, J. M. Pitarke, A.
G. Eguiluz, B. C. Larson, J.
Tischler and P. Zschack, Phys Rev B, $\bf
70$, 201201 (2005)\\
Many-body corrections and optical properties of graphene nanoribbons
D. Varsano$^2$, D. Prezzi$^{1;2}$, A.
Ruini$^{1;2}$, A. Marini$^{3}, E.
Molinari$^{1;2}$
1 INFM-CNR-S3, National Center on
nanoStructures and bioSystems at Surfaces,
I-41100 Modena, Italy,\\ 2 Dipartimento di
Fisica, Universit di Modena e a Reggio
Emilia, I-41100 Modena, Italy,\\ 3
Dipartimento di Fisica, Universit di a Roma
Tor Vergata, I-0133 Roma, Italy
Recent advances in the synthesis of single
layered graphite [1-3] have focused the
attention on novel quasi-one-dimensional
carbon-based systems, i.e. graphene
nanoribbons (GNRs) [4,5]. In particular, the
possibility of patterning graphene sheets in
a controllable manner opens exciting
opportunities for future nanoscale
optoelectronics applications. One of the most
interesting features of these systems is the
sensitivity of their properties to the
ribbon-edge shape [6,7], which dictates the
classification of GNR in armchair (A), zigzag
(Z) or chiral (C) ones.
Here we focus our attention on A-GNRs, which
can be further classified in three distinct
families: N=3p1, N=3p, N=3p+1, where N
indicates the number of dimer lines across
the ribbon width. In particular, we calculate
the optical spectra of nanometer-sized A-GNRs
belonging to different families and with
dierent edge terminations, namely
hydrogen-passivated and clean-edge ribbons.
As in the case of other one-dimensional
systems,
the spatial confinement is expected to induce
a strong enhancement of Coulomb interactions.
The resulting many-body effects are fully
accounted
within the GW-BSE scheme [8].
Indeed, in all the studied cases, the
inclusion of many-body corrections is shown
to be crucial in determining both the peak
position and its lineshape, and the optical
spectra are always dominated by strongly
bound excitons. Besides, we find a
significant dependence of both the energy
gap
and binding energy on the ribbon family.
This, together with the edge termination,
also determine the presence of optically
inactive excitonic states, thus affecting the
luminescence efficiency.\\
References: \\[1] K. S. Novoselov et al.,
Nature 438, 197 (2005).\\ [2] Y. Zhang et
al., Nature 438, 201 (2005).
\\[3] C. Berger et al., Science 312, 1191
(2006). \\[4] Z. Chen et al.,
condmat/0701599 (2007).\\ [5] M. Y. Han et
al., Phys. Rev. Lett., 98,
296805(2007).\\[6] Y. Son et al., PRL 97,
216803 (2006). \\[7] V. Barone et al., Nano
Lett. 6, 2748 (2006). \\[8] G. Onida et
al., Rev. Mod. Phys. 74, 601 (2002).
Ab initio optical absorption spectra of native and size-expanded xDNA base assemblies.
D. Varsano$^1$, A. Migliore$^2$, S.
Corni$^1$, A. Rubio$^3$, A. Garbesi$^1$ and
R. Di Felice$^1$
1 INFM-CNR-S3, National Center on
nanoStructures and bioSystems at Surfaces,
I-41100 Modena, Italy\\2 Department of
Chemistry, Center for Molecular Modeling,
University of Pennsylvania, Philadelphia, USA
\\ 3 Dpto. Fisica de Materiales, Facultad
de Quimica U. Pais Vasco, UPV/EHU, San
Sebastian, Spain.
We present the results of time-dependent
Density Functional Theory calculations of
the
optical absorption spectra of synthetic
nucleobases and of their hydrogen-bonded and
stacked base-pairs.
We focus on size-expanded analogs of the
natural nucleobases obtained through the
insertion of a benzene ring bonded to the
planar heterocycles (x-bases), according
to the protocol designed and realized by the
group of
Eric Kool (e.g., Gao, J.; Liu, H.; Kool, E.T.
{\it Angew. Chem. Int. Ed.} {\bf 2005},
44, 3118-3122, and references therein).
We find that the modifications of the
frontier electron orbitals with respect to
natural bases,
which are induced by the presence of the
aromatic ring, also affect the optical
response.
In particular, the absorption onset is pinned
by the benzene component of the HOMO of each
x-base
(xA, xG, xT, xC). In addition, the main trait
of the H-bonding inter-base coupling
is a conspicuous red-shift of spectral peaks
in the low-energy range.
Finally, the hypochromicity, a well known
fingerprint of stacking, is more pronounced
in stacked xG-C and xA-T pairs than in
stacked G-C and A-T pairs (also presented
here), index of enhanced stacking.
Optical Spectra of Si Nanocrystallites: Bethe-Salpeter and Time-Dependent Density-Functional Theory
L.E. Ramos$^1$, J. Paier$^2$, G. Kresse$^2$,
and F. Bechstedt$^1$
$^1$ Friedrich-Schiller-Universität Jena,
Institut für Festkörpertheory und -optik,
Jena, Germany \\ Institut für
Materialphysik, Universität Wien, Wien,
Austria.
We present the optical absorption spectra of
Si nanocrystallites containing up to 41 Si
atoms within a method based on many-body
perturbation theory (MBPT) and a method based
on time-dependent density-functional theory
(TDDFT). The method within the MBPT combines
the Green-function screened-Coulomb-potential
method (GW) and the solution of the
Bethe-Salpeter equations (BSE) for the
polarization function. The method based on
TDDFT is applied
for two different exchange-correlation (XC)
functionals, the local-density approximation
functional and the hybrid
Heyd-Scuseria-Ernzerhof functional (HSE) to
generate the XC potential in a generalized
Kohn-Sham equation.
We compare the optical and quasiparticle gaps
in different approximations and evaluate the
effect of setting the screened Coulomb
potential and the XC kernel to zero,
respectively in the GWBSE and TDDFT
approaches. We verify that the influence of
the electron-hole attraction on the optical
absorption spectra is more important in the
GWBSE scheme than in the TDDFT schemes, at
least for the two XC functionals studied.
With an appropriate choice of the functional,
the TDDFT approach can reproduce several
features of the GWBSE spectra.
Spectra of triatomic systems calculated using factorization method
T. \v{S}edivcov\'{a}-Uhl\'{i}kov\'{a},
A. Bordoni, N. Manini
Dipartimento di Fisica, Universit\`{a} di
Milano, Via Celoria 16,
20133 Milano, Italy; and European Theoretical
Spectroscopy Facility (ETSF)
The accurate and efficient method developed
by A. Bordoni and N. Manini\footnote{
A. Bordoni, N. Manini, {\em I. J. Quant.\
Chem.\/}, {\bf 107}, 782--797 (2007)}
and successfully used for 1D potential of
diatomic molecules (e.g.\ $\rm H_2$),
is now being extended triatomic species.
The exact
diagonalization of an algebraically
calculated matrix
based on powers of the Morse coordinate have
several advantages.
It includes anharmonicity from the beginning,
can be applied to a
rich class of potentials (also double
minimums), is (substantially) free from
approximations, gives exact results in the
limit of infinite basis size
and is computationally efficient due to the
matrix sparseness.
We present benchmark calculations on HCN
molecule.
The increasing degree of freedoms in
polyatomic systems leads to more intricate
form of both kinetic and potential energy.
The \it {ab initio} potential has been
fitted on a series of powers of two
different
Morse coordinates. The kinetic term is
constructed in internal coordinates and
goes beyond the harmonic coupling anharmonic
oscillator (HCAO) approach.
Efficient Calculations of Electronic Excitations with a Localized $GW$ Formalism
Xinguo Ren,$^1$ Patrick Rinke,$^{1,2}$
Volker Blum,$^1$ and Matthias Scheffler$^1$
$^1$Fritz Haber institue of the Max Planck
society, Berlin. Germany \\ $^2$ Materials
Research Lab, University of California at
Santa
Barbara, CA, USA
First principles predictions of the
electronic excitations of molecules,
clusters, and/or molecules adsorbed on
surfaces are very important from both a
theoretical and a technological point of
view. Many-body perturbation theory
within Hedin's $GW$ approach is a successful
framework for this task, and is frequently
applied to study periodic systems. However,
$GW$ studies of finite systems are still the
exception. This is due to the fact that most
$GW$
implementations utilize plane-wave basis
sets. The periodic boundary conditions impose
a supercell geometry whose required size
typically renders the computational cost
prohibitively expensive for finite systems.
It is the goal of the present work to develop
a $GW$ formalism using a localized basis set,
which by construction promises to give
an efficient, all-electron description of the
excitations of both confined and extended
systems on equal footing.
Our $GW$ formulation is based on a new
efficient DFT code FHI-aims [1], in which
numeric atom-centered orbitals are employed
as basis functions. As a first application,
we have studied a set of finite systems
spanning individual
atoms, small molecules (methane, silane,
benzene), small clusters (Na$_n$), and
biomolecules (alanine). In all cases, we
performed $G_0W_0$ calculations, in which
$GW$ is applied as a perturbation to an
underlying ground-state calculation. Our
approach requires only a moderate amount of
basis functions, which considerably increases
the efficiency compared to plane-wave based
approaches. A key feature of our $GW$
formalism is that intermediate quantities
like the polarizability and the screened
Coulomb potential are represented by a
second, auxiliary set of atom-centered basis
functions. Thanks to the resolution of
identity technique, the same auxiliary basis
functions enable us to do Hartree-Fock (HF),
and hence hybrid functional calculations on
the same platform. For all our test cases
$G_0W_0$ produces ionisation potentials in
much better agreement with experiment
compared to LDA, HF or hybrid functionals. By
applying $G_0W_0$ separately as perturbation
to LDA
(strong self-interaction) and HF
(self-interaction free, but no correlation)
we can systematically investigate the
mechanism behind this improvement. As implied
by its construction, $G_0W_0$ reliably
removes the self-interaction present in the
ground state and adds correlation resulting
from the electronic screening. It thus
significantly
reduces the spread in the single particle
levels of the ground state calculation
[severe under (over)estimation in LDA (HF)]
with only a small residual starting point
dependence remaining.
[1] V. Blum {\it et al.,}
{\it The FHI Ab Initio Molecular
Simulations (aims) project}, \\ ~~~~
Fritz-Haber-Institut, Berlin (2007).
First-principles Optical Properties of semiconducting surfaces and nanowires: the role of the excitonic effects
M.Palummo
Dipartimento di Fisica, Universita' "Tor
Vergata", Via della Ricerca Scientifica I ,
00133 Roma, Italy
The experimental characterization of
nanomaterials and also the ability to invent
for them new functionalities, depends heavily
on the understanding of their electronic
excitations and their dielectric response.
Parameter-free calculations of the optical
spectra, based on the Density-functional
theory (DFT)
joined with the many-body perturbation theory
(MBPT) have witnessed impressive advances in
recent years.
Several examples of Bethe-Salpeter
calculations in different systems from bulk
materials, to surfaces, nanostructures,
molecules and liquids, are today present in
the literature.
In the present speech, after an overview of
this theoretical/computational
approach, very well known in this community,
I aim to concentrate on several applications
regarding the surface optical spectra of some
semiconducting materials and of Ge and Si
nanowires.
Many-body effects and inelastic electronic transport through nanoscale devices
H. Ness~$^{1,2}$, L. K. Dash~$^{1}$ and R. W.
Godby~$^{1}$
$^{1}$~Department of Physics, University of
York, York YO10 5DD, UK; $^{2}$~CEA-Saclay,
DSM/DRECAM/SPCSI, B.462, F-91191
Gif-sur-Yvette, France.
We consider the problem of interaction
between particles (electrons e and phonons
ph) in the context of electronic transport in
nanoscale devices. We present a technique
based on non-equilibrium Green's functions
and
include the many-body effects under the form
of self-energies. Different levels of
approximation are used to determine the
corresponding e-e and e-ph self-energies.
We apply this technique to model systems
describing a lead-molecule-lead
heterojunction and calculate both the current
and current-current correlation functions.
We show that, for the e-ph interaction, it is
necessary to go beyond the commonly-used
self-consistent Born approximation (SCBA) to
obtain correct results for a wide range of
parameters. We also discuss the
fluctuation-dissipation theorem in the
context of non-equilibrium transport.
Finally, we briefly consider the calculation
of different self-energies for the e-e
interaction (HF,GW, etc.) and their extension
to the non-equilibrium case.
