Density-functional theory for the crystalline phases of a two-dimensional dipolar Fermi gas

TL;DR

This paper uses density-functional theory to study phase transitions in a two-dimensional dipolar Fermi gas, revealing a sequence from Fermi liquid to stripe and then to Wigner crystal phases.

Contribution

It introduces a density-functional approach that accurately predicts the transition sequence and emphasizes the importance of nonlocal Hartree-Fock contributions.

Findings

Transition from Fermi liquid to stripe phase identified

Transition from stripe to Wigner crystal at higher coupling

Nonlocal Hartree-Fock energy is crucial for instability prediction

Abstract

Density-functional theory is utilized to investigate the zero-temperature transition from a Fermi liquid to an inhomogeneous stripe, or Wigner crystal phase, predicted to occur in a one-component, spin-polarized, two-dimensional dipolar Fermi gas. Correlations are treated semi-exactly within the local-density approximation using an empirical fit to Quantum Monte Carlo data. We find that the inclusion of the nonlocal contribution to the Hartree-Fock energy is crucial for the onset of an instability to an inhomogeneous density distribution. Our density-functional theory supports a transition to both a one-dimensional stripe phase, and a triangular Wigner crystal. However, we find that there is an instability first to the stripe phase, followed by a transition to the Wigner crystal at higher coupling.