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Paper 51

The GW Space-Time Method for the Self-Energy of Large Systems

Martin M. Rieger1,3, L. Steinbeck2, I.D. White1, H.N. Rojas1,4 and R.W. Godby2

1Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, CB3 0HE, UK
2Department of Physics, University of York, Heslington, York YO10 5DD, UK
3Present address: Siemens AG, Semiconductor Group, Balanstraße 73, 81617 München, Germany
4Permanent address: Universidad Privada Boliviana, Casilla 3967, Cochabamba, Bolivia

Computer Physics Communications 117 211-228 (1999)

We present a detailed account of the GW space-time method. The method increases the size of systems whose electronic structure can be studied with a computational implementation of Hedin's GW approximation. At the heart of the method is a representation of the Green's function G and the screened Coulomb interaction W in the real-space and imaginary-time domain, which allows a more efficient computation of the self-energy approximation Σ = iGW. For intermediate steps we freely change between representations in real and reciprocal space on the one hand, and imaginary time and imaginary energy on the other, using fast Fourier transforms. The power of the method is demonstrated using the example of Si with artificially increased unit cell sizes.

PACS Numbers: 71.15.Th,71.20.-b,79.60.Jv

Keywords: GW

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Paper 52

Spectra and Total Energies from Self-Consistent Many-Body Perturbation Theory

Arno Schindlmayr1, Thomas J. Pollehn1 and R.W. Godby2

1Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, CB3 0HE, UK
2Department of Physics, University of York, Heslington, York YO10 5DD, UK

Physical Review B 58 12684-90 (1998)

With the aim of identifying universal trends, we compare fully self-consistent electronic spectra and total energies obtained from the GWapproximation with those from an extended GWΓ scheme that includes a nontrivial vertex function and the fundamentally distinct Bethe-Goldstone approach based on the T-matrix. The self-consistent Green's function G, as derived from Dyson's equation, is used not only in the self-energy but also to construct the screened interaction W for a model system. For all approximations we observe a similar deterioration of the spectrum, which is not removed by vertex corrections. In particular, satellite peaks are systematically broadened and move closer to the chemical potential. The corresponding total energies are universally raised, independent of the system parameters. Our results therefore suggest that any improvement in total energy due to self-consistency, such as for the electron gas in the GW approximation, may be fortuitous.

PACS numbers: 71.10.-w, 71.45.Gm, 71.15.Nc

Keywords: GW

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Paper 53

Enhancements to the GW Space-Time Method

L. Steinbeck1, A. Rubio2, L. Reining3, M. Torrent3, I.D. White4 and R.W. Godby1

1Department of Physics, University of York, Heslington, York YO10 5DD, UK
2Departamento Fisica Teorica, Universidad de Valladolid, E-47011 Valladolid, Spain
3Laboratoire des Solides Irradiés, URA 1380 CNCRS-CEA/DTA/DECM, Ecole Polytechnique, Palaiseau, F-91128, France
4Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, CB3 0HE, UK

Computer Physics Communications 125 105-118 (2000)

We describe the following new features which significantly enhance the power of the recently developed real-space imaginary-time GW scheme (Rieger et al., Comp. Phys. Commun. 117 211 (1999)) for the calculation of self-energies and related quantities of solids: (i) to fit the smoothly decaying time/energy tails of the dynamically screened Coulomb interaction and other quantities to model functions, treating only the remaining time/energy region close to zero numerically and performing the Fourier transformation from time to energy and vice versa by a combination of analytic integration of the tails and Gauss-Legendre quadrature of the remaining part and (ii) to accelerate the convergence of the band sum in the calculation of the Green's function by replacing higher unoccupied eigenstates by free electron states (plane waves).

PACS numbers: 71.15.Th, 71.20.-b, 79.60.Jv

Keywords: GW

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Paper 54

Self-Consistent Calculation of Total Energies of the Electron Gas Using Many-Body Perturbation Theory

P. García-González and R.W. Godby

Department of Physics, University of York, Heslington, York YO10 5DD, UK

Physical Review B 63 075112 (2001) (4 pages)

The performance of many-body perturbation theory for calculating ground-state properties is investigated. We present fully numerical results for the electron gas in three and two dimensions in the framework of the GW approximation. The overall agreement with very accurate Monte Carlo data is excellent, even for those ranges of densities for which the GW approach is often supposed to be unsuitable. The latter seems to be due to the fulfilment of general conservation rules. These results open further prospects for accurate calculations of ground-state properties circumventing the limitations of standard density functional theory.