Spin-wave excitations from time-dependent density-functional theory
Manfred Niesert, Arno Schindlmayr, Christoph
Friedrich and Stefan Blügel
Institut für Festkörperforschung,
Forschungszentrum Jülich, 52425 Jülich,
Germany
Spin waves constitute an important class of
low-energy excitations in magnetic solids
with a characteristic material-specific
dispersion and a direct relation to
magnetization dynamics. Until now most
theoretical studies are based on the
Heisenberg model of localized spins or on the
frozen-magnon method, but neither is
applicable to investigate the dynamics of
spin waves in metallic systems with itinerant
electrons. As a possible solution,
time-dependent density-functional theory
gives access to the full frequency-dependent
transverse spin susceptibility, from which
the lifetimes of spin-wave excitations as
well as related spectral information can be
extracted. We develop a practical scheme to
calculate spin-wave spectra from first
principles within this framework and
illustrate its performance by applications to
prototype ferromagnetic transition metals.
Our implementation uses the full-potential
linearized augmented-plane-wave method, and
dynamic exchange-correlation effects are in
the first instance described by the adiabatic
local-density approximation.
Electronic deexcitation in semiconductors: towards a complete \emph{ab initio} approach
Jelena Sjakste$^{1}$, Valeriy
Tyuterev$^{1,2}$, Nathalie Vast$^1$
$^1$ Laboratoire des Solides Irradi\'{e}s,
CEA/DSM-CNRS-Ecole Polytechnique 91128
Palaiseau, France \\ $^2$ Tomsk State
Pedagogical University, 634041 Tomsk, Russia
Today, ultrafast time-resolved spectroscopy
is a powerful tool
to study the dynamics of
carrier relaxation in semiconductors and
complex materials.
This technique gives access to detailed
information on the interaction processes
between elementary excitations. However,
theoretical description of these
processes is still incomplete and is often
based on adjustable parameters [1,2].
At excitation energies smaller than two times
the gap energy, the dynamics of
carrier relaxation is determined by their
interaction
with phonons. The excited electrons interact
with short-wavelength phonons (intervalley
scattering), with polar optical phonons
(Fr\"{o}hlich interaction), and with
acoustical long-wavelength phonons. To
interpret the experiments of time-resolved
spectroscopy, it is necessary to know the
relaxation rates related to each deexcitation
mechanism.
The goal of this work in progress is to
develop a general \emph{ab initio}
approach for all deexcitation processes
related to electron-phonon interactions.
An approach to electron interaction with
short-wavelength (intervalley) phonons is
already established [3-5]. Our approach,
which is based on Density Functional Theory
and
Density Functional Perturbation Theory,
provides electron relaxation rates in good
agreement with
experiment, and can yield electron-phonon
coupling parameters for the Monte Carlo
simulations of
optical and transport properties of
semiconductors. As a next step, we are
considering
electron interaction with long-wavelength
phonons: Fr\"{o}hlich interaction, which
is the dominant deexcitation
process at high temperatures and at low
carrier excitation energies, and
electron-acoustical long-wavelength phonon
interaction.
[1] C. Jacoboni and L. Reggiani, Rev. Mod.
Phys, \textbf{55} (1983) 645.\\
[2] J.~Shah, B.~Deveaud, T.~C.~Damen,
W.~T.~Tsang, A.~C.~Gossard, P.~Lugli,
Phys. Rev. Lett, \textbf{59} (1987)
2222.\\
[3] J. Sjakste, V. Tyuterev, N. Vast, Phys.
Rev. B \textbf{74} (2006) 235216.\\
[4] J. Sjakste, V. Tyuterev, N. Vast, Applied
Physics A \textbf{86} (2007) 301.\\
[5] J. Sjakste, N. Vast, V. Tyuterev, 2007,
accepted in Journal of Luminescence \\
Long-range and Long-Chain Molecules in TDDFT: Modelling the exact kernel
Neepa T. Maitra
Hunter College of the City University of New
York
Recent years have witnessed increasingly wide
and varied applications of TDDFT for
excitations and response. We discuss why the
usual approximations fail in certain cases
involving double excitations, long-range
charge transfer excitations, and
polarizabilities and dissociation of
long-range molecules, and derive model
kernels to try to fix these problems.
Implementation of an All-Electron $G_0W_0$ Code Based on
FP-(L)APW+lo
Ricardo I. Gomez-Abal$^1$, Xinzheng Li$^1$,
Hong Jiang$^1$, Christian Meisenbichler$^2$,
Claudia Ambrosch-Draxl$^2$ and Matthias
Scheffler$^1$
1 Fritz-Haber-Institute of the
Max-Planck-Society, Berlin, Germany \\ 2
Department of Material Physics, University of
Leoben, A-8700, Austria
The $GW$ approach, applied as a first order
correction to the Kohn-Sham
eigenvalues ($G_0W_0$), has become the method
of choice for the determination of
quasi-particle excitations in semiconductors
and insulators, for a review see
[1]. Most of the existing codes are based on
the pseudopotential (PP) method,
where only the pseudo-valence states are
included in the calculation of the self
energy. A few years ago, the first
full-potential (FP) all-electron
implementations appeared [2,3], showing
significant differences with PP results.
Nowadays, there is an emerging consensus that
$G_0W_0$ bandgaps are slightly
underestimated in weakly correlated systems,
provided that core states are
adequatelly treated. Improvements have been
obtained by the recently proposed
quasiparticle self-consistent GW method [4],
extending the ability to obtain
accurate predictions of excited state
properties for moderately correlated
materials. Even qualitative agreement with
experiments has been obtained for
some strongly correlated systems [5].
The FP-(L)APW+lo method provides currently
the most reliable results within
density-functional theory. We have developed
our own all-electron $G_0W_0$ code,
based on the Wien2k implementation of the
FP-(L)APW+lo method. As a basis set
for the expansion of non-local operators we
use the mixed basis set proposed in
Ref. [1], which allows the inclusion of core
and semicore states on the same
footing. We have also extended the linear
tetrahedron method to the calculation
of \textbf{q}-dependent Brillouin zone
integrations. The singularity of the
dielectric function as
$\textbf{q}\rightarrow 0$ is treated using
$\textbf{k}\cdot\textbf{p}$ perturbation
theory to obtain the limit
analytically. The frequency dependence of the
polarization is calculated
numerically, without the need for further
approximations like the plasmon pole
model. All these features make this the most
accurate implementation of the
$G_0W_0$ approximation to date.
In this poster, we show the computational
details of this implementation.
Through a set of tests on different materials
we analyse the efficency and
precision of the code as a function of the
various dimensioning parameters (i.e.
number of \textbf{k}-points, frequencies,
etc).
[1] F. Aryasetiawan and O. Gunnarsson, Rep.
Prog. Phys. {\bf
61}, 237 (1998).\\
[2] W. Ku and A. G. Eguiluz, Phys. Rev.
Lett. {\bf
89}, 126401 (2002).\\
[3] T. Kotani and M. van Schilfgaarde, Solid
State Commun. {\bf
121}, 461 (2002).\\
[4] S. Faleev, M. Van Schilfgaarde, and T.
Kotani, Phys. Rev. Lett.
{\bf 93}, 126406 (2004).\\
[5] M. Van Schilfgaarde, T. Kotani, and S.
Faleev, Phys. Rev. Lett. {\bf
96}, 226402 (2006).
Mobility gap of silica: many-body contribution
L. Martin-Samos(1), G. Bussi(2), A. Ruini(1)
M. J. Caldas(3) and E. Molinari(1)
(1) INFM-CNR S3, (2) Computational Science
ETH, (3) Instituto di Fisica Universidade di
Sao Paolo
Silica is one of the central material in a
wide range of technological applications, for
instance, in the MOS gorverning modern
electronic devices. In the recent past, with
the advent of nanodevices, the reduced
dimensions of the oxide layers and the
required abruptness of the
interface demands for an atomic-scale
understanding of the
microscopic processes governing electronic
performances, such as the
carrier mobility and energy levels. In
amorphous semiconductors and
insulators the free-carrier transport is
directly related to the
so-called mobility gap, that is defined as
the energy difference
between mobility edges, separating localized
states tails from
extended band states, and plays the same
role
of the electrical energy gap in crystalline
systems. Although
extensive studies have been carried out for
silica, the experimetal values
reported in the literature for the measured
mobility gap range from
8.8 to 11.5 eV. Under the theoretical point
of view, numerical studies have been
performed on particular silica polytypes
using mainly mean-field approches or model
Hamiltonian. and only very recently a
first-principles method based on many-body
perturbation theory has
been applied to study the optoelectronic of
quartz[1]
and cristobalite[2]. In any case, no unified
physical picture linking density, mobility
gaps and disorder has emerged.
In the present work, we go beyond the
previous studies by using a
multi-scale methodology, which comprises
generation of reasonably
large silica models and calculation of
quasi-particle electronic structure by means
of the GW
approach, through a state-of-the-art
first-principles technique within many-body
perturbation theory. We performed such
calculations for quartz, cristobalite and
different glass configurations with different
amount of disorder. We find that as expected,
disorder
introduces localized states in the gap of
silica, however the
mobility gap is only very weakly influenced
by such defects. We also find that, the local
fluctuations of the density is responsible
for the unexpected high many-body correction
in amorphous silica.
References
[1] E. K. Chang and M. Rohlfing and S. G.
Louie, Phys. Rev. Lett. 85, 2613 (2000)
[2] L. E. Ramos and J. Furthmuller and F.
Bechstedt, Phys. Rev. B 69, 85102 (2004)
Second order harmonic generation in crystalline semiconductors
Eleonora Luppi, Andrea Cucca, Lucia Reining,
Francesco Sottile and Valerie V{\'e}niard
Laboratoire des Solides Irradi{\'e}s, Ecole
Polytechnique Palaiseau, France
A comprehensive understanding of the
nonlinear optical properties of
solids is crucial for the improvement of
nonlinear materials and devices and
provides an opportunity to search for new
materials.\\
However, the theoretical description of
nonlinear effects in solids is a formidable
task and important difficulties have delayed
any accurate calculations for many
years.\\
We formulate a derivation for the calculation
of second-order susceptibility
tensor for crystals of any symmetry within
the Time Dependent Functional Theory
(TDDFT).\\
For cubic symmetries, we show how this
approach can be simplified and expressed in
terms of the second order
response function and of the dielectric
function.\\
Numerical results will be presented for SiC
and GaAs.\\
EELS in graphene and carbon nanotubes: Linear plasmon dispersion
R. Hambach (1,2), Ch. Giorgetti$ (1) and L.
Reining (1) C. Kramberger (3) and T. Pichler
(3)
(1) CNRS-LSI, Ecole Polytechnique,
Palaiseau,(2) IFTO,
Friedrich-Schiller-Universität
Jena,
Germany, (3) IFW Dresden, Germany
France
The fundamental analogy between graphene and
single walled carbon
nanotubes (SWCNT) is studied for collective
excitations. Using
the DP-code [1], we calculated momentum
resolved energy electron
loss spectra (EELS) for isolated graphene in
RPA. Despite its two
dimensional character, we find a linear
dispersion of the pi-plasmon
for in-plane momentum transfer. The
comparison with experiment
reveals its strong resemblance with the
dispersion in isolated,
vertically aligned SWCNTs along the tube
axis. Interwall interaction
between tubes can be modeled by means of two
layer graphene.
[1] www.dp-code.org
GW band-structure and self-energy real-space decay by means of maximally-localized
Wannier functions.
Andrea Ferretti, Layla Martin Samos, and
Alice Ruini
Dipartimento di Fisica, Universit\`a di
Modena e Reggio Emilia, I--41100 Modena,
Italy. \\ National Research Center S3 of
INFM-CNR, I--41100 Modena, Italy .
The use of maximally localized Wannier
functions (MLWFs) [1] recently became
very popular in the electronic structure
community, as a supplementary analysis tool.
On one hand, MLWFs are attractive because
they
constitute a localized basis set which is
complete and orthonormal, while
on the other hand, they also carry physical
information.
Among the many properties of WFs
once they are adopted as a basis, it is
possible to exploit the real-space
decay of the periodic Hamiltonian operator to
refine its spectrum in terms of a
better sampling of the Brillouin zone (BZ).
This feature is particularly appealing in
those cases where
dealing with a large number of ${\bf
k}$-points is expensive, like {\it e.g.} the
GW method.
In this work we show that BZ interpolation
using MLWFs is feasible also in the
case of the quasi-particle (QP) calculation
within the GW approximation.
We apply the method to silicon bulk as a test
case, as well as to realistic
systems like polymer crystals and quartz. The
computed QP-band structures are in
good agreement with reference data, where
available. We also discuss and compare
the real-space decay of the GW self-energy in
the analyzed cases.
