Exact-exchange density-functional theory for quasi-two-dimensional electron gases

TL;DR

This paper introduces an exact-exchange density-functional method for quasi-two-dimensional electron gases, revealing potential discontinuities and phase transitions, and extends the theory to finite temperatures to match experimental observations.

Contribution

It provides an analytical exact-exchange potential for a single subband and a numerical approach for multiple subbands, highlighting phenomena not captured by LDA.

Findings

Exact-exchange potential shows discontinuities at subband occupation

First-order phase transition occurs at zero temperature when a subband is filled

Finite-temperature extension matches experimental intersubband spacing data

Abstract

A simple exact-exchange density-functional method for a quasi-two-dimensional electron gas with variable density is presented. An analytical expression for the exact-exchange potential with only one occupied subband is provided, without approximations. When more subbands are occupied the exact-exchange potential is obtained numerically. The theory shows that, in contradiction with LDA, the exact-exchange potential exhibits discontinuities and the system suffers a zero-temperature first-order transition each time a subband is occupied. Results suggesting that the translational symmetry might be spontaneously broken at zero temperature are presented. An extension of the theory to finite temperatures allows to describe a drop in the intersubband spacing in good quantitative agreement with recent experiments.