Specific heat and thermal conductivity in the mixed state of MgB2

TL;DR

This paper models the specific heat and thermal conductivity in MgB2's mixed state, revealing near-linear specific heat behavior and a rapid decrease in phononic thermal conductivity with increasing magnetic field, aligning with experimental data.

Contribution

It provides a detailed theoretical calculation of thermal properties in MgB2's mixed state, incorporating effects of supercurrent flow and vortex scattering, and explains the field dependence of thermal conductivities.

Findings

C(H) is nearly linear near H_{c2}

kappa_e(H) shows upward curvature near H_{c2}

kappa_{ph}(H) decreases rapidly at small fields

Abstract

The specific heat C and the electronic and phononic thermal conductivities kappa_e and kappa_{ph} are calculated in the mixed state for magnetic fields H near H_{c2}. The effects of supercurrent flow and Andreev scattering of the Abrikosov vortex lattice on the quasiparticles are taken into account. The resulting function C(H) is nearly linear while kappa_e(H) exhibits an upward curvature near H_{c2}. The slopes decrease with impurity scattering which improves the agreement with the data on MgB_2. The ratio of phonon relaxation times tau_n/tau_s = g(omega_0,H) for phonon energy omega_0, which is nearly a step function at omega_0 = 2Delta for the BCS state, is smeared out and tends to one for increasing H. This leads to a rapid reduction of kappa_{ph}(H) in MgB_2 for relatively small fields due to the rapid suppression of the smaller energy gap.