Two-band theory of specific heat and thermal conductivity in the mixed state of MgB_2

Abstract

We solve the coupled gap equations for the $σ$- and $π$-bands of MgB$_2$ in the vortex state and calculate the resulting field dependencies of the specific heat coefficient $γ$ and the thermal conductivity $κ$. The crucial parameters of the theory are the interband pairing interaction $λ_{πσ}$ and the ratio $s=ξ_σ/ξ_π$ of the coherence lengths. For reasonably small $λ_{πσ}$ and s, the small gap $Δ_π$ decreases with increasing magnetic field $H$ much faster than the large gap $Δ_σ $. This gives rise to the observed rapid increase of $γ_π$ and $κ_π$ for small fields while $γ_σ$ and $κ_σ$ exhibit conventional field dependencies. Inclusion of intraband impurity scattering yields fairly good agreement with experiments for applied fields along the c axis.