Exact-exchange density functional theory of the integer quantum Hall effect: strict 2D limit

TL;DR

This paper develops a strict 2D exact-exchange density functional theory framework to accurately describe the integer quantum Hall effect, capturing discontinuities at Landau level fillings and improving upon the local-spin-density approximation.

Contribution

It introduces a novel strict-2D exact-exchange formalism within DFT for the IQHE, including magnetic field effects and inter-layer exchange, surpassing traditional LSDA approaches.

Findings

EE energy minimizes with discontinuous derivatives at integer filling factors

EE potential exhibits sharp discontinuities at each integer 

The formalism includes magnetic field effects and inter-layer exchange coupling

Abstract

A strict bidimensional (strict-2D) exact-exchange (EE) formalism within the framework of density-functional theory (DFT) has been developed and applied to the case of an electron gas subjected to a strong perpendicular magnetic field, that drives the system to the regime of the integer quantum Hall effect (IQHE). As the filling of the emerging Landau levels proceeds, two main features results: i) the EE energy minimizes with a discontinuous derivative at every integer filling factor $\nu$; and ii) the EE potential display sharp discontinuities at every integer $\nu$. The present contribution provides a natural improvement as compared with the widely used local-spin-density approximation (LSDA), since the EE energy functional fully contains the effect of the magnetic field, and includes an inter-layer exchange coupling for multilayer systems. As a consistency test, the LSDA is derived as the leading term of a low-field expansion of the EE energy and potential.