All the calculations have been performed
using the {\sc WanT} package [2] to compute
MLWFs
and the {\sc SaX} code [3] for the GW
corrections.
\begin{list}{[\arabic{ref}]}{\usecounter{r
ef}\setlength{\itemsep}{0cm}%
\setlength{\labelwidth}{0.5cm}
\setlength{\leftmargin}{0.8cm} %
\setlength{\labelsep}{0.1cm} }
\item
N. Marzari, and D. Vanderbilt, Phys. Rev. B
{\bf 56}, 12847 (1997).
\item
\textsc{WanT} project,
\texttt{http://www.wannier-transport.org}.
\item
\textsc{SaX} project,
\texttt{http://www.sax-project.org}.
\end{list}
Controlling Polarization at Insulating Surfaces: Electron Spectroscopy of Molecules Adsorbed on Thin Epitaxial Films
Christoph Freysoldt, Patrick Rinke, and
Matthias Scheffler
Fritz-Haber-Institut der
Max-Planck-Gesellschaft, Berlin, Germany
The spectroscopic characterization of
insulators has long been hampered by the fact
that many techniques such as scanning
tunneling microscopy or photoelectron
spectroscopy require electrically conducting
samples. Growing ultrathin films on metals or
doped semiconductors apparently offers a
simple solution to this problem as electrons
can now tunnel to and from the conducting
substrate. However, the direct transfer of
experimental conclusions from these films to
surfaces of macroscopic samples relies on the
two critical assumptions that a) the
thickness dependence and b) interactions with
the substrate are negligible for the
adsorption and other surface properties. We
have previously shown from a ground state
perspective that this is generally not the
case [1]. Here we extend the study to include
also the spectroscopic perspective for clean
and adsorbate-covered insulator films. We
present density-functional theory (DFT) and
$G_0W_0$ quasiparticle energy calculations
for NaCl/Ge(100) as prototypical
insulator/semiconductor system and consider
its interaction with CO as model adsorbate.
The NaCl/Ge(100) system has been
experimentally studied with a variety of
techniques. Using DFT calculations, we have
determined its hitherto unknown atomic
structure and find good agreement with all
experimental observations. For CO adsorbed on
NaCl/Ge, we predict by means of $G_0W_0$
calculations a considerable,
substrate-induced reduction of the
quasiparticle (HOMO-LUMO) gap by more than 3
eV compared to the gas phase and 1 eV
compared to the NaCl surface. As a function
of NaCl film thickness the CO gap increases
by 0.1-0.2 eV per NaCl layer. The physical
origin of this behavior is simple: the
charged excitation in the molecule polarizes
the underlying NaCl film and the Ge substrate
-- an effect naturally incorporated in the
$GW$ self-energy, but not in standard, local
DFT functionals. By varying the thickness of
the NaCl film the influence of the substrate
polarization on the molecule can be
controlled, which would be desirable from a
spectroscopic point of view. However, a
larger film thickness also comes at the
expense of a smaller tunneling current. We
expect that the effects reported here are
even more pronounced for metal substrates due
to their larger polarizability. We also
discuss the technical aspects of the $G_0W_0$
calculations arising from these polarization
effects.
[1] C. Freysoldt, P. Rinke, and M. Scheffler,
Phys. Rev. Lett., accepted.
Maximally-Localised Wannier Functions as Building Blocks of Electronic Structure
Arash A. Mostofi$^1$ and Nicola Marzari$^2$
$^1$Imperial College London, UK\\
$^2$Massachusetts Institute of Technology,
USA
We combine large-scale, ab initio electronic
structure calculations and the
maximally-localised Wannier function (MLWF)
approach in order to study the electronic
properties of complex nanostructures. MLWFs
provide an accurate, localised, minimal basis
set in which to diagonalise the Hamiltonian.
In the MLWF basis, Hamiltonians for large,
complex systems can be constructed directly
from the short-ranged Hamiltonians of smaller
constituent units by performing full
first-principles calculations on either
periodically-repeated or isolated fragments.
We apply our approach to the case of DNA
helices. The effects of sequence,
twist-angle, and solvation environment on the
electronic structure are investigated. This
work opens the way to obtaining a more
detailed understanding of charge transport
and conductance in DNA, bringing closer the
prospect of engineering its electronic
structure for use in nano-electronic circuits
and biotechnology applications.
Including Spin in the Bethe-Salpeter Equation: Excitonic Effects in the Antiferromagnet MnO
Claudia R\"{o}dl, Frank Fuchs, and
Friedhelm Bechstedt
Institut f\"{u}r Festk\"{o}rpertheorie
und -optik,
Friedrich-Schiller-Universit\"{a}t Jena,
Max-Wien-Platz 1, 07743 Jena, Germany
Over the past years there was impressive
progress in calculating optical spectra of
semiconductors beyond the random-phase
approximation. The Bethe-Salpeter equation
(BSE) was solved to take into account
two-particle interactions, especially
excitonic and local-field effects. We focus
on the problem of calculating optical spectra
for systems where spin plays an important
role. Therefore, we generalize the BSE with
respect to the spin degree of freedom in
order to deal with magnetic systems.
Prominent examples for spin-polarized
materials are antiferromagnets, e.g.
transition metal monoxides. Although
transition metal oxides are usually
considered as the standard test systems for
magnetic solids, they are hard to treat
numerically. We present explicit results for
MnO as the best natured example.
The main difficulty arises from the
circumstance that in spin-polarized systems
the separation between triplet and singlet
excitons no longer holds. Both submatrices of
the two-particle Hamiltonian are coupled by
the matrix elements of the bare Coulomb
potential which account for local-field
effects. The numerical cost for the
calculation of optical spectra increases due
to doubling of the rank of the corresponding
eigenvalue problem.
The ground state calculations are performed
with a density-functional plane-wave code
using the projector-augmented wave (PAW)
method for the description of wave functions.
Quasiparticle shifts are added to obtain
correct gap values. The BSE is solved
applying both, direct diagonalization and a
time-development scheme.
Defect Formation Energies without the Band Gap Problem: Combining DFT and \textit{GW} for the Silicon Self-Interstitial
Patrick Rinke,$^{1,2}$ Anderson
Janotti,$^{2}$ Chris Van de Walle,$^{2}$ \\
and Matthias Scheffler$^{1,2}$
$^1${\it Fritz-Haber-Institut der
Max-Planck-Gesellschaft, Berlin, Germany}\\
$^2${\it University of California Santa
Barbara, CA, USA}
Density-functional theory (DFT) has
contributed greatly to
our current microscopic understanding of the
physical and chemical properties of defects
in solids.
The standard local-density or generalized
gradient approximation
(LDA or GGA), however, suffer from certain
intrinsic deficiencies, most notably
the band gap problem (BGP), that limit their
predictive power.
For the example of the silicon
self-interstitial (Si$_{\rm I}$)
in silicon we illustrate
here that the BGP -- the fact that the
Kohn-Sham eigenvalue gap underestimates the
quasiparticle gap -- not only affects the
reliable computation of defect levels, but
in certain cases also that of formation
energies.
By combining LDA with
quasiparticle energy calculations in the $GW$
approximation we reason why and present a new
way to
calculate defect formation energies in
solids.
In the neutral charge state the Si$_{\rm I}$
has several stable and metastable atomic
configurations,
in all of which two electrons occupy a defect
level in the band gap that derives largely
from conduction band states.
The formation energies of all configurations,
however, are underestimated by about 1.5 eV
compared to
diffusion Monte Carlo (DMC) calculations
[1,2]. While this appears like a
disproportionally large amount, it
corresponds roughly to twice the band gap
underestimation of silicon in the LDA
($\sim$0.6~eV).
Recent DFT calculations employing a hybrid
functional
that yields an improved band gap for silicon
and formation energies for the Si$_{\rm I}$
in much better agreement with DMC [2] lend
further support to our BGP hypothesis.
By considering the formation of the neutral
state as addition of 2 electrons to
the 2+ state, the formation
energy can be decomposed into the formation
energy of the latter ($E_f(2+)$), plus 2
electron affinities and subsequent
relaxation energies. $E_f(2+)$ and the
relaxation energies are now free from the BGP
and can be
reliably computed in LDA [3]. For the
electron affinities we instead employ the
$GW$ method, which has become the
method of choice for calculating electron
addition and removal energies in solids. With
this combined approach
the formation energy increases by 1.1 eV
compared to the LDA, slightly less than twice
the band gap increase in
$GW$.
\\[-.7cm]
\small{
\begin{tabbing}
xxx\= \kill
[1] \> W.-K. Leung, R. J. Needs, G.
Rapagopal, S. Itoh, and S. Ihara, \\
\> Phys.\ Rev.\ Lett. {\bf 83}, 2351
(1999).\\
[2] \> E. R. Batista {\it et al.}, Phys.\
Rev.\ B {\bf 74}, 121102(R) (2006). \\
[3] \> M. Hedstr\"om, A. Schindlmayr, G.
Schwarz, and M. Scheffler,\\
\> Phys.\ Rev.\ Lett. {\bf 97},
226401 (2006).
\end{tabbing}
}
Fast polarizability and spin related stuff
L. Caramella$^1$, F. Sottile$^2$, L.
Reining$^2$, G. Onida$^1$
$^1$ European Theoretical Spectroscopy
Facility and Università degli Studi di
Milano, Italy\\ $^2$European Theoretical
Spectroscopy Facility and Laboratoire des
Solides Irradi{\'e}s, Ecole Polytechnique
Palaiseau, France
Polarizability is a key ingredient for ab
initio calculations in the framework of the
Time Dependent Density Functional Theory. We
show a quantitative analysis of the
performances of an Hilbert transform based
approach in speeding up the calculations of
this quantity. We conclude that the method is
particularly advantageous for systems
presenting strong anisotropies for which the
crystal local-field effects are important and
the inclusion of the off diagonal terms in
the GG'-matrix become not negligible.
Moreover, according to the recent interest
and trend on spintronic we implemented the
spin degree of freedom in the DP code
(www.dp-code.org) in order to be able to
describe and predict spin related effects of
materials. We are proceeding according to
different steps of complexity and we present
here some preliminary analysis of the
response of simple systems in the collinear
formalism.
BSE and real space multiple scattering approaches to core electron spectroscopy
J. A. Soininen$^1$, E. L. Shirley$^2$, and J.
J. Rehr$^3$
$^1$ Division of X-ray Physics, Department of
Physical Sciences, POB 64, FI-00014
University of Helsinki, Finland \\ $^2$
Physics laboratory, National Institute of
Standards and Technology,
100 Bureau Drive Stop 8441, Gaithersburg, MD
20899-8441, USA \\ $^3$ Department of
Physics, Box 351560, University of
Washington, Seattle, WA 98195-1560, USA
Due to recent developments in time-dependent
density functional theory and
many-body perturbation theory, it is now
possible to model optical
properties of a wide variety of systems
quantitatively from first
principles. However, similar statements
cannot yet be made for core-level
spectroscopies. Although in many cases the
calculated results are in
quantitative agreement with experiment, it is
easy to find examples where
this is not true.
We discuss here two approaches to core-level
spectroscopies. These are the
band-structure based Bethe-Salpeter equation
(BSE) approach[1], and the
real-space multiple scattering approach [2].
At first glance it might appear
that these approaches have little in common.
However, on closer examination
they share many of the same basic
ingredients. We briefly review how these
approaches account for the dominant many-body
effects, e.g. core
hole-photoelectron electron interaction and
final state quasiparticle
corrections. The importance of these effects
is clarified with a comparison
of the calculated spectrum and non-resonant
x-ray Raman scattering (XRS)
experiment. In many cases the information
available in core-level
spectroscopies can be accessed only with the
help of first-principles methods.
As an example, we discuss recent XRS studies
[3] of pure and Al-doped MgB$_2$.
We also mention some recent developments, as
well as future challenges in
first-principles modeling of core-level
spectroscopy.
[1] E.L. Shirley, Phys. Rev. Lett. {\bf
80}, 794 (1998);
J. A. Soininen and Eric L. Shirley, Phys.
Rev. B {\bf 64}, 165112 (2001)
[2] A. L. Ankudinov, B. Ravel, J. J. Rehr,
and S. D. Conradson,
Phys. Rev. B , {\bf 58}, 7565, (1998);
J. A. Soininen, A. L. Ankudinov,
and J. J. Rehr, Phys. Rev. B. {\bf 72},
045136 (2005).