PACS numbers: 71.10.-w, 71.10.Ca

Keywords: GW

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Paper 55

Efficient Total Energy Calculations from Self-Energy Models

Paula Sánchez-Friera and R.W. Godby

Department of Physics, University of York, Heslington, York YO10 5DD, UK

Physical Review Letters 85 5611-5614 (2000)

We propose a new method for calculating total energies of systems of interacting electrons, which requires little more computational resources than standard density-functional theories. The total energy is calculated within the framework of many-body perturbation theory by using an efficient model of the self-energy, that nevertheless retains the main features of the exact operator. The method shows promising performance when tested against quantum Monte Carlo results for the linear response of the homogeneous electron gas and structural properties of bulk silicon.

PACS numbers: 71.15.Nc, 71.45.Gm, 71.15.Mb

Keywords: GW

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Paper 56

GW Self-Energy Calculations for Surfaces and Interfaces

(review in a special CCP3 issue of Computer Physics Communications)

P. García-González and R.W. Godby

Department of Physics, University of York, Heslington, York YO10 5DD, UK

Computer Physics Communications 137 108-122 (2001)

The many-body GW approximation has become the most popular method in ab initio calculations of excited-state properties in real materials. GW overcomes many of the limitations of traditional density functional theories to predict one-electron excitation spectra for a wide variety of materials. In this article we review some applications of GW to real surfaces, from calculations of surface band structures in semiconductors to estimations of the lifetimes of surface states in metals.

PACS numbers: 31.15.Ar, 31.15.Lc, 73.20.At, 73.20.+y

Keywords: GW

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Paper 57

Diagrammatic Self-Energy Approximations and the Total Particle Number

Arno Schindlmayr1, P. García-González2 and R.W. Godby3

1Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin-Dahlem, Germany
2Departamento de Física Fundamental, Universidad Nacional de Educación a Distancia, Apartado 60141, 28080 Madrid, Spain
3Department of Physics, University of York, Heslington, York YO10 5DD, UK

Physical Review B 64 235106 (2001) (6 pages)

There is increasing interest in many-body perturbation theory as a practical tool for the calculation of ground-state properties. As a consequence, unambiguous sum rules such as the conservation of particle number under the influence of the Coulomb interaction have acquired an importance that did not exist for calculations of excited-state properties. In this paper we obtain a rigorous, simple relation whose fulfilment guarantees particle-number conservation in a given diagrammatic self-energy approximation. Hedin's G0W0 approximation does not satisfy this relation and hence violates the particle-number sum rule. Very precise calculations for the homogeneous electron gas and a model inhomogeneous electron system allow the extent of the non-conservation to be estimated.

PACS numbers: 71.45.Gm, 71.15.Qe

Keywords: GW

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Paper 58

Many-Body GW Calculations of Ground-State Properties: Quasi-2D Electron Systems and van der Waals Forces

P. García-González1 and R.W. Godby2

1Departamento de Física Fundamental, Universidad Nacional de Educación a Distancia, Apartado 60141, 28080 Madrid, Spain
2Department of Physics, University of York, Heslington, York YO10 5DD, UK

Physical Review Letters 88 056406 (2002) (4 pages)

We present GW many-body results for ground-state properties of two simple but very distinct families of inhomogenous systems in which traditional implementations of density-functional theory (DFT) fail drastically. The GW approach gives notably better results than the well-known random-phase approximation, at a similar computational cost. These results establish GW  as an superior alternative to standard DFT schemes without the expensive numerical effort required by quantum Monte Carlo simulations.

