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EXCAM Workshop 1997

Electronic Exchange and Correlation in Advanced Materials

Thursday 11 September - Friday 12 September 1997
CECAM, Lyon, France

Stefan Albrecht

Institution: Ecole Polytechnique
Postal address: 91128 Palaiseau, France
Telephone: ++ 33 1 69 33 40 90
Fax: ++ 33 1 69 33 30 22
E-mail: albrecht@seurat.polytechnique.fr


Excitons in solids: real space formulation

Stefan Albrecht, Lucia Reining
Laboratoire des Solides Irradies, CNRS-CEA, Ecole Polytechnique, F-91128 Palaiseau, France

Giovanni Onida, Rodolfo Del Sole
Istituto Nazionale per la Fisica della Materia, Dipartimento di Fisica dell'Universita di Roma Tor Vergata, Via della Ricerca Scientifica, I-00133 Roma, Italy

The description of the optical absorption process in solids often demands for the inclusion of excitonic effects beyond the one-particle picture. We treat such effects by solving an effective two-particle equation in a basis of Kohn-Sham eigenfunctions. This basis becomes very large, due to the large number of necessary k-points in the Brillouin zone sampling. We overcome this bottleneck by Fourier transforming to real space, thus using a basis given by pairs of bands -i.e. the possible products of a valence and a conduction band- and lattice vectors. We discuss the convergence of the various contributions, and their influence on the absorption spectrum at the example of silicon.

Friedhelm Bechstedt

Institution: Institut fuer Festkoerpertheorie und Theoretische Optik
Postal address: Max-Wien-Platz 1
D-07743 Jena
Telephone: 0049-3641-635902
Fax: 0049-3641-635182
E-mail: bechsted@ifto.physik.uni-jena.de
WWW home page: http://www.ifto.uni-jena.de


Excitons and ab initio electronic structure calculations

Friedhelm Bechstedt
Friedrich-Schiller-Universitaet, Max-Wien-Platz 1, D-07743 Jena, Germany

In order to calculate the optical properties of semiconductors the Bethe-Salpeter equation (BSE) for the polarization function and the Dyson equation for the single-particle Green function have to be solved simultaneously. We discuss such a solution including dynamical screening. To consider the binding effects between electrons and holes, i.e. the excitons, the inhomogeneous BSE is traced back to a homogeneous one. It may be solved in k space by direct diagonalization. First results are presented for silicon.

Massimiliano Corradini

Institution: Dipartimento di Fisica dell'Universita' di Roma Tor Vergata
Postal address: Via della Ricerca Scientifica,1 -00133 Roma,Italy
Telephone: +39 6 72594761
Fax: (39 6) 2023507
E-mail: CORRADINI@roma2.infn.it

Abstract (of poster)

A simple analytic form of the local-field factor of the homogeneous electron gas

M. Corradini, M. Palummo, G. Onida, R. Del Sole
Istituto Nazionale per la Fisica della Materia, Dipartimento di Fisica
dell'Universita' di Roma Tor Vergata, Via della Ricerca Scientifica
n. 1 - 00133 Roma (Italy)

We present a fitting formula for the local field factor G(q) obtained by a recent diffusion Monte Carlo calculation of Moroni et al./1/. Our aim was to obtain both the exact asymptotic behaviour in the small and large q regions for G(q), and a Fourier transform of the exchange correlation factor K(q) in terms of analytical functions (not depending by any additional parameter). Using Lorentzian and Gaussian functions for fitting G(q), K(x) is expressed as a simple Yukawa-like term, plus a Gaussian term.
/1/ S. Moroni, D. M. Ceperley, and G. Senatore, Phys. Rev. Lett. 75, 689, (1995).

Rodolfo Del Sole

Institution: Dipartimento di Fisica dell'Universita' di Roma Tor Vergata
Postal address: Via della Ricerca Scientifica n. 1 - 00133 Roma (Italy)
Telephone: +39/6/72 59 45 22
Fax: +39/6/20 23 507
E-mail: delsole@roma2.infn.it

Rex Godby

Institution: Department of Physics, University of York
Postal Address: York YO1 5DD, U.K.
Telephone: +44 1904 432231
Fax: +44 1904 432214
E-mail: rwg3@york.ac.uk
WWW home page: http://www-users.york.ac.uk/~rwg3/


Self-consistency, total energies and spectral functions for Hubbard systems

T. Pollehn** and R.W. Godby*
*Department of Physics, University of York, York YO1 5DD, U.K.
**Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, U.K.

We present aproximate results for Hubbard systems for which exact results are also calculated using exact diagonalisation. The quantities calculated are the spectral function and total energy, and the approximations used are GW, GW with a Hartree-Fock vertex ("generalised GW"), and the T-matrix approximation with and without exchange diagrams. We also investigate the effect of self-consistency in the self-energy within the GW approximation on the spectral function and total energy.