[3] A. Mattila, J. A. Soininen, S. Galambosi,
S. Huotari, G. Vank\'{o},
N. D. Zhigadlo, J. Karpinski, and K.
H\"{a}m\"{a}l\"{a}inen,
Phys. Rev. Lett. {\bf 94}, 247003
(2005); A. Mattila et al., submitted.
Optimal Control of Two-Dimensional Nanodevices
E. R{\"a}s{\"a}nen$^{1,2}$, A.
Castro$^{1,2}$, J. Werschnik$^{3,1,2}$, A.
Rubio${4,1,2}$, and E.K.U. Gross${1,2}$
$^1$Institut f{\"u}r Theoretische Physik,
Freie Universit{\"a}t Berlin, Germany \\
$^2$European Theoretical Spectroscopy
Facility (ETSF) \\ $^3$JENOPTIK Laser,
Optik, Systeme GmbH, Jena, Germany \\
$^4$Universidad del Pa{\'i}s Vasco, DIPC,
Donostia-San Sebasti{\'a}n, Spain
We present a scheme to completely control
single-electron quantum rings [1] and double
quantum dots [2] by terahertz laser pulses.
Our approach is developed in the framework of
quantum optimal control theory (OCT) [3]. The
theory yields, in principle, a laser pulse to
drive the system from any initial state to
any pre-defined target state. We show that
when applied to rings and double dots, the
optimized pulses generate the desired
transitions in significantly shorter times
and higher accuracies than previously used
finite-length continuous waves. In quantum
rings the controlled current-carrying states
can be used to manipulate a two-level
subsystem at the ring center, opening a path
into a coherent single-gate qubit that has
switching times of a few picoseconds. In
double quantum dots our OCT approach enables
a fast and
controlled single-electron transport which,
in contrast with the use of continuous waves,
is insensitive to the dot geometry. In both
systems the optimal pulse lengths are below
the typical relaxation and decoherence times,
which is promising for applications in
quantum computing. The required terahertz
frequency regime is routinely reached by,
e.g., quantum cascade lasers, and the
technology of pulse refinement is under rapid
development [4].
[1] E. R{\"a}s{\"a}nen, A. Castro, J.
Werschnik, A. Rubio, and E.K.U. Gross, Phys.
Rev. Lett. 98, 157404 (2007).
[2] E. R{\"a}s{\"a}nen, A. Castro, J.
Werschnik, A. Rubio, and E.K.U. Gross,
http://arxiv.org/abs/0707.0179.
[3] A.P. Peirce, M.A. Dahleh, and H. Rabitz,
Phys. Rev. A 37, 4950 (1988); R. Kosloff,
S.A. Rice, P. Gaspard, S. Tersigni, and D.J.
Tannor, Chem. Phys. 139, 201 (1989).
[4] M. Tonouchi, Nature Photonics 1, 97
(2007).
Defects in semiconductors and their optical spectra
Michel Bockstedte$^{1,2}$, Andrea
Marini$^{3}, and A. Rubio$^{1}$
$^{1}$Univerisdad del Pa\'{i}s Vasco
UPV/EHU, Dpto Fisica de Materiales,
$^{2}$Lst. f. Theoretische
Festk\"orperphysik, Universit\"at
Erlangen-N\"urnberg, D-91058 Erlangen,
Germany, $^3$CNISM e Dipartimento di Fisica,
Universita "Tor Vergata" di Roma,
I-00133 Roma, Italy.
Point defects in semiconductors, like dopant impurities, lattice
vacancies or interstitials, represent the smallest conceivable
nanoscale perturbations of an otherwise ideal three dimensional
lattice. Their localized electronic states within the fundamental band
gap enabled the design of electronic devices without which our daily
life would have been drastically different. Naturally much effort has
been dedicated to the investigation of the nature of the point defects
and their kinetics. The position of the defect levels within the band
gap and optical excitations of the defect electrons are defect
fingerprints typically used for the defect characterization. Other
important fingerprints characterized in experiments are localized
vibrational modes and the hyperfine tensors that describe the
interaction of the spin of a localized defect electron with the
nuclear spin of the surrounding atoms. The quantitative prediction of
the latter fingerprints by density functional theory (DFT) in
conjunction with the local density approximation (LSDA) enabled
recently the identification of fundamental defect centers and defect
complexes in Silicon Carbide. On the other hand, the evaluation of
defect levels is affected by the well known DFT band gap error and
finger prints of the excited state cannot be assessed on rigorous
grounds in a ground state theory. On the basis of many body theory we
address these defect fingerprints making use of the GW approximation
and including excitonic effects by solving the Bethe-Salpeter
equation. We apply this approach to the carbon vacancy in SiC. The
current interpretation of optical experiments on this center indicates
in contrast to general expectation and the results of DFT-LDA theory that
Frank-Condon shifts should be negligible. Inclusion of quasiparticle
and excitonic effects beyond the DFT-LSDA picture does not resolve the
discrepancies, but rather suggest a different interpretation. The
presentation briefly reviews the major achievements in the
identification of point defects and their clusters in SiC and
examplarily addresses the optical excitation of the carbon vacancy.
Analysis of the Difference between All-Electron and Pseudopotential Based $G_0W_0$ Calculations
Xinzheng Li $^1$, Ricardo I. Gomez-Abal $^1$,
Claudia Ambrosch-Draxl $^2$, and Matthias
Scheffler $^1$
$^1$ Fritz-Haber-Institut der MPG,
Dahlem-14195, Berlin, Germany \\ $^2$
Material Physics Department, University of
Leoben, A-8700, Austria
In recent years, the $GW$ approach, typically
applied as a first order
correction to the Kohn-Sham (KS) eigenvalues
($G_0W_0$ approximation),
has achieved great success in describing
single-particle excitations
in weakly correlated semiconductors and
insulators [1]. For implementation
simplicity and computational efficiency, most
of the existing
codes are based on the pseudopotential (PP)
method, in which the self-energy
is calculated only from the pseudo-valence
states.
It is well-known in DFT that such a linear
treatment of the core-valence
exchange-correlation interaction is not
always valid. Although within PP-$G_0W_0$
the
core-valence interaction can only be included
at the KS level, its reported results
usually show a better agreement with
experiment than the all-electron
calculations available so far [2-4].
The reasons for this disturbing discrepancy
can be traced back to two approximations
underlying the PP-$G_0W_0$, namely, the
exclusion of the core electrons in
the calculation of the self-energy
(core-valence linearization) and the use
of pseudo-valence wave functions
(pseudoization).
We calculated the $G_0W_0$ corrections to the
band gaps for a set
of materials (e.g. Si, GaAs, NaCl, AlP, ...)
using both all-electron-
and PP-$G_0W_0$. The all-electron
calculations are performed using our
recently
developed $G_0W_0$ code based on the Wien2k
implementation of the FP-(L)APW+lo method.
By removing the core states in the
all-electron $G_0W_0$
calculation, we can analyze seperately the
effects of core-valence linearization
and pseudoization. Our results show that the
effect of core-valence
linearization alone does not explain the
difference between all-electron-
and PP-$G_0W_0$ calculations. The effect of
pseudoization turns out to be important as
well.
For materials composed by elements in the
second and third rows of the periodic table,
like Si and AlP, it even is the dominant
reason for the
better agreement between PP-$G_0W_0$
calculations and experiments.
For material including very shallow $d$
states, like GaAs, the core-valence
linearization
is dominant. To avoid these errors,
all-electron results have to be taken
as benchmark in $G_0W_0$ calculations.
Time-dependent density-functional theory in the real-time domain: a route to non-linear response properties and ab-initio many-electron Optimal Control theory.
Alberto Castro and E. K. U. Gross
Institut f{\"{u}}r Theoretische Physik,
Freie Universit{\"{a}}t Berlin
We discuss the current state of the art of
the explicitly time-dependent formulation of
time-dependent density-functional theory
(TDDFT). In particular, we present two
applications: (i) Non-linear molecular
optics, either in the very high-field
(non-perturbative) regime, or in the
moderate-field regime where TDDFT provides a
means to calculate the low-order
(magneto)-optical coefficients -- i.e.
hyper-polarizabilities, second harmonic
generation, etc; (ii) Optimal Control Theory
(OCT) for many-electrons systems. We present
some possible routes, based on real-time
TDDFT, to implement the theory of optimal
control without making use of simplifying
models or having to tackle with the full
wave-function. We will show our working
computational scheme for OCT -- currently
utilized for one-electron systems -- and work
is in the way to extend it to the many
electron case.
Numeric Atom-Centered Orbitals for Parallel and Scalable DFT in Periodic
P.Havu$^1$, V.Havu$^1$, V.Blum$^1$,
P.Rinke$^2$, and M.Scheffler$^1$
1) Fritz-Haber-Institut der
Max-Planck-Gesellschaft, Berlin \\ 2)
Materials Research Lab, University of
California, Santa Barbara
We present the concepts of our new full
potential, all electron
local-orbital based electronic structure
code, FHI-aims (``ab initio
molecular simulations'') [1], with special
emphasis on periodic systems.
FHI-aims uses numeric atom-centered
orbitals (NAO's)
$u_{k}(r)Y_{lm}(\Omega)$ as basis
functions. Due to the flexible shape
of the radial functions $u_k(r)$, small
efficient basis
sets can be constructed by adding only a
few specific functions, yet
with an accuracy comparable to other
state-of-the-art
methods (e.g. the full potential, linear
augment plane wave
(FP-LAPW) method) and the efficiency of
plane-wave pseudopotential
methods in large scale calculations. We
demonstrate the accuracy of the
method for surface energies of Au and Pt, in
particular Au(100), which
shows a quasihexagonal "5x20"
reconstruction in experiment. For
periodic systems the primary challenge with
numeric atom-centered
orbitals is the significant overlap of basis
functions from
different unit cells, leading to many
({\bf k} dependent)
Hamiltonian and overlap matrix elements to
be integrated and
stored even in small unit cells. We
minimize this integration
effort by evaluating only those parts of
all integrals that lie
within one unit cell, employing sparse
matrix storage in the
process. All matrices are then constructed
from these pieces in a
separate step. Together with a density-matrix
based charge
density update and an electrostatic
potential constructed from
intermediate, finite analytical multipoles
and a long-range
Ewald sum [2], we demonstrate $O(N)$-like
scaling of all
grid-based techniques in our approach for
the large-scale 5x20
reconstruction of Au(100).
[1] V. Blum, R. Gehrke, P. Havu, V. Havu,
X. Ren, and M. Scheffler, \emph{The FHI Ab
Initio Molecular Simulations (aims) project},
Berlin
(2007). \\
[2] B. Delley, J. Phys. Chem. {\bf 100},
6107 (1996).
CVV Auger spectra by first principles
G. Fratesi$^1$, M. I. Trioni$^2$, and G. P.
Brivio$^1$
1. CNISM and Dipartimento di Scienza dei
Materiali, Universit\`a di Milano-Bicocca,
Via Cozzi 53, 20125 Milano, Italy \\ 2.
CNISM, UdR Milano-Bicocca, Via Cozzi 53,
20125 Milano, Italy
In core-valence-valence (CVV) Auger decays, a
valence electron is
emitted from the sample upon filling of an
atomic core hole by another
valence electron. The resulting spectrum
provides information on the
environment of the emitting atom and on
many-body correlations.
For weakly interacting particles, the
spectrum is well described by
the self-convolution of the single particle
density of states.
Conversely, Cini and Sawatzky (CS)~[1]
proposed to compute the density
of states of the two interacting holes by a
Dyson equation having as
kernel the hole-hole interaction, which is
commonly taken as a fitting
parameter.
We propose a procedure, based on density
functional theory (DFT), for
the ab initio evaluation of CVV Auger spectra
in the framework of the
CS model.
The single particle density of states is
evaluated directly, while
other quantities are estimated by evaluting a
correction due to
environment with respect to a reference
atomic calculation.
There, the binding energy of the primary
electron and the interaction
of the two holes are extracted by
calculations with constrained
occupations. The evaluation of spin orbit
contributions, multiplet
splitting, and Auger matrix elements, is
already well established for
the atom.
Subsequently, to describe a generic
environment, one adds to the
energy of screening a correction computed by
taking derivatives of the
total energy with respect to particle
numbers, or equivalently of the
DFT eigenvalues.
Results for bulk Zn and Cu will be presented
and compared to
experiments~[2]. The overall agreement is
rather good for a parameter
free theory, and allows for investigation of
environment specific
effects.
[1] M. Cini, Solid State Communications {\bf
24}, 681 (1977);
C. A. Sawatzky, Physical Review Letters {\bf
39}, 504 (1977).
[2] S. P. Kowalczyk, R. A. Pollak, F. R.
