Density ordering instabilities of quasi-two-dimensional fermionic polar molecules in single-layer and multi-layer configurations: exact treatment of exchange interactions

TL;DR

This paper investigates density ordering instabilities in quasi-two-dimensional fermionic polar molecules, incorporating exchange interactions exactly, revealing how these interactions influence phase diagrams and instability thresholds in single and multi-layer systems.

Contribution

It provides an exact treatment of exchange interactions using the Bethe-Salpeter equation, improving upon RPA approximations and revealing their stabilizing effect on the normal liquid phase.

Findings

In-plane density wave instability occurs before out-of-plane instability.

Unstable wave-vector is about twice the Fermi wave-vector and varies with density and interaction.

Exchange interactions increase the critical interaction strength for density-wave instability.

Abstract

We study the in-plane and out-of-plane density ordering instabilities of quasi-two-dimensional fermionic polar molecules in single-layer and multi-layer configurations. We locate the soft modes by evaluating linear response functions within the conserving time-dependent Hartree-Fock (TDHF). The short-range exchange effects are taken into account by solving the Bethe-Salpeter integral equation numerically. An instability phase diagram is calculated for both single-layer and multi-layer systems and the unstable wave-vector is indicated. In all cases, the in-plane density wave instability is found to precede the out-of-plane instability. The unstable wave-vector is found to be approximately twice the Fermi wave-vector of one of the subbands at a time and can change discontinuously as a function of density and dipolar interaction strength. In multi-layer configurations, we find a large enhancement of density wave instability driven by dilute quasiparticles in the first excited subband. Finally, we provide a simple qualitative description of the phase diagrams using a RPA-like approach. Compared to previous works done within the RPA approximation, we find that inclusion of exchange interactions stabilize the normal liquid phase further and increase the critical dipolar interaction strength corresponding to the onset of density-wave instability by over a factor of two.