Exposing the quantum geometry of spin-orbit coupled Fermi superfluids

TL;DR

This paper uncovers how the quantum metric of helicity bands influences superfluid density in spin-orbit coupled Fermi superfluids, revealing a significant geometrical contribution across different coupling regimes.

Contribution

It demonstrates that inter-helicity contributions to superfluid density are directly linked to the quantum metric, a novel insight into the geometry of spin-orbit coupled superfluids.

Findings

Inter-helicity contribution accounts for up to 25% of superfluid density.

Quantum metric directly influences superfluid properties.

Effects are observable in cold Fermi gases.

Abstract

The coupling between a quantum particle's intrinsic angular momentum and its center-of-mass motion gives rise to the so-called helicity states that are characterized by the projection of the spin onto the direction of momentum. In this paper, by unfolding the superfluid-density tensor into its intra-helicity and inter-helicity components, we reveal that the latter contribution is directly linked with the total quantum metric of the helicity bands. We consider both Rashba and Weyl spin-orbit couplings across the BCS-BEC crossover, and show that the geometrical inter-helicity contribution is responsible for up to a quarter of the total superfluid density. We believe this is one of those elusive effects that may be measured within the highly-tunable realm of cold Fermi gases.