PACS numbers: 71.15.Nc, 71.15.Mb, 71.45.Gm

Keywords: GW DFT

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Paper 59

Image Resonance in the Many-Body Density of States at a Metal Surface

G. Fratesi1, G. P. Brivio1, P. Rinke2 and R. W. Godby2

1INFM and Dipartimento di Scienza dei Materiali, Università di Milano-Bicocca, via Cozzi 53, 20125 Milano, Italy
2Department of Physics, University of York, York YO10 5DD, United Kingdom

Physical Review B 68 195404 (2003) (5 pages)

The electronic properties of a semi-infinite metal surface without a bulk gap are studied by a formalism able to account for the continuous spectrum of the system. The density of states at the surface is calculated within the GW approximation of many-body perturbation theory. We demonstrate the presence of an unoccupied surface resonance peaked at the position of the first image state. The resonance encompasses the whole Rydberg series of image states and cannot be resolved into individual peaks. Its origin is the shift in spectral weight when many-body correlations are taken into account.

PACS number: 73.20.At

Keywords: GW

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Paper 60

Long-Range Contribution to the Exchange-Correlation Kernel of Time-Dependent Density Functional Theory

Silvana Botti, Francesco Sottile, Nathalie Vast, Valerio Olevano, and Lucia Reining
Laboratiores des Solides Irradiés, CNRS-CEA, École Polytechnique, F-91128 Palaiseau, France

Hans-Christian Weißker
Institut für Festkörpertheorie und Theoretische Optik, Friedrich-Schiller-Universität, D-07743 Jena, Germany

Angel Rubio
Departamento de Física de Materiales, Facultad de Ciencias Quémicas, Universidad del Pais Vasco, Donostia International Physics Center (DIPC) and Centro Mixto CSIC-UPV/EHU, Donostia, E-20018 San Sebastián, Basque Country, Spain

Giovanni Onida
Istituto Nazionale per la Fisica della Materia, Dipartimento di Fisica dell'Universitá di Milano, via Celoria 16, I-20133 Milano, Italy

Rodolfo Del Sole
Istituto Nazionale per la Fisica della Materia, Dipartimento di Fisica dell'Universitá di Roma "Tor Vergata", via della Ricerca Scientifica, I-00133 Roma, Italy

R.W. Godby
Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom

Physical Review B 69 155112 (2004) (14 pages)

We discuss the effects of a static long-range contribution -α/q2 to the exchange-correlation kernel fxc of time-dependent density functional theory. We show that the optical absorption spectrum of solids exhibiting a strong continuum exciton effect is considerably improved with respect to calculations where the adiabatic local density approximation is used. We discuss the limitations of this simple approach, and in particular why the same improvement cannot be found for the whole spectral range including the valence plasmons and bound excitons. On the other hand, we also show that within the range of validity of the method, the parameter depends linearly on the inverse of the dielectric constant, and we demonstrate that this fact can be used to predict continuum excitonic effects in semiconductors. Results are shown for the real and imaginary part of the dielectric function of Si, GaAs, AlAs, diamond, MgO and SiC, and for the loss function of Si.

PACS numbers: 71.10.-w, 78.20.Bh, 71.35.-y, 71.15.Qe

Keywords: DFT

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Paper 61

Maximum-Entropy Theory of Steady-State Quantum Transport

P. Bokes and R. W. Godby

Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom

Physical Review B 68 125414 (2003) (5 pages);    Erratum: Phys. Rev. B 72 199904(E) (2005) (1 page).

We develop a theoretical framework for describing steady-state quantum transport phenomena, based on the general maximum-entropy principle of nonequilibrium statistical mechanics. The general form of the many-body density matrix is derived, which contains the invariant part of the current operator that guarantees the nonequilibrium and steady-state character of the ensemble. Several examples of the theory are given, demonstrating the relationship of the present treatment to the widely used scattering-state occupation schemes at the level of the self-consistent single-particle approximation. The latter schemes are shown not to maximize the entropy, except in certain limits.

PACS numbers: 73.23.Ad, 05.60.Gg, 05.30.Ch

Keywords: Transport

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Paper 62

Density Functional Theories and Self-Energy Approaches

R. W. Godby1 and P. García-González2

1Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
2Departamento de Física de la Materia Condensada, Universidad Autonoma de Madrid

Chapter in “A Primer in Density Functional Theory” (Lecture Notes in Physics vol. 620), ed. Carlos Fiolhais, Fernando Nogueira and M. A. L. Marques, Springer (Heidelberg), 2003.

