Specific heat and thermal conductivity in the vortex state of the two-gap superconductor MgB_2

TL;DR

This paper models the specific heat and thermal conductivity in the vortex state of MgB_2, a two-gap superconductor, considering supercurrent flow, Andreev scattering, and impurity effects, and compares results with experiments.

Contribution

It provides a comprehensive calculation of thermodynamic and transport properties in MgB_2's vortex state, including impurity effects and vertex corrections, which were not fully addressed before.

Findings

Gamma_s(H)/gamma_n becomes linear above 0.1 H/H_{c2}

Impurity scattering effects are reduced by vertex corrections

Rapid decrease in phononic thermal conductivity near H_{c2}

Abstract

The specific heat coefficient gamma_s(H) and the electronic thermal conductivity kappa_{es}(H) are calculated for Abrikosov's vortex lattice by taking into account the effects of supercurrent flow and Andreev scattering. First we solve the gap equation for the entire range of magnetic fields. We take into account vertex corrections due to impurity scattering calculated in the Born approximation. The function gamma_s(H)/gamma_n increases from zero and becomes approximately linear above H/H_{c2} \sim 0.1. The dependence on impurity scattering is substantially reduced by the vertex corrections. The upward curvature of kappa_{es}(H)/kappa_{en}, which is caused by decreasing Andreev scattering for increasing field, is reduced for increasing impurity scattering. We also calculate the temperature dependence of the scattering rates 1/tau_{ps}(H) of a phonon and 1/tau_{es}(H) of a quasiparticle due to quasiparticle and phonon scattering, respectively. At low temperatures the ratio tau_{pn}/tau_{ps}(H) increases rapidly to one as H tends to H_{c2} which yields a rapid drop in the phononic thermal conductivity kappa_{ph}. Our results are in qualitative agreement with the experiments on the two-gap superconductor MgB_2.