Lars Hedin

Institution: MPI-FKF
Postal address: Heisenbergstrasse 1, D-70569 Stuttgart, Germany
Telephone: +49-711-689 1593
Fax: +49-711-689 1595
E-mail: hedin@audrey.mpi-stuttgart.mpg.de
WWW home page: http://www/docs/frames.html


The transition from the adiabatic to the sudden limit in core electron photoemission

John Michiels(1), Lars Hedin(1) and John Inglesfield(2)
(1) MPI-FKF, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
(2) Univ of Wales, College of Cardiff, PO Box 913, Cardiff CF2 3YB, GB
We compare different approximations to calculate core electron photoemission, trying to understand the transition from the adiabatic to the sudden limits. We study a model case of an atom embedded in a semi-infinite jellium. At low photoelectron energies we use the Inglesfield-Bardyszewski-Hedin quantum-mechanical approximation (QM), at somewhat higher energies a semi-classical approach with quantum-mechanically calculated loss from a photoelectron moving on a trajectory (SC), and at high energies the Spicer three-step model (TRANSP). Comparisons are also made with the Tougaard approach. SC agrees quite well with QM already at say twice the plasmon energy above threshold, while TRANSP does not agree until the order of tenths of plasmons energies. The approach to the sudden limit is illustrated by a curve over the integrated intensity of the satellites relative to that of the main peak as a function of photo-electron energy. For energies when the satellite electrons have an energy below the plasmon threshold while the primary electron has an energy above, this curve has a pronounced peak due to the comparatively long mean free part of the electrons in the satellite. As models for the dielectric function of the semi-infinite jellium, we use the Inglesfield and the Bechstedt coupling functions, as well as the RPA infinite-barrier function. The latter includes interference between the incoming and reflected electrons. We derive a general expression for the relation between an RPA-type dielectric function and the fluctuation potential needed in the QM approach. The Inglesfield, Bechstedt and RPA fluctuation potentials show only minor differences, except at very low energies.

Ref. Bardyszewski W and Hedin L, 1985, Physica Scripta 32, 439-50
A new approach to the theory of photoemission in solids

Giovanni Onida

Institution: Dipartimento di Fisica dell'Universita' di Roma Tor Vergata
Postal address: Via della Ricerca Scientifica n. 1 - 00133 Roma (Italy)
Telephone: +39/6/72 59 45 23
Fax: +39/6/20 23 507
E-mail: onida@roma2.infn.it

Maurizia Palummo

Institution: Tor Vergata University - Dep. of Physics
Postal address: Via della Ricerca Scientifica 1
Telephone: 06/7259-4-508/523
Fax: FAX 06/72594507
E-mail: palummo@axtov1.roma2.infn.it

Olivia Pulci

Institution: Institut fuer Festkoerpertheorie und Theoretische Optik
Postal address: Max-Wien-Platz 1,D-07743 Jena,Germany
Telephone: 0049-3641-636684
Fax: 0049-3641-635182
E-mail: pulci@ifto.physik.uni-jena.de


Self-Energy effects on electronic and optical properties of GaAs(110)

O. Pulci$^{1,2}$, R. Del Sole$^{1}$, G. Onida$^{1}$, F. Bechstedt$^{2}$, L.Reining$^{3}$

1 Istituto Nazionale per la Fisica della Materia - Dipartimento di Fisica dell' Universit\'a di Roma Tor Vergata -- Via della Ricerca Scientifica, I--00133 Roma, Italy;

2 Institut fuer Festkoepertheorie und Theoretische Optik, Friedrich--Schiller--Universitaet Max-Wien-Platz 1, 07743;

3 Ecole Polytechnique, 91128 Palaiseau, France

We have calculated the QP bandstructure of GaAs(110) in the GW approximation using the DFT-LDA eigenvalues and eigenfunctions as the starting point, and computing the QP energies in first--order perturbation theory by evaluating the diagonal components of $<\Sigma - V_{xc}>$. Some preliminary results for the non-diagonal components are presented.

The importance of the choice of the number and type of k-points, in which the screening function and the integrals appearing in the exchange end correlation part of the Self--Energy are calculated, is discussed in details. Our calculation of GW energies shows that filled states undergo different QP corrections, depending on their surface localization.

Keeping into account this result, we calculate the optical spectra of GaAs(110) with the inclusion of QP corrections, and discuss its changes with respect to the rigidly shifted LDA spectrum.

Lucia Reining

Institution: Ecole Polytechnique
Postal address: 91128 Palaiseau, France
Telephone: 0033-1-69333690
Fax: 0033-1-69333022
E-mail: reining@monet.polytechnique.fr


First-principles calculations of photoemission spectra in clusters

Lucia Reining, Laboratoire des Solides Irradie's, Ecole Polytechnique,
91128 Palaiseau, France, and Giovanni Onida, Dipartimento di Fisica,
Universita' di Roma "Tor Vergata", I-00133 Roma, Italy

We discuss a method for first-principles calculations of photoemission spectra in small clusters, going well beyond a standard DFT-LDA approach. Starting with a DFT-LDA calculation, we evaluate self-energy contributions to the quasiparticle energies in the GW scheme. The contributions of structural relaxations are taken into account. We show the importance of these effects at the example of the photoemission spectrum of SiH4. We also briefly discuss results for longer hydrogenated silicon chains.