Keywords: GW DFT

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Paper 63

Comment on “Band-Gap Problem in Semiconductors Revisited: Effects of Core States and Many-Body Self-Consistency

Kris Delaney1, P. García-González2, Angel Rubio3, Patrick Rinke4, and R. W. Godby1

1Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
2Departamento de Física de la Materia Condensada, Universidad Autonoma de Madrid
3Dpto. Física Materiales, UPV, Centro Mixto CSIC-UPV, and Donostia International Physics Center (DICP), San Sebastián, Spain
4Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin-Dahlem, Germany

Physical Review Letters 93 249701 (2004) (1 page)

PACS Numbers: 71.15.Qe, 71.10.-w

Keywords: GW

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Paper 64

Image States in Metal Clusters

Patrick Rinke1, Kris Delaney1, P. García-González2 and R. W. Godby1

1Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
2Departamento de Física de la Materia Condensada, Universidad Autonoma de Madrid

Physical Review A 70 063201 (2004) (5 pages)

The existence of image states in small clusters is shown for the first time, using an ab initio many-body approach. We present image state energies and wavefunctions for spherical jellium clusters up to 186 atoms, calculated in the GW approximation, which by construction contains the dynamic long-range correlation effects that give rise to image effects. In addition we find that image states are also subject to quantum confinement. To extrapolate our investigations to clusters in the mesoscopic size range we propose a semi-classical model potential, which we test against our full ab initio results.

PACS Numbers: 36.40.Cg, 73.20.At, 73.22.Dj

Keywords: GW

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Paper 65

Assessment of Density Functional Approximations: Long-Range Correlations and Self-Interaction Effects

J. Jung1, P. García-González2, J.E. Alvarellos2 and R. W. Godby3

1Departamento de Física Fundamental, Universidad Nacional de Educación a Distancia, Apartado 60141, E-28080 Madrid, Spain
2Departamento de Física de la Materia Condensada, Universidad Autonoma de Madrid, E-28049 Madrid, Spain
3Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom

Physical Review A 69 052501 (2004) (7 pages)

The complex nature of electron-electron correlations is made manifest in the very simple but non-trivial problem of two electrons confined within a sphere. The description of highly non-local correlation and self-interaction effects by widely used local and semi-local exchange-correlation energy density functionals is shown to be unsatisfactory in most cases. Even the best such functionals exhibit significant errors in the Kohn-Sham potentials and density profiles.

PACS Numbers: 31.15.Ew, 31.25.-v, 71.15.Mb

Keywords: DFT

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Paper 66

Conductance and Polarization in Quantum Junctions

P. Bokes1,2 and R. W. Godby1

1Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
2Department of Physics, Faculty of Electrical Engineering and Information Technology, Slovak Technical University, Ilkovičova 3, 812 19 Bratislava, Slovak Republic

Physical Review B 69 245420 (2004) (8 pages)

We revisit the expression for the conductance of a general nanostructure -- such as a quantum point contact -- as obtained from the linear response theory. We show that the conductance represents the strength of the Drude singularity in the conductivity σ(k,k';iω→0). Using the equation of continuity for electric charge we obtain a formula for conductance in terms of polarization of the system. This identification can be used for direct calculation of the conductance for systems of interest even at the ab-initio level. In particular, we show that one can evaluate the conductance from calculations for a finite system without the need for special "transport" boundary conditions.

PACS numbers: 73.23.-b, 73.63.-b, 05.60.Gg

Keywords: Transport

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Paper 67

Effects Beyond the Random-Phase Approximation in Calculating the Interaction Between Metal Films

J. Jung1, P. García-González2, J.F. Dobson3 and R. W. Godby4

1Departamento de Física Fundamental, Universidad Nacional de Educación a Distancia, Apartado 60141, E-28080 Madrid, Spain
2Departamento de Física de la Materia Condensada, Universidad Autonoma de Madrid, E-28049 Madrid, Spain
3School of Science, Griffith University, Nathan, Queensland 4111, Australia
4Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom

Phys. Rev. B 70 205107 (2004) (11 pages)

The performance of the adiabatic-connection fluctuation-dissipation theorem (ACFDT) is discussed through the implementation of a non-local energy optimized exchange-correlation kernel to account for short range correlation effects. Whereas total electron correlation energies are rather sensitive to the details of the kernel, any physically well motivated approximation describes binding energies (including surface energies) within the same level of accuracy.

