Quasiclassical Theory for Thermodynamic Properties of the Two-Band Superconductor MgB$_2$ under Magnetic Fields

TL;DR

This paper develops an approximate quasiclassical model to describe the thermodynamic properties of MgB$_2$ under magnetic fields, fitting key parameters to experimental data and analyzing anisotropic effects in its two-band superconductor behavior.

Contribution

It introduces an analytic quasiclassical approach with fitted parameters to accurately model MgB$_2$'s thermodynamics under magnetic fields, capturing anisotropic properties and band velocity effects.

Findings

Reproduces temperature and field dependence of thermodynamic quantities.

Shows velocity ratio influences low-field ZEDOS and energy gaps.

Demonstrates weak H and T dependence of coherence length anisotropy in bands.

Abstract

Consistent account is provided of strongly anisotropic properties in thermodynamics of MgB$_2$ under magnetic field $H$ using approximate analytic solution in the quasiclassical formalism. With the strength of the pairing interactions and the Fermi velocities of two bands as fitting parameters, it is possible to reproduce in wide regions of the phase diagram the $H$- and temperature dependences of relevant quantities such as the zero-energy density of states (ZEDOS), two energy gaps, the specific heat and the $H_{c2}$ anisotropy. It is demonstrated that the velocity ratio of two bands affects considerably the low-field behavior of the ZEDOS and energy gaps. The ratio also affects the high-temperature behavior of the $H_{c2}$ anisotropy. The anisotropy of the coherence length in the $\sigma$ band depends weakly on $H$ and $T$, whereas the coherence length in the $\pi$ band remains isotropic even in the presence of the inter-band coupling.