Kohn-Sham theory of rotating dipolar Fermi gas in two dimensions

TL;DR

This paper models a rotating two-dimensional dipolar Fermi gas using Kohn-Sham equations, revealing vortex formation, symmetry breaking, and Wigner clustering as the system approaches quantum Hall regimes.

Contribution

It provides the first ab initio Kohn-Sham analysis of a rotating dipolar Fermi gas, highlighting vortex and Wigner cluster formations in a strongly interacting quantum system.

Findings

Vortex array develops near the lowest Landau level

System boundaries become square-shaped during vortex formation

At low filling factors, fermions form Wigner clusters

Abstract

A two-dimensional dipolar Fermi gas in harmonic trap under rotation is studied by solving "ab initio" Kohn-Sham equations. The physical parameters used match those of ultracold gas of fermionic $^{23}Na^{40}K$ molecules, a prototype system of strongly interacting dipolar quantum matter, which has been created very recently. We find that, as the critical rotational frequency is approached and the system collapses into the lowest Landau level, an array of tightly packed quantum vortices develops, in spite of the non-superfluid character of the system. In this state the system looses axial symmetry, and the fermionic cloud boundaries assume an almost perfect square shape. At higher values of the filling factor the vortex lattice disappears, while the system still exhibits square-shaped boundaries. At lower values of the filling factor the fermions become instead localized in a "Wigner cluster" structure.