Angel Rubio

Institution: Departamento Fisica Teorica. University of Valladolid
Postal address: C/ Prado de la Magdalena s/n
Telephone: ++34-83-423263
Fax: ++34-83-423013
E-mail: arubio@mileto.fam.cie.uva.es
WWW home page: http://www.fam.cie.uva.es/~arubio

Arno Schindlmayr

Institution: University of Cambridge
Postal address: Theory of Condensed Matter, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom
Telephone: +44 (0)1223 337340
Fax: +44 (0)1223 337356
E-mail: as10031@phy.cam.ac.uk


Iterative improvement and conservation properties of the GW approximation

Arno Schindlmayr1 and R. W. Godby2

1 Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, United Kingdom

2 Department of Physics, University of York, Heslington, York YO1 5DD, United Kingdom

Most ab initio many-body calculations for real materials use the GW approximation for the electronic self-energy, in which the exact propagators are replaced by intermediate quantities from the first cycle of an iterative solution of Hedin's coupled equations. We investigate the convergence of this approach by comparing plasmon spectra of a model Hamiltonian calculated in this way with results from a second iteration. Excitation energies are indeed improved due to the nontrivial vertex function, while a qualitatively correct satellite spectrum emerges as a result of the renormalisation of internal propagators. Not unexpectedly, however, we also observe an incorrect transfer of spectral weight across the frequency axis. In the second part of the talk, we use an analytically solvable model system to demonstrate that there is a genuine, albeit small, violation of particle number conservation in the standard non-self-consistent GW approximation. We also show how the numerical magnitude of this violation can be reduced by an alignment of the chemical potentials in Dyson's equation for a range of complementary self-energy functionals.

Lutz Steinbeck

Institution: Department of Physics, University of York
Postal address: Heslington, York YO1 5DD, UK
Telephone: (+44) (0) 1904 432221
Fax: (+44) (0) 1904 432214
E-mail: ls9@york.ac.uk


Recent development of the space-time GW method

L. Steinbeck, M.M. Rieger*, I.D. White*, and R.W. Godby

Department of Physics, University of York, Heslington, York YO1 5DD, UK
*Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK

Some aspects of the recent technical development of the real-space imaginary-time GW method are discussed. In the calculation of the Green function, polarizability, and self energy in real space these quantities are restricted to a "megacell" (interaction cell) the shape and size of which must be consistent with the k point grid used for the computation of the dielectric matrix and the screened Coulomb interaction in reciprocal space. The Coulomb interaction is cut off at the edge of the Wigner-Seitz cell of the megalattice. Besides describing this megacell idea, the treatment of the long-range part of the dielectric function and the scaling of the computational time with system size are briefly discussed.

Ulf von Barth

Institution: Dept. of Theor. Phys., Lund University.
Postal address: Solvegat 14A, S-22362 Lund, Sweden.
Telephone: +46-46-2229069
Fax: +46-46-2224438
E-mail: barth@teorfys.lu.se


A screened-exchange model for the exchange-correlation energy of molecules and solids.

U. von Barth and R. van Leeuwen

Dept. of Theor. Phys.
Lund University, Sweden.

In the present work we have made an attempt to construct an accurate approximation to the functional for the exchange-correlation energy of density-functional theory. The approximation is based on modelling the exact exchange-correlation hole by means of that of Hartree-Fock theory multiplied by a correlation factor causing the hole to become deeper and more localized. The hole can be made to obey several exact relations such as a sum rule and a cusp condition. Already, very crude versions of the correlation factor give an accurate description of the true in hole in such diverse systems as the H2 molecule, the He atom, and the electron gas. By adjusting parameters in the correlation factor we can obtain accurate correlation energies in these very different systems. Needless to say, the excahnge energies are exact. The model is presently being tested in a variety of systems.

Ian White

Institution: Cavendish Laboratory
Postal address: Madingley Road, Cambridge CB3 OHE
Telephone: 01223 337460
E-mail: idw1000@phy.cam.ac.uk

Dynamic image potential at an Al(111) surface

I. D. White(*) , R. W. Godby(+), M. M. Rieger(*), R. J. Needs(*)

*Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge

+Department of Physics, University of York, Heslington, York Y01 5DD

Density-functional theory (DFT) performed within any local approximation for exchange and correlation, such as the LDA, fails to reproduce the correct asymptotic image form of the surface barrier experienced by electrons. Using the recently developed space-time method for many-body perturbation theory calculations, we calculate the non-local, energy- dependent self-energy for electrons at an Al(111) surface within the GW approximation.

The effect of the self-energy can be studied in terms of a state-dependent local potential, which yields the form of the crossover between the bulk and image potential. The relative contribution of exchange and correlation to the image potential has been disputed in previous theoretical studies. We find that, although the exchange hole can give the asymptotic potential experienced by occupied state electrons, this is not the case for unoccupied states, and that a correct physical description always requires the inclusion of correlation effects.

Nathalie Vast

Institution: Commissariat a l'Energie Atomique
Telephone: (33) 1 45 95 64 72
Fax: (33) 1 43 86 74 10
E-mail: vast@limeil.cea.fr

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