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

TL;DR

This paper investigates how two-dimensional fermionic systems transition from long-range to short-range interactions, analyzing phase stability, collective excitations, and temperature effects to understand Wigner crystallization.

Contribution

It introduces a model with mixed long- and short-range interactions and maps out the phase diagram, highlighting the evolution of Wigner crystallization in this context.

Findings

Phase diagram as a function of density and interaction range

Energy comparison between Wigner crystal and Fermi liquid phases

Analysis of collective modes and finite temperature effects

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.