Lifshitz Point in the Phase Diagram of Resonantly Interacting $^6Li$-$^{40}K$ Mixtures

TL;DR

This paper studies a highly imbalanced $^6$Li-$^{40}$K mixture at unitarity, revealing a Lifshitz point indicating a transition towards a supersolid phase, supported by an effective thermodynamic potential aligned with Monte Carlo results.

Contribution

It introduces an effective thermodynamic potential for the mixture, predicting a Lifshitz point and supersolid instability in the phase diagram, which is novel for mass-imbalanced fermionic systems.

Findings

Identification of a Lifshitz point in the phase diagram.

Effective mass of Cooper pairs becomes negative.

Agreement with Monte Carlo results for the normal state.

Abstract

We consider a strongly interacting ${}^{6}$Li-${}^{40}$K mixture, which is imbalanced both in the masses and the densities of the two fermionic species. At present, it is the experimentalist's favorite for reaching the superfluid regime. We construct an effective thermodynamic potential that leads to excellent agreement with Monte Carlo results for the normal state. We use it to determine the universal phase diagram of the mixture in the unitarity limit, where we find, in contrast to the mass-balanced case, the presence of a Lifshitz point. This point is characterized by the effective mass of the Cooper pairs becoming negative, which signals an instability towards a supersolid phase.