McFeely, L. Ley, and
D. A. Shirley, Physical Review B {\bf 8},
2387 (1973).
Exciton-Phonon coupling in the finite temperature optical absorption of semiconductors
Andrea Marini
CNISM e Dipartimento di Fisica
dell'Universit\`a di Roma ``Tor
Vergata'',
Via della Ricerca Scientifica, I--00133 Roma,
Italy
The description of excitonic states
based on the Ab-Initio Bethe-Salpeter
equation (BSE)
constitutes an efficient and successful tool
to calculate the
optical properties of a wide range of
electronic systems[1].
Nevertheless the state-of-the art
implementation of the BSE neglects
the contribution of the nuclear motion that
is crucial to
explain the temperature dependence of the
optical absorption[2]
and to correctly account for the zero point
motion effect
in the zero temperature limit[3].
Moreover, the observation of phonon sidebands
in the photoluminescence (PL) spectra[4],
or the time-decay of excitons in
time-resolved PL[5] suggest a new, dynamical
picture of the excitonic states induced by
the exciton-phonon scatterings.
This is the goal of the present work: to
derive an extension of the (dynamical[6])
BSE
the include exciton-phonon coupling, either
indirect (quasiparticle mediated) or
direct, corresponding to and additional four
point phononic kernel.
The exciton-phonon BSE will then be applied
to the finite temperature spectra
of semiconductors with resonant and bound
excitons. I will discuss how the
exciton-phonon
coupling correctly describes the zero-point
motion effect, the excitonic
damping, the finite temperature effects and
the phononic sidebands.
[1] G.Onida, L.Reining and A.Rubio, Rev. Mod.
Phys. {\bf 74}, 601 (2002).\\[0.1mm]
[2] P. B. Allen and M. Cardona, Phys. Rev. B
27, 4760 (1983), and references
therein.\\[0.1mm]
[3] P. Lautenschlager, M. Garriga, L. Vina,
and M. Cardona, Phys. Rev. B 36, 4821 (1987).
\\[0.1mm]
[4] V. Perebeinos, J. Tersoff, and P.
Avouris, Phys. Rev. Lett. 94, 027402 (2005).
\\[0.1mm]
[5] A. Hagen, et. al., Phys. Rev. Lett. 95,
197401 (2005). \\[0.1mm]
[6] A. Marini, R. Del Sole, Phys. Rev. Lett.,
91, 176402 (2003).
Ab-initio calculation of electronic and optical properties of ZnO
P.Gori$^1$, O.Pulci$^2$ and A. Cricenti$^1$
$1$ISM-CNR, Rome, Italy \\\\ $2$INFM-CNR
and
ZnO is a widely studied material for its
applications for spintronics, piezoelectric
devices, chemical sensors and
optoelectronics. The latter are favored by
an
exciton binding energy of 60 meV, which,
being larger than room temperature thermal
energy (26 meV), allows efficient excitonic
emission without the need of cooling
devices.
ZnO-based room temperature polariton lasers
can also be realized [1]. Finally, the
possibility of tailoring its interesting
properties exploiting quantum-size effects
makes ZnO a very promising
material for nanostructures [2].
From the theoretical point of view, ZnO is
also challenging because of the difficulty
of
a proper treatment of semicore Zn 3d
electrons. In this work, we study the
electronic structure of wurtzite and
zincblende ZnO, including quasiparticle
effects in the GW approximation. It is shown
how the choice of the number of electrons to
be considered as valence in Zn
pseudopotential affects the resulting
electronic band structure.
We then present calculated optical spectra,
both for zincblende and wurtzite phases of
ZnO, including excitonic effects through the
solution of the Bethe-Salpeter equation.
These results are compared with the ones
obtained when excitonic effects are taken
into account in an approximate fashion using
the so-called \'RORO kernel\' [3], which
keeps into account the long-range Coulomb
tail of the exchange-correlation kernel of
TDDFT.
[1] M. Zamfirescu, A. Kavokin, B. Gil, G.
Malpuech, and M. Kaliteevski,
Phys. Rev. B 65, 161205 (2002).
[2] Z.R. Tian, J.A. Voigt, J. Liu, B.
McKenzie, M.J. McDermott,
M.A. Rodriguez, H. Konishi and H. Xu,
Nat. Materials, 2, 821 (2003).
[3] L. Reining, V. Olevano, A. Rubio, and G.
Onida,
Phys. Rev. Lett. 88, 066404 (2002).
The bandgap within reduced density matrix functional theory
N. Helbig$^1$, N.N. Lathiotakis$^2,3$, E.K.U.
Gross$^2$, X. Gonze$^1$
$^1$ Unit\'e de Physico-Chimie et de
Physique des Mat\'eriaux, Universit\'e
Catholique de Louvain, Louvain-la-Neuve,
Belgium\\ $^2$ Institut f\"ur
Theoretische Physik, Freie Universit\"at
Berlin, Germany\\ $^3$ Theoretical and
Physical Chemistry Institute, NHRF, Athens,
Greece
Reduced-density-matrix-functional theory
(RDMFT) uses the one-body density matrix as
basic variable instead of the density which
is used in DFT. The eigenvalues of the
one-body density matrix are known as
occupation numbers while its eigenfunctions
are called natural orbitals. In practical
calculations, the variation of the total
energy with respect to the one-body density
matrix is replaced by a variation with
respect to the occupation numbers and the
natural orbitals.
Within RDMFT it is possible to calculate the
fundamenta gap (i.e. the band gap in case of
periodic systems) as the discontinuity of the
chemical potential as a function of the
particle number. Using this method for finite
systems yields results which are in very good
agreement with CI calculations and
experimental data. For the application of
RDMFT to periodic systems one has the choice
of describing the natural orbitals either as
Wannier- or as Bloch states. We discuss the
consequences of both choices and present
numerical results for one- and
three-dimensional systems.
Combining many body techniques with QM/MM for the calculation of optical We develop a method to compute with high precision the optical properties solution
A. Mosca Conte (1), O. Pulci (1), E. Ippoliti
(2), P. Carloni (2), R. Del Sole (1)
(1) Dipartimento di Fisica,
dell'Universita' di Roma Tor Vergata, Via
della Ricerca Scientifica, 1 - 00173 Roma,
Italy; \\ (2) SISSA, Via Beirut, 4 - 34014
Trieste, Italy
We develop a method to compute with high
precision the optical properties
of large scale systems. Realistic systems,
especially in chemical and
biological fields, are too large to be
treated entirely by quantum
calculations, but at the same time cannot be
treated totally by a
classical model because the physical
phenomena studied involve electronic
charge redistribution or electronic energy
transitions like for example in
the case of a chemical reaction or of an
optical spectrum. Fortunately in
many of these systems only a small part of
the molecule needs to be
treated by quantum calculations; in chemical
reactions this part coincides
with the active site of a compound.
In this work we use this method to study
optical properties of a solution.
The DFT eigenvalues and eigenvectors are
calculated by QM/MM and are used
to solve GW and Bethe-Salpeter equations.
We apply this new scheme to the study of
indole in water and in vapor phase.
The optical spectrum obtained considering the
solvent as 'classical' is
compared with those obtained introducing
explicitly water molecules.
Solvent shift, the number of snapshots needed
and the effect of water on
the electronic and optical properties of
indole are discussed.
Quasiparticle calculations in $\alpha$-SiO$_2$
M. Giantomassi, G.-M Rignanese and X. Gonze
Unit\'e de Physico-Chimie et de Physique
des Mat\'eriaux, \\ Universit\'e
Catholique de Louvain, Belgium
We present results for the quasiparticle
energies of $\alpha$-SiO$_2$
obtained within the GW approximation using
the LDA band structure as starting point.
An efficient algorithm based on the spectral
representation of the
polarizability is employed to describe the
dynamical dependency of the screened
interaction $W(\omega)$.
The self-energy operator $\Sigma(\omega)$
is numerically evaluated using two different
techniques:
the contour deformation method and an
analytic continuation from the imaginary axis
to the real axis.
Alternatively, one can approximate
$W(\omega)$ through plasmon-pole models.
We compare the results for the optical gap
and the quasiparticle corrections calculated
from both the fully frequency-dependent
method and the plasmon-pole approximation.
Quasiparticle calculations of band offsets of SiO$_2$ and ZrSiO$_4$ with Si
R. Shaltaf$^1,2$, J. Bouchet$^2$,
G.-M.Rignanese$^1,2$ , X. Gonze$^1,2$,
F.Giustino $^3,4$ and A. Pasquarello$^3,4$
$^1$European Theoretical Spectroscopy
Facility (ETSF) \\$^2$ Unit'e
Physico-Chimie et de Physique des
Mat'eriaux(PCPM)\\Universit'e catholique
de Louvain Place Croix du Sud, B-1348
Louvain-la-NeuveBelgique $^3$Ecole
Polytechnique F'ed'erale de Lausanne
(EPFL)Institute of Theoretical Physics,
CH-1015 Lausanne,Switzerland
The size reduction of MOS transistor
requires the usage of high-dielectric
materials to replace SiO$_2$ as gate oxide
layers. As the high- k/Si interface is
formed, it is crucial that the band offsets
be large enough to prevent electron or hole
injection. In this study we have used
rst-principle DFT calculations within the
local density approximation to study the
band offsets of SiO$_2$/Si and ZrSiO$_4$/Si.
We
have included many body corrections as
calculated by GW approximation. Indeed we
have examined the capability of the
quasiparticle corrections to predict the
band offsets for a well known system as
SiO$_2$/Si. The calculated band
discontinuities were found to be in a good
agreement with the experimental results.
--
Combining many body techniques with QM/MM for the calculation of optical properties of large scale systems: an application to indole in water solution
A. Mosca Conte (1), O. Pulci (1), E. Ippoliti
(2), P. Carloni (2), R. Del Sole (1)
(1) Dipartimento di Fisica,
dell'Universita' di Roma Tor Vergata, Via
della Ricerca Scientifica, 1 - 00173 Roma,
Italy; \\ (2) SISSA, Via Beirut, 4 - 34014
Trieste, Italy
We develop a method to compute with high
precision the optical properties
of large scale systems. Realistic systems,
especially in chemical and
biological fields, are too large to be
treated entirely by quantum
calculations, but at the same time cannot be
treated totally by a
classical model because the physical
phenomena studied involve electronic
charge redistribution or electronic energy
transitions like for example in
the case of a chemical reaction or of an
optical spectrum. Fortunately in
many of these systems only a small part of
the molecule needs to be
treated by quantum calculations; in chemical
reactions this part coincides
with the active site of a compound.
In this work we use this method to study
optical properties of a solution.
The DFT eigenvalues and eigenvectors are
calculated by QM/MM and are used
to solve GW and Bethe-Salpeter equations.
We apply this new scheme to the study of
indole in water and in vapor phase.
The optical spectrum obtained considering the
solvent as 'classical' is
compared with those obtained introducing
explicitly water molecules.
Solvent shift, the number of snapshots needed
and the effect of water on
the electronic and optical properties of
indole are discussed.
Electronic excitations and excited-state forces of the H:Si(001)-(2x1) monohydride surface
M. Rohlfing $^1$, N.-P. Wang $^2$, P. Krueger
$^3$, J. Pollmann $^3$
$^1$ Universitaet Osnabrueck, $^2$
Universitaet Hamburg, $^3$ Universitaet
Muenster
We investigate electronic excitations of the
H:Si(001)-(2x1) monohydride surface using
first
principles approaches. Density-functional
theory is used to calculate the ground state
geometry
of the system. The quasiparticle band
structure is calculated within the GW
approximation.
Taking the electron-hole interaction into
account, electron-hole pair states and
optical
excitations are obtained from the solution of
the Bethe-Salpeter equation for the
electron-hole
two-particle Green function. In this work we
focus, in particular, on localized
excitations of
the silicon-hydrogen bonds at the surface
layer. These excitations give rise to an
outward-directed
force on the hydrogen atoms, which may well
explain their optically induced desorption
from the
surface as observed in recent experiments.
The localization of the excitation is
described by an
additional confinement potential in addition
to standard many-body perturbation theory.
[1] N.-P. Wang, M. Rohlfing, P. Krueger, and
J. Pollmann, Phys. Rev. B 74, 155405 (2006).
Theoretical spectroscopy for finite systems
J.A. Berger, F. Sottile, and L. Reining
LSI, Ecole Polytechnique, Route de Saclay,
91128, Palaiseau, France
This work deals with the calculation of
linear-response properties of finite systems
using time-dependent density-functional
theory as well as many-body perturbation
theory,
namely GW and the Bethe-Salpeter equation. In
particular we are interested in the
performance of
these methods when applied to large finite
systems, e.g. biological systems.