PACS numbers: 71.10.-w, 71.15.Mb, 71.15.Nc, 71.45.Gm

Keywords: DFT

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Paper 68

A Brief Introduction to the ABINIT Software Package

Xavier Gonze, Gian-Marco Rignanese, Matthieu Verstraete, Jean-Michel Betiken, Yann Pouillon, Razvan Caracas, Francois Jollet, Marc Torrent, Glues Zerah, Masayoshi Mikami, Philippe Ghosez, Marek Veithen, Jean-Yves Raty, Valerio Olevano, Fabien Bruneval, Lucia Reining, Rex Godby, Giovanni Onida, D. R. Hamann and Douglas C. Allan

Zeitschrift für Kristallographie 220 558–562 (2005) (Special issue on Computational Crystallography)

A brief introduction to the ABINIT software package is given. Available under a Free software license, it allows to compute directly a large set of properties useful for solid state studies, including structural and elastic properties, prediction of phase (meta)stability or instability, specific heat and free energy, spectroscopic and vibrational properties. These are described, and corresponding applications are presented. The emphasis is also laid on its ease of use and extensive documentation, allowing newcomers to quickly step in.

Keywords: GW

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Paper 69

Asymptotic Self-Consistency in Quantum Transport Calculations

H. Mera1, P. Bokes2 and R.W. Godby1

1Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
2Department of Physics, Faculty of Electrical Engineering and Information Technology, Slovak Technical University, Ilkovičova 3, 812 19 Bratislava, Slovak Republic

Physical Review B 72 085311 (2005) (6 pages)

Ab-initio simulations of quantum transport commonly focus on a central region which is considered to be connected to infinite, periodic leads through which the current flows.  The electronic structure of these distant leads is normally obtained from an equilibrium calculation, ignoring the self-consistent response of the leads to the current. We examine the consequences of this, and show that the electrostatic potential, Δφ, is effectively being approximated by the difference between electrochemical potentials, Δμ, and that this approximation is incompatible with asymptotic charge neutrality. In a test calculation for a simple metal-vacuum-metal junction, we find large errors in the non-equilibrium properties calculated with this approximation, in the limit of small vacuum gaps. We provide a simple scheme by which these errors may be corrected.

PACS numbers: 05.60.Gg, 73.40.-c, 41.20

Keywords: Transport

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Paper 70

Current-constraining variational approaches to quantum transport

P. Bokes1,2, H. Mera2, and R.W. Godby2

1Department of Physics, Faculty of Electrical Engineering and Information Technology, Slovak Technical University, Ilkovičova 3, 812 19 Bratislava, Slovak Republic
2Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom

Physical Review B 72 165425 (2005) (10 pages)

Presently, the main methods for describing a non-equilibrium charge-transporting steady state are based on time-evolving it from the initial zero-current situation. An alternative class of theories would give the statistical non-equilibrium density operator from principles of statistical mechanics, in a spirit close to Gibbs ensembles for equilibrium systems, leading to a variational principle for the non-equilibrium steady state. We discuss the existing attempts to achieve this using the maximum entropy principle based on constraining the average current. We show that the current-constrained theories result in a zero induced drop in electrostatic potential, so that such ensembles cannot correspond to the time-evolved density matrix, unless left- and right-going scattering states are mutually incoherent.

