The BCS Critical Temperature at High Density

TL;DR

This paper derives an asymptotic formula for the BCS critical temperature at high density, confirming previous predictions and identifying conditions for superconducting domes based on the interaction potential.

Contribution

It provides a rigorous derivation of the high-density behavior of the BCS critical temperature and clarifies the conditions for superconducting domes in BCS theory.

Findings

Confirmed the high-density behavior of $T_c$ proposed by Langmann et al.

Derived an asymptotic formula for $T_c$ depending on the interaction potential.

Identified conditions under which superconducting domes occur.

Abstract

We investigate the BCS critical temperature $T_c$ in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential $V$ on the Fermi-surface. Our results include a rigorous confirmation for the behavior of $T_c$ at high densities proposed by Langmann, Triola, and Balatsky (Phys. Rev. Lett. 122, 2019) and identify precise conditions under which superconducting domes arise in BCS theory.