The existing theory we use for extended
systems
needs to be reformulated in order to make
these calculations for large finite systems
feasible.
In this work we will discuss how we can
obtain an efficient formulation for these
systems.
Excitation energies in open-shell systems: facts, ideas, speculations...
P. Romaniello, D. Sangalli, and G. Onida
Istituto Nazionale per la Fisica della
Materia and Dipartimento di Fisica
dell’Università di Milano, via Celoria 16,
I-20133 Milano, Italy
The theoretical description of excited states
of open-shell molecules is a difficult task,
full of subtleties which are not always
understood or made clear. We want to
understand the failures of the present
"state of the art'' DFT- and MBPT -based
methodologies, which cannot properly describe
those excited states which have
multiple-excitation character. It appears
clear that these states would be described if
the exact TDDFT kernel were used; however,
when the adiabatic approximation to the
exchange-correlation kernel is used, the
calculated excitation energies have strict
single-excitation character, and are fewer
than the real ones. A frequency dependent
kernel could create extra poles which would
describe states with multiple excitation
character [1]. The question is: how to
introduce the correct $\omega$-dependence in
a general formulation? Maybe an answer can be
obtained by starting from the Bethe-Salpeter
equation, where a four-point kernel appears.
Methods to derive a two-point kernel for
TDDFT from the BSE kernel have been devised
in the literature [2], and could be extended
to the spin-polarized case.
[1] M. E. Casida, A. Ipatov, and F. Cordova,
Linear-Response Time-Dependent
Density-Functional Theory for Open-Shell
Molecules, Lect. Notes Phys. 706, 243-257
(2006).
[2] F. Bruneval, F. Sottile, V. Olevano, R.
del Sole, and L. Reining, Phys. Rev. Lett.,
94, 186402, (2005).
Transport properties in nanotubes doped with DR1-Azobenzene
Juan María García-Lastra, Kristian Sommer
Thygesen and Ángel Rubio
Departamento de Física de Materiales,
Facultad de Químicas, Universidad del País
Vasco, San Sebastián 20018, Spain.
DR1-Azobenzene has two isomers. The most
stable is the trans conformation, whose
dipole moment is 9 D, while the cis
conformation has a 6 D dipole moment. It is
possible to pass from the trans- to cis-
conformation (and vice versa) upon UV
illumination. Recent experiments have
demonstrated that DR1-Azobenzene can be
physisorbed by nanotubes by means of
anthracene, which acts as an “anchor”
molecule. This physisorption produces changes
in the transport properties of the nanotubes.
In this way the transport properties of the
nanotubes can be controlled through the
isomerization process of DR1-Azobenzene with
UV light.
A crucial point to understand how the
DR1-Azobenzene molecules affect the transport
properties is to know their arrangement on
the surface of the nanotube. In order to do
this, we have built a model Hamiltonian which
includes the interaction of anthracene with
the nanotube surface and the dipole-dipole
interaction among the DR1-molecules. The
different parameters for this model
Hamiltonian are obtained from BLYP
calculations. Once the arrangement is known,
we may evaluate the changes in the transport
properties.
New advances in time-dependent density functional theory and quantum transport
Sokrates T. Pantelides
Department of Physics and Astronomy,
Vanderbilt University, Nashville, TN 37235
USA
A new code for fully nonlinear time-dependent
density-functional-theory simulations has
been written, tested and applied to a variety
of phenomena [1]. Excellent and unique
results are obtained for a case where photon
emission/absorption is negligible:
calculations of the "stopping power" of
channeled ions in crystals has produced
results that resolve long-standing issues and
identify the microscopic mechanisms that
control the so-called Z1 oscillations. In
cases where photon emission/absorption is
dominant, the results are mixed and puzzling.
A new method has been developed for transport
calculations in molecules and nanostructures
[2]. The method maps the "open" scattering
problem onto a "closed" eigenvalue-like
problem. It has been implemented using the
newly developed Lagrange function basis sets
[3] and converged currents are demonstrated
for the first time. Results will be reported
for a benzene ring and for carbon-nanotube
field-effect transistors.
1. R. Hatcher, M. Beck. A. Tackett and S. T.
Pantelides, submitted for publication
2. K. Varga and S. T. Pantelides, Phys. Rev.
Lett. 98, 076804 (2007).
3. K. Varga, Z. Zhang, and S. T. Pantelides,
Phys. Rev. Lett. 93, 176403 (2004).
Towards an \textit{ab intio} description of \textit{f}-electron systems: an all-electron \textit{GW} perspective
Hong Jiang, Xinzheng Li, Ricardo
G\'{o}mez-Abal, Patrick Rinke, and Matthias
Scheffler
Fritz-Haber-Institut der
Max-Planck-Gesellschaft, Berlin, Germany
\textit{f}-electron systems, i.e. materials
containing atoms with incompletely filled
\textit{f}-shells, have received increased
attention recently due to their diverse
properties and wide range of applications.
The physics and chemistry of these systems,
however, remain largely elusive, because of
the intricate nature of \textit{f}-electrons
and understanding them is regarded as one of
the big challenges in condensed matter
physics. In many materials the strong
localization of the \textit{f}-electrons
competes with the coupling to itinerant
electrons. % and combines aspects of core and
valence electrons.
The former gives rise to large many-body
exchange and correlation effects, while the
latter requires a quasiparticle description.
In these regimes density-functional theory in
the local-density approximation (LDA) and its
semi-local extensions is usually not
adequate. Many-body perturbation theory in
the \textit{GW} approximation (GWA),
however,
offers a quasiparticle perspective and has
become the method of choice for the
description of quasiparticle band structures
in weakly correlated solids. Since exchange
is treated at the exact-exchange level, the
GWA appears to be a suitable
method to identify those \textit{f}-electron
systems, in which the interactions are
exchange dominated, and a natural starting
point for methods that require a more
sophisticated treatment of many-body
interactions.
So far applications of the GWA to
\textit{f}-electron systems are rare due to
the high computational effort involved. We
have developed an all-electron (AE)
\textit{GW} code based on the full-potential
(linear) augmented plane wave (+ local
orbital) method. As a first application to
\textit{f}-electron systems we have
investigated cubic ZrO$_2$, HfO$_2$ and
CeO$_2$. These materials have attracted
growing interest in recent years as promising
candidates for replacing SiO$_2$ as the gate
dielectric in silicon-based field effect
transistors. Moreover, CeO$_2$ plays an
important role in catalysis. From a
conceptual point of view they are
interesting, because ZrO$_2$ has no
\textit{f}-electrons, CeO$_2$ an empty and
HfO$_2$ a fully
occupied \textit{f}-shell. They therefore
provide a good starting point for
investigating the role of
\textit{f}-electrons. Our AE-GW calculations
show that \textit{f}-electrons have no
effects on the quasiparticle corrections in
HfO$_2$; the
difference in electronic properties of
ZrO$_2$ and HfO$_2$ are already well
described at the LDA level. In CeO$_2$, the
\textit{f}-band falls in between the O
2\textit{p} valence and Ce 5\textit{d}
conduction bands, and are therefore important
at all levels of theory. We find that $GW$
moves these bands into better agreement with
experiment compared to the LDA.
Exact Born-Oppenheimer decomposition of the many-body wavefunction for the complete system of electrons and nuclei.
Ali Abedi$^1$*, Neepa~T. Maitra$^2$,
N.I~Gidopoulos$^3$ and E.K.U.~Gross$^1$
\textit{$^1$Institut f\"ur Theoretische
Physik , Freie Universit\"at Berlin ,
Arnimallee 14 , D-14195}\newline
\textit{Berlin, Germany}\newline
\textit{$^2$ Hunter College of the City
University of New York, NYC, U.S.}\newline
\textit{$^3$ISIS Facility, Rutherford
Appleton Laboratory, Chilton, Didcot,
Oxon,OX11 0QX,}\newline
\textit{England, U.K.}\newline
We propose a new set of equations to treat
non-adiabatic couplings between
electrons and nuclei in molecular systems.
The key idea behind the equations
is to rewrite the many-body wave-function as
a Born-Oppenheimer-type product of the
nuclear
,$X(R,t)$, and electronic ,$\Phi_R(r,t)$,
wave function. From the variational
principle,
we deduce formally exact equations for
$X(R,t)$ and $\Phi_R(r,t)$. These represent
the time-dependent generalization of already
existing static equations (N.I~Gidopoulos and
E.K.U.~Gross, cond-mat/0502433).
These equations suggest time-dependent
potential energy surfaces and a
time-dependent Berry phase as rigorous
concepts.
These concepts will be illustrated by simple
examples.
Edge-induced spin Hall effect in a clean 2D homogeneous electron gas
P. Bokes (1),(2)
(1) Dept. of Physics, University of York,
YO10 5DD York, U.K.
, (2) Dept. of Physics, Slovak University of
Technology FEI STU,
Bratislava, Slovakia
We analyze the importance of the confining
potential close to the
edge of the electronic system on the spin
Hall effect in a 2D homogeneous
electronic gas. We show that in similarity
with the extrinsic spin Hall effect,
the spin-orbit interaction and the current
flow induce accumulation
of the out of plane up and down spin density
on the right and left edge
of the system respectively. We quantify the
amplitude and spatial extent
of the uncompensated spin density for a
system exhibiting the conventional
spin Hall effect. While the amplitude of the
spin accumulation is comparable
to the experimental values, the spatial
extent of the spin accumulation due to the
edge is restricted to the distances of the
order of Fermi wavelength (cca 10nm).
Simplicity of the system allows for a full
non-perturbative treatment within
the Green's function formalism for variable
temperature, current density,
and the amplitude of the confining
potential.
The conductance and polarizability of nanostructures
Matthieu Verstraete, Peter Bokes, and Rex
Godby
Physics Dept. University of York, UK
We present ab-initio and tight binding
results for the conductance of nanowires. Our
formalism extracts the transport properties
directly from the non-local polarizability,
giving an intrinsic characterization of the
device, without leads. The system-size and
temperature dependencies are examined and
show non-trivial behavior, in particular in a
periodic supercell setup. This method is
ideally suited to incorporation in standard
ground- and excited-state electronic
structure methods, irrespective of basis set
and implementation details.
The Role of Bound States in Time-Dependent Quantum Transport
E.Khosravi$^1$,S.Kurth $^1$,G.Stefanucci $^1$
and E.K.U.~Gross$^1$
$^1$Institut f\"ur Theoretische Physik,
Freie Universit\"at Berlin,Berlin, Germany
We present a description of transport based
on the time evolution of the non-interacting
time-dependent Schr\"odinger equation and
develop a numerical algorithm for the time
propagation which is suited for
implementation of time-dependent density
functional theory. The algorithm is used to
study time-dependent transport phenomena such
as the role of bound state and transients in
simple model systems. The presence of at
least two bound states in the biased
electrode-device-electrode system, leads to
the current oscillations that remain undamped
in the long-time limit. we also investigate
the dependence of the TD-current on the
history of applied bias, gate voltage and
initial state.
Wave-vector-dependence Study of the Dielectric and Energy-loss Functions of small Carbon Nanotubes.
X.Lopez-Lozano$^1$, A. G. Marinopoulos, S.
Botti$^1$, C. Giorgetti$^1$, L. Reining $^1$
$^1$ Laboratoires des Solides Irradiés,
École Polytechnique , Route de Saclay,
91128. Palaiseau Cedex, France.
The anisotropic optical response of
small-diameter single-walled
carbon nanotubes is studied by means of ab
initio calculations within the
framework of the random-phase approximation.
The dielectric and energy-loss functions
are investigated for different non-zero
momentum-transfer vectors. The importance
of the inclusion of local field effects and
plasmon dispersion are discussed.
