Multi-band superconductors have enhanced critical temperatures

TL;DR

This paper proves that inter-band coupling in multi-band superconductors always raises the critical temperature, with the increase depending linearly or quadratically on the coupling strength based on the band structure.

Contribution

It introduces a multi-band BCS functional and rigorously shows how inter-band interactions influence the critical temperature.

Findings

Inter-band coupling always increases the critical temperature.

The increase is linear with coupling strength for multiple equally strong bands.

The increase is quadratic if only one dominant band exists.

Abstract

We introduce a multi-band BCS free energy functional and prove that for a multi-band superconductor the effect of inter-band coupling can only increase the critical temperature, irrespective of its attractive or repulsive nature and its strength. Further, for weak coupling and weaker inter-band coupling, we prove that the dependence of the increase in critical temperature on the inter-band coupling is (1) linear, if there are two or more equally strongly superconducting bands, or (2) quadratic, if there is only one dominating band.