Quantum Melting of a Wigner crystal of Rotating Dipolar Fermions in the Lowest Landau Level

TL;DR

This paper investigates the stability and properties of a Wigner crystal formed by rotating dipolar fermions in the lowest Landau level, revealing a narrower stable regime than previously estimated.

Contribution

It introduces a new analysis of the stability of dipolar fermion Wigner crystals using an ansatz wave function and Lindeman's criterion, refining prior stability estimates.

Findings

Particle crystal stable below filling factor 1/15

Hole crystal stable between filling factors 14/15 and 1

Stable regime narrower than previous studies

Abstract

We have investigated the behavior and stability of a Wigner crystal of rotating dipolar fermions in two dimensions. 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, elastic moduli and collective modes of Wigner crystals in the lowest Landau level. We then calculate the mean square of the displacement vector of Wigner crystals. The critical filling factor, below which the crystalline state is expected, is evaluated at absolute zero by use of the Lindeman's criterion. We find that the particle (hole) crystal is locally stable for filling factor is less than 1/15 (between filling factors 14/15 and 1), where the stable regime of the crystal is much narrower than the result from Baranov, Fehrmann and Lewenstein, [Phys. Rev. Lett. 100, 200402 (2008)].