Gauge Invariant Linear Response Theories for Ultracold Fermi Gases with Pseudogap

TL;DR

This paper develops gauge invariant linear response theories for ultracold Fermi gases across the BCS-BEC crossover, ensuring consistency with fundamental constraints and addressing challenges in the strongly interacting regime.

Contribution

It constructs gauge invariant density and spin response theories for Fermi gases in the BCS-BEC crossover, especially below T_c, using a $t$-matrix approach aligned with the $G_0G$ formalism.

Findings

Successfully satisfies Ward identities and $Q$-limit Ward identity.

Provides a consistent framework for linear response in strongly interacting Fermi gases.

Addresses gauge invariance issues in the BCS-BEC crossover regime.

Abstract

Recent experimental progresses allow for exploring some important physical quantities of ultracold Fermi gases, such as the compressibility, spin susceptibility, viscosity, optical conductivity and spin diffusivity. Theoretically, these quantities can be evaluated from suitable linear response theories. For BCS superfluid, it has been found that the gauge invariant linear response theories can be fully consistent with some stringent consistency constraints. When the theory is generalized to stronger-than-BCS regime, one may meet serious difficulties to satisfy the gauge invariance conditions. In this paper, we try to construct density and spin linear response theories which are formally gauge invariant for a Fermi gas undergoing BCS-Bose-Einstein Condensation (BEC) crossover, especially below the superfluid transition temperature $T_c$. We adapt a particular $t$-matrix approach which is close to the $G_0G$ formalism to incorporate non-condensed pairing in the normal state. We explicitly show that the fundamental constraints imposed by the Ward identities, $Q$-limit Ward identity are indeed satisfied.