Crystalline Solutions of Kohn-Sham Equations in the Fractional Quantum Hall Regime

TL;DR

This paper explores the formation of crystalline phases in the fractional quantum Hall regime using a Kohn-Sham density functional approach, highlighting how exchange correlation strength influences crystal stabilization.

Contribution

It introduces a detailed analysis of crystalline solutions within a Kohn-Sham framework for the fractional quantum Hall effect, emphasizing the role of exchange correlation potential strength.

Findings

A crystal phase is stabilized at high exchange correlation strength.

The behavior of self-consistent solutions varies with the exchange potential.

Properties of the crystal phase are characterized in detail.

Abstract

A Kohn-Sham density functional approach has recently been developed for the fractional quantum Hall effect, which maps the strongly interacting electrons into a system of weakly interacting composite fermions subject to an exchange correlation potential as well as a density dependent gauge field that mimics the "flux quanta" bound to composite fermions. To get a feel for the role of various terms, we study the behavior of the self-consistent solution as a function of the strength of the exchange correlation potential, which is varied through an {\it ad hoc} multiplicative factor. We find that a crystal phase is stabilized when the exchange correlation interaction is sufficiently strong relative to the composite-fermion cyclotron energy. Various properties of this crystal are examined.