Specific Heat Discontinuity in Impure Two-Band Superconductors

TL;DR

This paper calculates the specific heat discontinuity and Ginzburg-Landau coefficients in disordered two-band superconductors, revealing how disorder affects thermodynamic properties and explaining experimental observations in MgB2.

Contribution

It provides explicit formulas for thermodynamic quantities in disordered two-band superconductors, including the effects of impurity scattering, and explains sample dependence in MgB2.

Findings

Specific heat discontinuity decreases with disorder.

The ratio of discontinuity to normal specific heat increases with disorder.

Explicit solutions for thermodynamic values at any scattering rate.

Abstract

The Ginzburg-Landau coefficients, and the jump of the specific heat are calculated for a disordered two-band superconductor. We start with the analysis of a more general case arbitrary anisotropy. While the specific heat discontinuity at the critical temperature T_c decreases with increasing disorder, its ratio to the normal state specific heat at T_c increases and slowly converges to the isotropic value. For a strong disorder the deviation from the isotropic value is proportional to the elastic electron scattering time. In the case of a two-band superconductor we apply a simplified model of the interaction independent on momentum within a band. In the framework of this model all thermodynamic values can be found explicitly at any value of the scattering rate. This solution explains the sample dependence of the specific heat discontinuity in MgB_2 and the influence of the disorder on the critical temperature.