Hartree-Fock Theory of a Current-Carrying Electron Gas

TL;DR

This paper investigates the limitations of using equilibrium-based local density approximation in non-equilibrium electron gases, analyzing how current influences exchange energy and potential within a Hartree-Fock framework.

Contribution

It introduces a Hartree-Fock approach to study non-equilibrium electron gases, highlighting the current-dependent behavior of single-particle spectra and exchange holes.

Findings

Single-particle spectrum depends significantly on current.

Exchange hole shows notable current dependence.

Exchange energy and local exchange potential are nearly unaffected by current.

Abstract

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 h omogeneous 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.