Strong-coupling properties of unbalanced Eliashberg superconductors

TL;DR

This paper explores the thermodynamic behavior of unbalanced Eliashberg superconductors where electron-boson coupling differs in various channels, revealing a finite critical coupling with diverging critical temperature.

Contribution

It introduces the concept of unbalanced coupling in Eliashberg theory and predicts a finite critical coupling where the critical temperature diverges while the gap remains finite.

Findings

Critical temperature diverges at a finite coupling strength.

The zero-temperature gap remains finite at the divergence point.

Specific heat, magnetic field, and penetration depth are analyzed.

Abstract

In this paper we investigate the thermodynamical properties of ``unbalanced'' superconductors, namely, systems where the electron-boson coupling $\lambda$ is different in the self-energy and in the Cooper channels. This situation is encountered in a variety of situation, as for instance in d-wave superconductors. Quite interesting is the case where the pairing in the self-energy is smaller than the one in the gap equation. In this case we predict a finite critical value $\lambda_c$ where the superconducting critical temperature $T_c$ diverges but the zero temperature gap is still finite. The specific heat, magnetic critical field and the penetration depth are also evaluated.