PACS numbers: 73.63.-b, 73.23.Ad, 05.60.Gg

Keywords: Transport

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Paper 71

Quantum conductance of homogeneous and inhomogeneous interacting electron systems

P. Bokes1, J. Jung2,3 and R. W. Godby3

1Department of Physics, Faculty of Electrical Engineering and Information Technology, Slovak Technical University, Ilkovičova 3, 812 19 Bratislava, Slovak Republic
2 Physics Division, National Center for Theoretical Sciences, P.O. Box 2-131, Hsinchu, Taiwan
3Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom

arXiv.org cond-mat/0604317

Note: the results in this paper were subsequently published as part of Paper 76: see below

We obtain the conductance of a system of electrons connected to leads, within time-dependent density-functional theory, using a direct relation between the conductance and the density response function. Corrections to the non-interacting conductance appear as a consequence of the functional form of the exchange-correlation kernel at small frequencies and wavevectors. The simple adiabatic local-density approximation and non-local density-terms in the kernel both give rise to significant corrections in general.  In the homogeneous electron gas, the former correction remains significant, and leads to a failure of linear-response theory for densities below a critical value.

PACS numbers: 73.63.-b, 71.15.Mb, 73.40.Jn, 05.60.Gg

Keywords: Transport

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See also: Paper 61,Paper 66, Paper 69, Paper 70

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Paper 72

Dielectric anisotropy in the GW space-time approach

Christoph Freysoldt1, Philipp Eggert1, Patrick Rinke1, Arno Schindlmayr1,2, R.W. Godby3 and Matthias Scheffler1

1Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
2Institut für Festkörperforschung, Forschungszentrum Jülich, 52425 Jülich, Germany
3Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom

Computer Physics Communications, 176 1-13 (2007)

Excited-state calculations, notably for quasiparticle band structures, are nowadays routinely performed within the GW approximation for the electronic self-energy. Nevertheless, certain numerical approximations and simplifications are still employed in practice to make the computations feasible. An important aspect for periodic systems is the proper treatment of the singularity of the screened Coulomb interaction in reciprocal space, which results from the slow 1/r decay in real space. This must be done without introducing artificial interactions between the quasiparticles and their periodic images in repeated cells, which occur when integrals of the screened Coulomb interaction are discretised in reciprocal space. An adequate treatment of both aspects is crucial for a numerically stable computation of the self-energy. In this article we build on existing schemes for isotropic screening and present an extension for anisotropic systems. We also show how the contributions to the dielectric function arising from the non-local part of the pseudopotentials can be computed efficiently. These improvements are crucial for obtaining a fast convergence with respect to the number of points used for the Brillouin zone integration and prove to be essential to make GW calculations for strongly anisotropic systems, such as slabs or multilayers, efficient.

PACS numbers: 71.15.Qe, 71.45.Gm

Keywords: GW

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Paper 73

Hartree-Fock Theory of a Current-Carrying Electron Gas

H. Mera1,2, P. Bokes3 and R. W. Godby2

1Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
2Niels Bohr Institute and Nano-Science Center, Universitetsparken 5, DK-2100 Copenhagen
3Department of Physics, Faculty of Electrical Engineering and Information Technology, Slovak Technical University, Ilkovičova 3, 812 19 Bratislava, Slovak Republic

Physical Review B 76 125319 (2007) (5 pages)

State-of-the-art simulation tools for non-equilibrium quantum transport systems typically take the current-carrier occupations to be described in terms of equilibrium distribution functions characterised by two different electro-chemical potentials, while for the description of electronic exchange and correlation, the local density approximation (LDA) to density functional theory (DFT) is generally used. However this involves an inconsistency because the LDA is based on the homogeneous electron gas in equilibrium, while the system is not in equilibrium and may be far from it. In this paper we analyze this inconsistency by studying the interplay between non-equilibrium occupancies obtained from a maximum entropy approach and the Hartree-Fock exchange energy, single-particle spectrum and exchange hole, for the case of a two-dimensional homogeneous electron gas. The current-dependence of the local exchange potential is also discussed.
It is found that the single-particle spectrum and exchange hole have a significant dependence on the current which has not been taken into account in practical calculations. The exchange energy and the local exchange potential, however, are shown to change very little with respect to their equilibrium counterparts. The weak dependence of these quantities on the current is explained in terms of the symmetries of the exchange hole.

