The BCS Critical Temperature for Potentials with Negative Scattering Length

TL;DR

This paper derives an explicit formula for the critical temperature in the BCS theory for low-density fermionic systems with negative scattering length, extending understanding of superconductivity in such regimes.

Contribution

It provides a rigorous proof of the critical temperature formula for the BCS gap equation with potentials having negative scattering length and no bound states.

Findings

Critical temperature formula derived for low-density limit

Applicable to potentials with negative scattering length

No bound states assumed in the analysis

Abstract

We prove that the critical temperature for the BCS gap equation is given by $T_c = \mu (8/\pi e^{\gamma -2} + o(1)) e^{\pi/(2\sqrt \mu a)}$ in the low density limit $\mu\to 0$. The formula holds for a suitable class of interaction potentials with negative scattering length $a$ in the absence of bound states.