Liquid crystal phases of ultracold dipolar fermions on a lattice

TL;DR

This paper investigates the emergence of liquid crystal phases, such as nematic and smectic, in ultracold dipolar fermions on a 2D lattice, revealing phase transitions driven by interaction strength and density.

Contribution

It provides a combined theoretical analysis using Hartree-Fock and linear response methods to map the phase diagram and characterize the liquid crystal phases in dipolar fermion systems.

Findings

Identification of nematic and smectic phases with broken rotational symmetry.

Observation of a first-order transition from nematic to smectic phase.

Zero sound mode is strongly Landau damped, indicating no well-defined collective excitations.

Abstract

Motivated by the search for quantum liquid crystal phases in a gas of ultracold atoms and molecules, we study the density wave and nematic instabilities of dipolar fermions on the two-dimensional square lattice (in the $x-y$ plane) with dipoles pointing to the $z$ direction. We determine the phase diagram using two complimentary methods, the Hatree-Fock mean field theory and the linear response analysis of compressibility. Both give consistent results. In addition to the staggered ($\pi$, $\pi$) density wave, over a finite range of densities and hopping parameters, the ground state of the system first becomes nematic and then smectic, when the dipolar interaction strength is increased. Both phases are characterized by the same broken four-fold (C$_4$) rotational symmetry. The difference is that the nematic phase has a closed Fermi surface but the smectic does not. The transition from the nematic to the smectic phase is associated with a jump in the nematic order parameter. This jump is closely related to the van Hove singularities. We derive the kinetic equation for collective excitations in the normal isotropic phase and find that the zero sound mode is strongly Landau damped and thus is not a well defined excitation. Experimental implications of our results are discussed.