Wigner Crystallization in Two Dimensions: Evolution from Long- to Short-Ranged Forces

Abstract

We study fermions in two dimensions interacting via a long-ranged 1/r potential for small particle separations and a short-ranged 1/r^3 potential for larger separations in comparison to a length scale \xi. We compute the energy of the Wigner crystal and of the homogeneous Fermi liquid phases using a variational approach, and determined the phase diagram as a function of density and \xi at zero temperature. We discuss the collective modes in the Fermi liquid phase, finite temperature effects on the phase diagram, and possible experimental realizations of this model.