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

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.