Temperature dependence of the pair coherence and healing lengths for a fermionic superfluid throughout the BCS-BEC crossover

TL;DR

This paper investigates how pair coherence and healing lengths in a fermionic superfluid vary with temperature across the BCS-BEC crossover, providing theoretical insights and connecting with experimental data.

Contribution

It introduces a diagrammatic approach to calculate correlation functions and physical quantities across the BCS-BEC crossover and temperature range, including new insights into the normal phase.

Findings

Pair coherence length decreases with temperature.

Inter-pair correlations develop below a crossover temperature T*.

Fermi surface signatures persist despite pairing correlations.

Abstract

We calculate the pair correlation function and the order parameter correlation function, which probe, respectively, the intra-pair and inter-pair correlations of a Fermi gas with attractive inter-particle interaction, in terms of a diagrammatic approach as a function of coupling throughout the BCS-BEC crossover and of temperature, both in the superfluid and normal phase across the critical temperature $T_{c}$. Several physical quantities are obtained from this calculation, including the pair coherence and healing lengths, the Tan's contact, the crossover temperature $T^{*}$ below which inter-pair correlations begin to build up in the normal phase, and the signature for the disappearance of the underlying Fermi surface which tends to survive in spite of pairing correlations. A connection is also made with recent experimental data on the temperature dependence of the normal coherence length as extracted from the proximity effect measured in high-temperature (cuprate) superconductors.