Superfluid density, Josephson relation and pairing fluctuations in a multi-component fermion superfluid

TL;DR

This paper generalizes the Josephson relation to multi-component fermion superfluids, linking superfluid density to pairing fluctuations and Green functions, with applications demonstrated in lattice models like the Haldane model.

Contribution

It introduces a generalized Josephson relation for multi-component fermion superfluids, connecting superfluid density to pairing fluctuations and Green functions, applicable to multi-band lattice systems.

Findings

Superfluid density expressed via two-particle Green functions.

Simplified Josephson relation when only one gapless mode exists.

Application of the relation to the Haldane model in lattice systems.

Abstract

In this work, a Josephson relation is generalized to a multi-component fermion superfluid. Superfluid density is expressed through a two-particle Green function for pairing channels. When the system has only one gapless collective excitation mode, the Josephson relation is simplified, which is given in terms of the order parameters and the trace of two-particle Green functions. In the presence of inversion symmetry, the superfluid density is directly related to the inverse of pairing fluctuation matrix. The results of the superfluid density in Haldane model show that the generalized Josephson relation can be also applied into a multi-band fermion superfluid in lattice.