Notes on calculating temperature of the superconducting transition: interacting fermi gas and phonon mechanisms in non-adiabatic regime

TL;DR

This paper investigates the mathematical structure of superconducting transition temperature equations in non-adiabatic regimes, focusing on interacting Fermi gases and phonon mechanisms, deriving integral equations free of divergences.

Contribution

It provides a detailed analysis of the equations governing Tc in non-adiabatic conditions, including derivation of divergence-free integral equations in this regime.

Findings

Derived integral equations for Tc in non-adiabatic regimes

Equations contain no divergent terms in the anti-adiabatic limit

Applicable to interacting Fermi gases and phonon-mediated pairing

Abstract

We analyze the mathematical structure of equations for temperature Tc of the superconductivity transition in a gas of interacting Fermi particles or at the phonon-mediated pairing in a metal in case of non-adiabatic conditions, i. e., when the characteristic phonon frequency is comparable or larger than the Fermi energy . The integral equations for Tc are derived in the logarithmical approximation. The equations contain no divergent terms in the anti-adiabatic limit.