PACS numbers: 71.10.-w, 71.10.Ca, 71.70.Gm, 73.23.-b

Keywords: Transport

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Paper 74

Self-interaction in Green's-function theory of the hydrogen atom

W. Nelson1*, P. Bokes2, Patrick Rinke3 and R.W. Godby1

1Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom and European Theoretical Spectroscopy Facility
2Department of Physics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovičova 3, 841 04 Bratislava, Slovak Republic and European Theoretical Spectroscopy Facility
3Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany and European Theoretical Spectroscopy Facility
*Present address: Department of Physics, King's College, London, Strand, London WC2R 2LS, United Kingdom

Physical Review A  75 032505 (2007) (4 pages)

Atomic hydrogen provides a unique test case for computational electronic structure methods, since its electronic excitation energies are known analytically. With only one electron, hydrogen contains no electronic correlation and is therefore particularly susceptible to spurious self-interaction errors introduced by certain computational methods. In this paper we focus on many-body perturbation-theory (MBPT) in Hedin's GW approximation. While the Hartree-Fock and the exact MBPT self-energy are free of self-interaction, the correlation part of the GW self-energy does not have this property. Here we use atomic hydrogen as a benchmark system for GW and show that the self-interaction part of the GW self-energy, while non-zero, is small. The effect of calculating the GW self-energy from exact wavefunctions and eigenvalues, as distinct from those from the local-density approximation, is also illuminating.

PACS numbers: 31.25Jf, 31.15 Lc, 31.15 Ar

Keywords: GW

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Paper 75

Vertex corrections in localized and extended systems

Andrew J. Morris1, Martin Stankovski1, Kris T. Delaney2, Patrick Rinke3, P. García-González4 and R.W. Godby1

1Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
2
Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
3Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin-Dahlem, Germany
4Departmento de Física Fundamental, U.N.E.D., Apartado 60141, E-28080 Madrid, Spain

Physical Review B 76 155106 (2007) (9 pages)

Within many-body perturbation theory we apply vertex corrections to various closed-shell atoms and to jellium, using a local approximation for the vertex consistent with starting the many-body perturbation theory from a DFT-LDA Green’s function. The vertex appears in two places – in the screened Coulomb interaction, W, and in the self-energy, Σ – and we obtain a systematic discrimination of these two effects by turning the vertex in Σ on and off. We also make comparisons to standard GW results within the usual random-phase approximation (RPA), which omits the vertex from both. When a vertex is included for closed-shell atoms, both ground-state and excited-state properties demonstrate only limited improvements over standard GW. For jellium we observe marked improvement in the quasiparticle band width when the vertex is included only in W, whereas turning on the vertex in Σ leads to an unphysical quasiparticle dispersion and work function. A simple analysis suggests why implementation of the vertex only in W is a valid way to improve quasiparticle energy calculations, while the vertex in Σ is unphysical, and points the way to development of improved vertices for ab initio electronic structure calculations.

PACS numbers: 71.45.Gm, 31.25.Eb, 31.25.Jf, 71.10.Ca

Keywords: GW

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Paper 76

Ab-initio formulation of the 4-point conductance of interacting electronic systems

P. Bokes1,2, J. Jung3,1 and R.W. Godby1

1Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
2Department of Physics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovičova 3, 841 04 Bratislava, Slovak Republic
3Physics Division, National Center for Theoretical Sciences, P.O. Box 2-131, Hsinchu, Taiwan

Physical Review B 76 125433 (2007) (8 pages)

We derive an expression for the 4-point conductance of a general quantum junction in terms of the density response function. Our formulation allows us to show that the 4-point conductance of an interacting electronic system possessing either a geometrical constriction and/or an opaque barrier becomes identical to the macroscopically measurable 2-point conductance. Within time-dependent density-functional theory the formulation leads to a direct identification of the functional form of the exchange-correlation kernel that is important for the conductance. We demonstrate the practical implementation of our formula for a metal-vacuum-metal interface.

