Superfluid density and Berezinskii-Kosterlitz-Thouless transition of a spin-orbit coupled Fulde-Ferrell superfluid

TL;DR

This paper explores the superfluid density and BKT transition in a 2D spin-orbit coupled Fermi gas, revealing anisotropic properties and phase transitions with potential experimental observability.

Contribution

It provides a theoretical analysis of the superfluid density tensor and BKT transition temperatures in various exotic Fulde-Ferrell superfluid phases with spin-orbit coupling.

Findings

Superfluid density tensor becomes anisotropic due to FF pairing.

Discontinuous jump in superfluid density at phase transition at zero temperature.

Predicted BKT temperatures are around 10% of the Fermi temperature, accessible experimentally.

Abstract

We theoretically investigate the superfluid density and Berezinskii-Kosterlitz-Thouless (BKT) transition of a two-dimensional Rashba spin-orbit coupled atomic Fermi gas with both in-plane and out-of-plane Zeeman fields. It was recently predicted that, by tuning the two Zeeman fields, the system may exhibit different exotic Fulde-Ferrell (FF) superfluid phases, including the gapped FF, gapless FF, gapless topological FF and gapped topological FF states. Due to the FF paring, we show that the superfluid density (tensor) of the system becomes anisotropic. When an in-plane Zeeman field is applied along the \textit{x}-direction, the tensor component along the \textit{y}-direction $n_{s,yy}$ is generally larger than $n_{s,xx}$ in most parameter space. At zero temperature, there is always a discontinuity jump in $n_{s,xx}$ as the system evolves from a gapped FF into a gapless FF state. With increasing temperature, such a jump is gradually washed out. The critical BKT temperature has been calculated as functions of the spin-orbit coupling strength, interatomic interaction strength, in-plane and out-of-plane Zeeman fields. We predict that the novel FF superfluid phases have a significant critical BKT temperature, typically at the order of $0.1T_{F}$, where $T_{F}$ is the Fermi degenerate temperature. Therefore, their observation is within the reach of current experimental techniques in cold-atom laboratories.