The BCS Energy Gap at High Density

TL;DR

This paper derives an asymptotic formula for the BCS energy gap at high density, revealing its dependence on interaction potential and establishing the universal ratio between the energy gap and critical temperature.

Contribution

It provides a new asymptotic formula for the BCS energy gap at high densities and proves the universality of its ratio to the critical temperature.

Findings

Derived an asymptotic formula for the energy gap.

Proved the universality of the gap-to-temperature ratio.

Connected the energy gap behavior with the interaction potential.

Abstract

We study the BCS energy gap $\Xi$ in the high-density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential $V$ on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3 (2022)) on the critical temperature $T_c$ at high densities, we prove the universality of the ratio of the energy gap and the critical temperature.