Superconducting transition temperature: Interacting Fermi gas and phonon mechanisms in the nonadiabatic regime

Abstract

We analyze the mathematical structure of equations for temperature ${T}_{C}$ of the superconductivity transition in a gas of interacting Fermi particles or at the phonon-mediated pairing in a metal in the case of nonadiabatic conditions ${\ensuremath{\omega}}_{0}\ensuremath{\ge}{E}_{F}$, i.e., when the characteristic phonon frequency ${\ensuremath{\omega}}_{0}$ is comparable or larger than the Fermi energy ${E}_{F}$. As the methods of calculating ${T}_{C}$ in common superconductors are not applicable in the nonadiabatic regime, the integral equations for ${T}_{C}$ are derived in the logarithmic approximation. The new equations contain no divergent terms in the antiadiabatic limit. The results can be immediately generalized to anisotropic band superconductors.