PACS numbers: 73.63.-b, 71.15.Mb, 73.40.Jn, 05.60.Gg

Keywords: Transport

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Paper 77

Comment on ‘Dynamical corrections to the DFT-LDA electron conductance in nanoscale systems

J. Jung1,2,P. Bokes2,3 and R.W. Godby3

1Physics Division, National Center for Theoretical Sciences, P.O. Box 2-131, Hsinchu, Taiwan
2Department of Physics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovičova 3, 841 04 Bratislava, Slovak Republic
3
Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom

Physical Review Letters 98 259701 (2007)

We comment on the treatment of the electronic viscosity in the paper "Dynamical corrections to the DFT-LDA electron conductance in nanoscale systems", Na Sai, Michael Zwolak, Giovanni Vignale and Massimiliano Di Ventra, Phys. Rev. Lett. 94 186810 (2005), using calculations for a model metal-vacuum-metal system.

PACS numbers: 73.63.Nm, 68.37.Ef, 71.15.Mb, 73.40.Jn

Keywords: Transport

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Paper 78

Stroboscopic wavepacket description of non-equilibrium many-electron problems

P. Bokes1,2, F. Corsetti1 and R.W. Godby1

1Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
2Department of Physics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovičova 3, 841 04 Bratislava, Slovak Republic

Physical Review Letters 101 046402 (2008) (4 pages). 

We introduce the construction of a orthogonal wavepacket basis set, using the concept of stroboscopic time propagation, tailored to the efficient description of non-equilibrium extended electronic systems. Thanks to three desirable properties of this basis, significant insight is provided into non-equilibrium processes (both time-dependent and steady-state), and reliable physical estimates of various many-electron quantities such as density, current and spin polarization can be obtained. The use of this novel tool is demonstrated for time-dependent switching-on of the bias in quantum transport, and new results are obtained for current-induced spin accumulation at the edge of a 2D doped semiconductor caused by edge-induced spin-orbit interaction.

PACS numbers: 71.15.-m, 72.10.Bg, 72.25.-b, 73.63.-b

Keywords: Transport DFT

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Paper 79

First-principles conductance of nanoscale junctions from the polarizability of finite systems

Matthieu J. Verstraete1,3, P. Bokes2,3 and R.W. Godby1,3

1Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
2Department of Physics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovičova 3, 841 04 Bratislava, Slovak Republic
3European Theoretical Spectroscopy Facility (ETSF)

Journal of Chemical Physics 130 124715 (2009) (8 pages)

A method for the calculation of the conductance of nanoscale electrical junctions is extended to ab-initio electronic structure methods and applied to realistic models of metallic wires and break-junctions of sodium and gold. The method is systematically controllable and convergeable, and can be straightforwardly extended to include more complex processes and interactions. Important issues about the order in which are taken both the thermodynamic and the static (small field) limits are clarified, and characterized further through comparisons to model systems.

PACS numbers: 73.63.Rt, 71.15.-m

Keywords: Transport GW

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Paper 80

Non-equilibrium electronic structure of interacting single-molecule nanojunctions: vertex corrections and polarization effects for the electron-vibron coupling

L. K. Dash1,2, H. Ness1,2 and R. W. Godby1,2

1Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
2European Theoretical Spectroscopy Facility (ETSF)

Journal of Chemical Physics 132 104113 (2010) (20 pages)

We consider the interaction between electrons and molecular vibrations in the context of electronic transport in nanoscale devices. We present a method based on non-equilibrium Green’s functions to calculate both equilibrium and non-equilibrium electronic properties of a single-molecule junction in the presence of electron-vibron interactions. We apply our method to a model system consisting of a single electronic level coupled to a single vibration mode in the molecule, which is in contact with two electron reservoirs. Higher-order diagrams beyond the usual self-consistent Born approximation (SCBA) are included in the calculations. In this paper we consider the effects of the double-exchange diagram and the diagram in which the vibron propagator is renormalized by one electron-hole bubble. We study in detail the effects of the first- and second-order diagrams on the spectral functions for a large set of parameters and for different transport regimes (resonant and off-resonant cases), both at equilibrium and in the presence of a finite applied bias. We also study the linear response (linear conductance) of the nanojunction for all the different regimes. We find that it is indeed necessary to go beyond the SCBA in order to obtain correct results for a wide range of parameters.

PACS numbers: 71.38.-k, 73.40.Gk, 85.65.+h, 73.63.-b

Keywords: Transport

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