Hartree-Fock theory of a current-carrying two-dimensional homogeneous electron gas

H. Mera, P. Bokes, and R. W. Godby
Phys. Rev. B 76, 125319 – Published 24 September 2007

Abstract

State-of-the-art simulation tools for nonequilibrium quantum transport systems typically take the current-carrier occupations to be described in terms of equilibrium distribution functions characterized by two different electrochemical potentials, while for the description of electronic exchange and correlation, the local density approximation (LDA) to density functional theory 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 nonequilibrium 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 since it is not captured by the commonly used functionals. 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.

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  • Received 8 September 2006

DOI:https://doi.org/10.1103/PhysRevB.76.125319

©2007 American Physical Society

Authors & Affiliations

H. Mera1,2, P. Bokes1,3, and R. W. Godby1

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

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Issue

Vol. 76, Iss. 12 — 15 September 2007

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