Crystalline solutions of the Kohn-Sham equations in the fractional quantum Hall regime

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 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.