The Compressibility in Strongly Correlated Superconductors and Superfluids: From BCS to BEC

TL;DR

This paper provides a theoretical analysis of the compressibility in strongly correlated superfluids and superconductors, emphasizing thermodynamic approaches and their agreement with experiments and simulations.

Contribution

It introduces a thermodynamic method for calculating compressibility that satisfies sum rules and gauge invariance, offering improved reliability over correlation function schemes.

Findings

Thermodynamic calculations of $ppa$ show semi-quantitative agreement with experiments.

The approach satisfies sum rules and gauge invariance constraints.

Results align with quantum Monte Carlo simulations.

Abstract

We present a theoretical study of the compressibility, $\kappa$, in a Fermi gas with attractive contact interactions, providing predictions for the strongly-attractive regime and the superfluid phase. Our work emphasizes the compressibility sum rule and gauge invariance as constraints on $\kappa$ and we show how within a particular $t$-matrix approach, these can be satisfied in the normal phase when no approximations are made. For tractability, approximations must be introduced, and it is believed that thermodynamical approaches to $\kappa$ are more reliable, than correlation function based schemes. Contrasting with other studies in the literature, we present thermodynamic calculations of $\kappa$; these yield semi-quantitative agreement with experiment and provide physical insight into similar results obtained via quantum Monte Carlo simulations.