Density functional theory of the fractional quantum Hall effect

TL;DR

This paper develops a new density functional theory approach for the fractional quantum Hall effect using composite fermion variables, effectively addressing fractional occupation issues and accurately modeling edge density profiles.

Contribution

It introduces a composite fermion-based density functional framework that naturally handles fractional occupations in the quantum Hall regime.

Findings

Successfully models fractional Hall edge density profiles.

Reproduces edge reconstruction phenomena.

Validates approach against expected physical behavior.

Abstract

A conceptual difficulty in formulating the density functional theory of the fractional quantum Hall effect is that while in the standard approach the Kohn-Sham orbitals are either fully occupied or unoccupied, the physics of the fractional quantum Hall effect calls for fractionally occupied Kohn-Sham orbitals. This has necessitated averaging over an ensemble of Slater determinants to obtain meaningful results. We develop an alternative approach in which we express and minimize the grand canonical potential in terms of the composite fermion variables. This provides a natural resolution of the fractional-occupation problem because the fully occupied orbitals of composite fermions automatically correspond to fractionally occupied orbitals of electrons. We demonstrate the quantitative validity of our approach by evaluating the density profile of fractional Hall edge as a function of temperature and the distance from the delta dopant layer and showing that it reproduces edge reconstruction in the expected parameter region.