Static and dynamical properties of a two-dimensional Wigner crystal of rotating dipolar Fermi gases

TL;DR

This paper investigates the properties and stability of a two-dimensional Wigner crystal formed by rotating dipolar Fermi gases, revealing how correlation energies and elastic moduli vary with filling factors and suggesting the existence of a new liquid state at half filling.

Contribution

It introduces a Hartree-Fock based analysis of correlation energies and elastic properties of dipolar Wigner crystals, highlighting their nonmonotonic shear moduli and stability regimes.

Findings

Correlation energy differs for particle and hole crystals depending on filling factor.

Shear moduli exhibit nonmonotonic behavior as a function of filling factor.

Wigner crystal stability varies with filling factor, indicating a possible new liquid state at v=1/2.

Abstract

Using an ansatz wave function for the ground state of rotating two-dimensional dipolar fermions, which occupy only partially the lowest Landau level, we study the correlation energy and elastic properties of the Wigner crystal of rotating dipolar Fermi gases. From a simple Hartree-Fock approach, we show that the correlation energy of a particle crystal is lower and higher than the correlation energy of a hole crystal for filling factors v<1/2 and v>1/2, respectively. Furthermore we find that the shear moduli of these dipolar crystals have a nonmonotonic behavior as a function of the filling factor. We also examine the stability of a Wigner crystal. The Wigner crystal with the sample width being zero is locally stable for 0< v <1/2, while the corresponding hole crystal is locally stable for 1/2< v <1. Due to the WC being unstable around v=1/2, we also conclude that a new liquid state, not a quantum Hall state, can exist at v=1/2.