Approaching ground state Born-Oppenheimer molecular dynamics in a modified time-dependent density functional theory approach
J. L. Alonso$^1$, X. Andrade$^2$, P.
Echenique$^1$, F. Falceto$^1$, D. Prada$^1$
and A. Rubio$^2$
$^1$Departamento de F{\'{\i}}sica
Te\'orica, Universidad de Zaragoza, Pedro
Cerbuna 12, E-50009 and Instituto de
Biocomputaci\'on y F{\'{\i}}sica de
Sistemas Complejos (BIFI), Edificio
Cervantes, Corona de Arag\'on 42, E-50009
Zaragoza, Spain. \\ $^2$European
Theoretican Spectroscopy Facility,
Departamento de F{\'{\i}}sica de
Materiales, Universidad del Pa{\'{i}}s
Vasco,Centro Mixto CSIC-UPV, and Donostia
International Physics Center (DIPC), Edificio
Korta, Av. Tolosa 72, E-20018 San
Sebasti\'an, Spain
To mimic ground state Born-Oppenheimer
molecular dynamics (gsBOMD), we propose a
Lagrangian inspired by Ehrenfest dynamics in
time-dependent density functional theory
(TDDFT). The electronic orbitals are evolved
by a time-dependent Schr{\"o}dinger-like
equation, where the time derivative of the
orbitals is multiplied by a parameter $\mu$,
which controls, similarly to Car-Parrinello
(CP) dynamics, the time scale of the
fictitious electronic motion. The approach
presented here automatically preserves the
orthonormality of the orbitals and conserves
the total physical energy for all values of
$\mu$. We show that the new dynamics
smoothly approaches gsBOMD in the $\mu \to
0$ limit as expected, and that it remains
close to it along a wide range of values of
$\mu > 1$. As in CP, there is a compromise
between the time-step (TS) and the closeness
to gsBOMD given by the value of \(\mu\).
These properties are illustrated with a model
system and with realistic molecular
calculations.
Optical properties of 3-tert-butyl-cyclohexene from first principle methods
Katalin Ga\'al-Nagy (1), Olivia Pulci (2),
Giovanni Onida (1), and Rodolfo del Sole (2)
(1) Dipartimento di Fisica and ETSF,
Universit{\`a} degli Studi di Milano, via
Celoria 16, I-20133 Milano, Italy\\
(2) Dipartimento di Fisica, Universita'
"Tor Vergata", Via della Ricerca
Scientifica I , 00133 Roma, Italy
We are interested in the ab-initio
description of the optical rotation
of 3-tert-butyl-cyclohexene, a molecule
composed of a cyclohexene ring
$C_6H_{10}$ and a butyl group $C(CH_3)_3$.
For this molecule there is
a discrepancy between experimental data and
TDDFT (using local
orbitals) results [1]. Our scope is to study
the dichroism effects in
this molecule within a plane-wave approach in
order to explain this
discrepancy. In a first step, we have studied
the standard optical
properties, meaning the dielectric function,
for the two existing
conformers a and b of this molecule within
the independent particle
approximation in DFT-LDA using a plane-wave
expansion and within TDDFT
using local orbitals. Preliminary results
will be shown.
[1] D. M. McCann and P. J. Stephens, J. Org.
Chem 71, 6074 (2006)
Wannier function approach to electron correlation in transition metals
Ersoy Sasioglu, Arno Schindlmayr, Christoph
Friedrich and Stefan Blügel
Institut für Festkörperforschung,
Forschungszentrum Jülich, 52425 Jülich,
Germany
First-principles calculations of
quasiparticle energies in real
materials are typically based on the $GW$
approximation (GWA), which
is known to produce good results for systems
with weak or intermediate
correlation strength. However, it fails to
describe short-range
interactions in more strongly correlated
systems and does not contain
spin fluctuations that play an important role
in the transport and
thermodynamic properties of magnetic
materials. In order to treat such
local correlations in transition metals and
rare earths we develop a
computational method that goes beyond the GWA
by including appropriate
vertex corrections in the form of a
multiple-scattering T-matrix,
which describes the coupling of electrons and
holes with different
spins. To reduce the numerical cost for the
calculation of the
four-point T-matrix we exploit a
transformation to maximally localized
Wannier functions that takes advantage of the
short spatial range of
the electronic correlation in the partially
filled \textit{d} or
\textit{f} orbitals of magnetic materials.
Our implementation is based
on the all-electron full-potential linearized
augmented plane-wave
(FLAPW) method. As a first step, we calculate
the dynamical spin
susceptibility of the non-interacting
Kohn-Sham electrons and the
matrix elements of the Coulomb potential in
the Wannier basis. The
obtained values for the latter agree with
previous calculations.
Efficient all-electron implementation of the $GW$ approximation within the full-potential linearized augmented plane-wave method
Christoph Friedrich, Arno Schindlmayr, and
Stefan Blügel
Institut für Festkörperforschung,
Forschungszentrum Jülich, 52425 Jülich,
Germany
The $GW$ approximation for the electronic
self-energy yields quasiparticle band
structures in very good agreement with
experiment, but almost all implementations so
far are based on the pseudopotential
plane-wave approach, which limits their range
of applicability. We have developed an
implementation within the full-potential
linearized augmented plane-wave (FLAPW)
method, which treats core and valence
electrons on an equal footing. Furthermore,
there is no artificial partitioning of core
and valence densities. Within this method a
large variety of materials can be treated,
including d- and f-electron systems, oxides
and magnetic systems. Our implementation
employs a mixed basis set for the
representation of basis-function products in
the interstitial and muffin-tin regions. An
expansion of the wave functions around
$\mathbf{k}=\mathbf{0}$ using $\mathbf{k
\cdot p}$ perturbation theory allows us to
treat the divergence of the Coulomb
interaction analytically. The anisotropy of
the dielectric screening is fully taken into
account. A transformation of the mixed basis
functions to the eigenfunctions of the
Coulomb potential allows a reduction of the
basis-set size without compromising the
accuracy, which leads to a considerable
speed-up in computation time. As a
demonstration we show performance tests and
results for selected solids.
Excitonic effects in semiconducting polymers - a comparison of TDDFT with the Bether-Salpeter Equation
S. Sagmeister, P. Puschnig, C. Ambrosch-Draxl
Chair of Atomistic Modelling and Design of
Materials, Department Materials Physics,
University of Leoben, Austria
We perform first-principles calculations to
study the optical properties
of semiconducting polymers. Time-dependent
density functional theory (TDDFT) on the one
hand, and many-body perturbation theory
(MBPT) on the other hand are employed to
investigate the excitonic effects in the
dielectric function. Both methods are
implemented within an all-electron
full-potential linearized augmented planewave
(FPLAPW) scheme. The two semiconducting
polymers, poly-acetylene (PA) and
poly-para-phenylenevinylene (PPV), are
discussed as examples for quite small (PA)
and considerably larger (PPV) excitonic
effects in the crystalline environment.
While the exciton binding energies are
accessible through the solution of the
Bethe-Salpeter Equation (BSE) within MBPT
only, the excitonic spectra can be obtained
within both theoretical approaches and
compared to each other. Thereby,
the BSE results provide a benchmark for the
performance of the exchange-correlation
(xc)-kernels within TDDFT. We show how
sensitively the spectra behave with respect
to the parameters of the semi-empirical
long-range-kernels. Furthermore, we
investigate whether a physical interpretation
of these parameters is possible and what
limits the applicability of this type of
xc-kernels for these strongly anisotropic
materials.
Limitations of present DFT calculations of transport
Kieron Burke
Departments of Chemistry and Physics, UC
Irvine, Irvine, California, USA
I will discuss several distinct reasons for
why present DFT calculations of transport,
which combine ground-state DFT and the
Landauer formula, might be highly
inaccurate.
(1) Even within the standard approach, common
approximate functionals do not include a
derivative discontinuity or correct for
self-interaction. This can both misalign
levels and broaden resonance peaks when a
molecule is weakly coupled to leads.
(2) In the weak bias limit, one can use Kubo
linear response theory to deduce the exact
conductance. We find the Landauer formula
misses XC field effects, which likely reduce
the conductance.
(3) For finite bias, several alternative
schemes are being constructed that may or may
not reduce to the Landauer formula (with XC
corrections).
All references can be found in the review:
arXiv:cond-mat/0703591
(http://chem.ps.uci.edu/~kieron/dft/)-
The electron spin degree of freedom in the calculation of excited-state properties.
F. De Fausti, A. Marini, M. Palummo, C.
Hogan, R. Del Sole.
Department of Physics of the University of
Rome 'Tor Vergata'
The inclusion and proper description of the
electron spin is central to the physics
of all magnetic materials, ranging from
paramagnetic atoms and molecules, to
collinear systems such as ferromagnet and
non-collinear systems.
To study physical phenomena involving excited
states, it is often necessary to
include many-body effects through Green's
function theory or time dependent DFT,
although state-of-the-art approaches are
still based on DFT calculations as a first
approximation.
In this presentation, I will show how we have
implemented the spin degree of freedom
in Many Body Perturbation Theory. First
applications are focused on bulk GaSb, which
has a large spin-orbit splitting (0.8 eV) and
therefore should be treated in a
non-collinear framework. We have calculated
the self-energy corrections to the
spin-orbit electronic band structure within
the GW approach and carried out the
solution of the Bethe-Salpeter equation, as
required for an appropriate description
of the electron-hole interaction.
Towards an Exact Treatment of Exchange and Correlation in Materials
Matthias Scheffler
Fritz-Haber-Institut der
Max-Planck-Gesellschaft
Recent studies have shown that the errors of
present-day exchange-correlation functionals,
for example LDA and GGA, are rather short
ranged.[1-3] For extended systems, \emph{the
correction} to LDA can therefore be evaluated
by properly chosen clusters and employing
highest-quality quantum chemistry or quantum
Monte Carlo methods. This approach is
applicable to bulk systems as well as to
defects in the bulk and at surfaces.
In particular we address in this talk LDA and
GGA errors due to self-interaction and due to
the lack of van der Waals interactions.
Furthermore, for the description of metallic
bulk systems our study reveals the
problematic performance of Hartree-Fock,
Møller-Plesset perturbation theory, and of
the popular B3LYP functional.
[1] Q.-M. Hu, K. Reuter and M. Scheffler,
Phys. Rev. Lett. 98, 176103 (2007).
[2] C. Filippi, S.B. Healy, P. Kratzer, E.
Pehlke, and M. Scheffler, Phys. Rev. Lett.
89, 166102 (2002)]
[3] C. Tuma and J. Sauer, Chem. Phys. Lett.
387, 388 (2004); Phys. Chem. Chem. Phys. 8,
3955 (2006).
Temperature effects in the optical
response of clusters using time dependent density functional theory
James R. Chelikowsky
Center for Computational Materials \\
Institute for Computational Engineering and
Sciences \\ Departments of Physics and
Chemical Engineering \\ University of Texas
\\ Austin, TX 78712, USA
Many properties of atomic clusters are known
to be size-dependent, {\it e.g.}, the
structural and optical
properties. There are, however, factors other
than size that can play an important role in
determining
the properties of nano-scale systems.
Temperature, in particular, has been shown to
have
a strong effect on the optical response of
open-shell sodium clusters. I will
illustrate an approach to incorporate the
role of temperature
in the optical absorption spectra of sodium
clusters by combining pseudopotentials,
Langevin molecular
dynamics and time-dependent density
functional theory. I will also present a new
computational procedure to address the
electronic structure of large systems based
on a real space implementation of
pseudopotentials.
\vskip 24pt
\leftline{\bf References}
\vskip -12pt
\begin{enumerate}
\footnotesize
\item I. Vasiliev, S. {\"O}{\u
g}{\"u}t, and
J.R. Chelikowsky: ``{\it Ab Initio}
Excitation Spectra and Collective Electronic
Response in Atoms and
Clusters,'' {\it Phys. Rev. Lett.} {\bf
82}, 1919 (1999).
\item L. Kronik, I. Vasiliev and J.R.
Chelikowsky: ``{\it Ab initio} Calculations
for
Structure and Temperature Effects on the
Polarizabilities of Na$_n$ ($n \leq 20$)
Clusters,'' {\it Phys. Rev. B} {\bf 62},
9992 (2000).
\item J.R. Chelikowsky, L. Kronik and I.
Vasiliev: ``Time dependent density
functional calculations for
the optical spectra of molecules, clusters
and nanocrystals,'' {\it J. Phys. Cond.
Matt.} {\bf 15}, R1517 (2003).
\item I. Vasiliev, S. \"{O}\u{g}\"{u}t,
and J. R. Chelikowsky: ``First Principles
Density Functional Calculations for
Optical Spectra of Clusters and
Nanocrystals,'' {\it Phys. Rev. B}{\bf
65}, 115416 (2002).
\item M. Lopez del Puerto, M.L. Tiago, and
J.R. Chelikowsky, ``Ab initio calculation of
temperature effects in the optical
response of open-shell sodium clusters,''
{\it J. Chem. Phys.} (2007), in press.
\end{enumerate}
TDDFT in Molecules and Polymers for photovoltaic applications
Michel Côté and Jean Frédéric Laprade
Département de physique, Université de
Montréal, Canada
The search of new types of polymers with
specific physical properties such as the
optical gap is of great interest to better
address applications like photovoltaic
devices. Electronic structure calculations
can help in the design of new polymers by
identifying the most promising candidates,
and in this respect, being able to
accurately compute optical gaps is crucial.
