Properties of the superconducting state in a two-band model

TL;DR

This paper uses Eliashberg theory to explore the thermodynamic properties of a two-band s-wave superconductor, highlighting non-universal ratios, effects of coupling anisotropy, impurity scattering, and providing formulas relevant to materials like MgB2.

Contribution

It offers a detailed analysis of two-band superconductivity, including strong coupling effects, impurity impacts, and analytic formulas for anisotropic coupling scenarios.

Findings

Dimensionless ratios are non-universal even in weak coupling.

Strong coupling corrections significantly affect thermodynamic properties.

Impurity scattering influences interband superconductivity behavior.

Abstract

Eliashberg theory is used to investigate the range of thermodynamic properties possible within a two-band model for s-wave superconductivity and to identify signatures of its two-band nature. We emphasize dimensionless BCS ratios (those for the energy gaps, the specific heat jump and the negative of its slope near Tc, the thermodynamic critical field Hc(0), and the normalized slopes of the critical field and the penetration depth near Tc), which are no longer universal even in weak coupling. We also give results for temperature-dependent quantities, such as the penetration depth and the energy gap. Results are presented both for microscopic parameters appropriate to MgB2 and for variations away from these. Strong coupling corrections are identified and found to be significant. Analytic formulas are provided which show the role played by the anisotropy in coupling in some special limits. Particular emphasis is placed on small interband coupling and on the opposite limit of no diagonal coupling. The effect of impurity scattering is considered, particularly for the interband case.