Signatures of pairing and spin-orbit coupling in correlation functions of Fermi gases

TL;DR

This paper derives and analyzes spin and density correlation functions in spin-orbit coupled Fermi superfluids, revealing signatures of Rashba effects and pseudogap phases through new sum rules and correlation behaviors.

Contribution

It introduces new $f$-sum rules for spin correlations and demonstrates how these functions reveal spin-orbit coupling and pseudogap features in Fermi gases.

Findings

Density correlations are insensitive to Rashba effects.

Spin correlations provide signatures of Rashba band structure.

Correlation functions help identify pseudogap presence.

Abstract

We derive expressions for spin and density correlation functions in the (greatly enhanced) pseudogap phase of spin-orbit coupled Fermi superfluids. Density-density correlation functions are found to be relatively insensitive to the presence of these Rashba effects. To arrive at spin-spin correlation functions we derive new $f$-sum rules, valid even in the absence of a spin conservation law. Our spin-spin correlation functions are shown to be fully consistent with these $f$-sum rules. Importantly, they provide a clear signature of the Rashba band-structure and separately help to establish the presence of a pseudogap.