One particular class of polymers of
interest
is the ladder-type polymers. These have more
than one bond linking the neighboring
monomers together, eliminating the possible
dihedral degree of freedom. These polymers
are known generally to exhibit small band
gaps, due partly to their planar
configurations which maximize the alignment
of the $\\pi$ orbitals. Moreover, these
ladder-type polymers have the potential to
exhibit very high intrachain mobility. In
this presentation, we will report the
results of time-dependant density-functional
theory (TDDFT) calculations with both the
PBE and B3LYP functionals on ladder-type
polymers which include hetero-atoms like B,
C, N, Si, P, S, Ga, Ge, In, Sn and Hg. The
oscillator strength of these different
polymers will also be address.
Understanding correlations in V0$_2$: self-consistent quasiparticle calculations and alternatives
Mat teo Gatti $^{1,2}$, Fabien
Bruneval$^{1,2,3}$, Ilya V. Tokatly$^{4,5}$,
Valerio Olevano $^{6,2}$ and Lucia Reining
$^{1,2}$
$^1$ LSI, Ecole Polytechnique, CNRS,
Palaiseau (France) \\ $^2$ European
Theoretical Spectroscopy Facility (ETSF)
\\ $^3$ ETH Z\"urich, USI Campus, Lugano
(Switzerland) \\ $^4$ Lehrstuhl f\"ur
Theoretische Festk\"orperphysik,
Universit\"at Erlangen-N\"urnberg,
Erlangen (Germany)\\ $^5$ Moscow Institute
of Electronic Technology, Zelenograd (Russia)
\\ $^6$ Institut N\'eel, CNRS, Grenoble
(France)
Vanadium dioxide (V0$_2$) is a prototype
material for the discussion of correlation
effects in solids. Here we present a
parameter-free GW calculation of
VO$_2$ and show that correlation effects in
the photoemission spectra of
both the metallic and the insulating phases
of VO$_2$ are correctly
reproduced, provided that quasiparticle
energies and wavefunctions are
calculated self-consistently [1].
These calculations are computationally
demanding and one is naturally lead
to look for possible alternatives.
In fact, spectra are derived from
contractions of many-body Green's
functions. So one calculates more information
than needed.
We hence illustrate an in principle exact
alternative approach to construct
effective potentials and kernels for the
direct calculation of electronic spectra
[2]. In particular, a dynamical but local and
real potential yields the
spectral function needed to describe
photoemission. We discuss for model
solids the frequency dependence of this
``photoemission
potential'' stemming from the nonlocality
of the corresponding
self-energy.
[1] M. Gatti, F. Bruneval, V. Olevano, and
L. Reining, submitted to Phys.
Rev. Lett. (2007).
[2] M. Gatti, V. Olevano, L. Reining, and
I.V. Tokatly, Phys. Rev. Lett.
{\bf 99}, 057401 (2007).
Time Dependent Density Functional Theory and Strongly Correlated Systems: Insight From Numerical Studies
Claudio Verdozzi
Division of Mathematical Physics, Lund
University - Sweden
We illustrate the potential of Time Dependent
Density Functional Theory (TDDFT)
for describing the nonequilibrium behavior of
strongly correlated (lattice) models.
Starting from an exact time-evolution of the
many-body wavefunction,
we determine, via reverse engineering, the
exact exchange
correlation (xc) potential v_xc for small
Hubbard chains of different lengths and
electron
fillings and exposed to time-dependent
perturbations.
We compare some of the exact results to those
of adiabatic-like treatments, in order to
extract
some of the properties that approximate xc
potentials should have.
Finally, we provide details of work in
progress and future directions.
Efficient ab-initio calculations of bound and continuum excitons
Margherita Marsili$^{1,2}$, Francesco
Sottile$^{1,3}$, Valerio Olevano$^{1,4}$, and
Lucia Reining $^{1,3}$
$^1$European Theoretical Spectroscopy
Facility (ETSF), $^2$ INFM-CNR-CNISM
Dipartimento di fisica, Universit\'a di
Roma Tor Vergata, $^3$ LSI CNRS-CEA/DSM,
Ecole Polytechnique, Palaiseau , $^4$ LEPES,
Grenoble
We present a scheme that yields different
approximations for the exchange-correlation
kernel of time-dependent density-functional
theory (TDDFT). A specific choice of the
approximation leads to the kernel that has
been recently derived through the comparison
with the Bethe-Salpeter equation
\cite{sottile,adragna}. Another choice of
the approximations leads to a static
formulation of the kernel. We have checked
the validity of this static approximation for
a variety of materials such as Si, SiC, C and
Ar. In all cases it is able to well reproduce
the excitonic effects in the absorbtion
spectra of these materials. Moreover the
simplest static approximation yields a
significant improvement of the scaling of the
calculation with the size of the system.
Superconducting transition in doped diamond and silicon
D. Connetable, E. Bourgeois, {\underline{X.
Blase}}
LPMCN, Universite Lyon I and CNRS, Lyon,
France.
After introducing the field by presenting the
case of the doped silicon clathrates [1], we
study the superconducting transition in
highly-doped diamond [2] and silicon [3].
Both experimental and theoretical aspects
will be overviewed. At large boron doping,
that is beyond the Mott metal-insulator
transition, diamond and silicon have been
shown to become superconducting with a $T_C$
up to 10 K in the diamond case. The study of
the electronic properties and electron-phonon
coupling strength $\lambda$ allows to
identify the modes responsible for the
superconducting transition and provides
support to a standard BCS mechanism, even
though some questions remain opened
concerning the value of the Coulomb repulsion
parameter $\mu^*$ and the relation between
the doping rate and $T_C$. Strategies to
increase $T_C$ are discussed. Increasing the
boron content in diamond may not be so
efficient as boron tend to cluster in
electronically inactive dimers [4]. In the
case of silicon, changing boron by aluminum
is shown to enhance $T_C$ by one order of
magnitude, an effect due to a negative
pressure effect [5]. \\
\vskip 1cm
\noindent
[1] "Superconductivity in doped sp3
semiconductors: the case of the clathrates',
D. Connetable et al., Phys. Rev. Lett. 91,
247001 (2003).\\
\noindent
[2] "Role of the Dopant in the
Superconductivity of Diamond",
X. Blase, Ch. Adessi, D. Connétable, Phys.
Rev. Lett. 93, 237004 (2004).\\
\noindent
[3] "Superconductivity in doped cubic
silicon", E. Bustarret, C. Marcenat, P.
Achatz, J. Kacmarcik, F. Levy, A. Huxley, L.
Ortega, E. Bourgeois, X. Blase, D. Debarre,
J. Boulmer, Nature (London) 444, 465-468
(2006).\\
\noindent
[4] "Impurity dimers in superconducting
B-doped diamond: Experiment and
first-principles calculations", E.
Bourgeois, E. Bustarret, P. Achatz, F. Omnes,
X. Blase, Phys. Rev. B 74, 094509
(2006).\\
\noindent
[5] "Superconductivity in doped cubic
silicon: an ab initio study", E. Bourgeois
and X. Blase, Appl. Phys. Lett. 90, 142511
(2007).
Mechanisms of photo-induced processes on MgO nano-particles
Paolo E. Trevisanutto$^1,2$, Peter V.
Sushko$^2$, Alexander L. Shluger$^2$
$^1$ Institut Neél, CNRS Grenoble, $^2$
University College of London, LCN London
Recent experimental data clearly demonstrate
that using both femto- and nano-second laser
pulses with photon energies tuned to excite
particular surface features at the MgO
surface, one can achieve a very effective
desorption of atomic O and Mg species.
Moreover, new experiments show that emission
spectra obtained on MgO nanocubes with maxima
at 3.4 eV and 3.3 eV results from the
excitation of 4-fold and 3-fold coordinated
anions at 5.4 eV and 4.6 eV. In this
presentation we demonstrate new mechanism
responsible for desorption of Oxygen and
Magnesium atoms and new mechanisms of
photo-induced radiative and non-radiative
processes on low-coordinated sites.
Recently we demonstrated that photo-induced
desorption can be used for probing surface
spectroscopic features [1-3]. The technique
is sensitive enough to detect energy shifts
between the bulk and surface excitons as
small as 0.2 eV. In addition, a significant
degree of control over the desorbed species
can be achieved if the knowledge of the
surface electronic structure is fully
exploited [1-3]. We extended this approach to
more complex oxide surfaces. The experimental
and theoretical studies demonstrate that
excitation energies of corner and step sites
at the MgO (001) surface are strongly shifted
with respect to the bulk and terrace exciton
energies [4]. Recent experiments demonstrated
that selective excitation of the kink and
corner surface features using 4.7 eV laser
pulses leads to desorption of O atoms with
average kinetic energies of about 0.3 eV.
Since the valence of anions in MgO is twice
that of anions in alkali-halides, the
desorption mechanism is expected to be more
complex and involves several steps.
To model the photon-induced processes in MgO
we employ an embedded cluster approach, which
combines a quantum-mechanical treatment of a
site of interest with a self-consistent
classical description of the remaining part
of the system. The method is implemented in a
computer code GUESS; it allows one to account
consistently for the ionic and electronic
contributions to the defect-induced lattice
polarization and for their effect on the
defect itself, and to treat excited states
using different ab initio techniques.
We modeled desorption from a 3-coordinated
oxygen corner site at an MgO surface and
developed a three-step mechanism for these
processes [5-6]. The results of our
calculations suggest that the first photon of
ca. 4.5 eV can induce an optical transition
at the oxygen corner site. This first excited
state relaxes with a significant displacement
of the corner oxygen away from its original
site. The relaxed state corresponds to a
charge transfer exciton configuration O–
… Mg+. This system can relax radiatively
towards the ground state and the calculated
value is 3.4 eV. However, calculations have
shown also that nonradiative transitions to
lowest triplet and ground state are allowed.
If the system remains in the excited state,
excitation with another photon at about 4.8
eV will ionise the corner (where the oxygen
species has now a hole). Further photon at
4.8 eV excites the corner neutralizing the
charge of Oxygen. The adiabatic potential
energy surface for this excited state is such
that oxygen atom prefers to leave the surface
with the maximum kinetic energy of several
tenths on an eV. The surface site relaxes
with the formation of a F+ centre at the
corner site previously occupied by the
desorbed oxygen atom. Our results are in good
agreement with the experimental photon
energies and kinetic energies of desorbed
species.
References
[1] V. E. Puchin, A. L. Shluger, N. Itoh,
Phys. Rev. B, 47, 10760 (1993)
[2] K. M. Beck, A. G. Joly, N. F. Dupuis,
P. Perozzo, W. P. Hess, P. V. Sushko, A. L.
Shluger,
J. Chem. Phys., 120, 2456 (2004)
[3] W. P. Hess, A. G. Joly, K. M. Beck, P.
V. Sushko, A. L. Shluger., Surf. Sci. 564
(2004)
[4] A. L. Shluger, P. V. Sushko, L. N.
Kantorovich, Phys. Rev. B, 59, 2417 (1999).
[5] W. P. Hess, A. G. Joly, K. M. Beck, M.
Henyk, P. V. Sushko, P. E. Trevisanutto, A.
L. Shluger , J. Phys. Chem. B, 109 (42),
19563 (2005)
[6] P. E. Trevisanutto, P. V. Sushko, A. L.
Shluger, K. M. Beck, M. Henyk, A. G. Joly, W.
P. Hess,
Surf. Sci, 593, 210 (2005)
Local and nonlocal vertex corrections in GW for localised and extended systems
M. Stankovski$^1$, A. Morris$^2$, B.
Robinson$^1$ and R. Godby$^1$
$^1$ University of York, UK\\$^1$ Cavendish
labs, Univ. of Cambridge, UK
In the framework of Hedin's $GW$
approximation, the non-local self energy is
usually calculated in a one-shot manner with
an initial Green's function constructed from
Kohn-Sham orbitals. In principle, there is a
vertex associated with such a starting point
(Del Sole \emph{et al.} PRB {\bf 49}, 8024
(1994)). Inclusion of this vertex has proven
to give unsatisfactory total energies and
spectral properties in two test systems,
jellium and closed-shell atoms. It is
therefore desirable to go beyond a local
potential in the construction of the initial
non-interacting Greens function. We have
investigated the effect of simple initial
self-energy approximations which include two
different types of non-locality. The formally
correct vertex for these starting points have
then been implemented and some show
significant improvement on $G_{0}W_{0}$
calculations for the same test systems.