Temperature dependence of the specific heat and the penetration depth of anisotropic-gap BCS superconductors for a factorizable pairing potential

TL;DR

This paper derives an explicit formula for the temperature dependence of specific heat and penetration depth in anisotropic-gap BCS superconductors, enabling better fitting of experimental data and understanding of superconducting properties.

Contribution

It introduces a new interpolation formula for specific heat that accounts for gap anisotropy and applies it to various models and experimental data.

Findings

The formula accurately interpolates between low-temperature and T_c behaviors.

It successfully fits experimental data for MgB_2, YBa_2Cu_3O_{7-delta}, and Sr_2RuO_4.

Provides a unified approach for analyzing anisotropic superconductors.

Abstract

An explicit expression for the temperature dependence of the specific heat of clean anisotropic-gap superconductors is derived within the weak-coupling BCS approximation. The specific heat is presented as a functional of the superconducting gap on the Fermi surface. The obtained formula interpolates between the correct low coupling jump at T_c and the low temperature behavior for T<<T_c. For isotropic superconductors the formula gives a relation between the specific heat and the superconducting gap. For anisotropic superconductors, the interpolation formula incorporates averaging of powers of the gap anisotropy function over the Fermi surface and provides a suitable set for fitting model Hamiltonians to experimental data. The work of the interpolation formula is illustrated by (i) the Pokrovsky formula for the specific heat jump, (ii) Gor'kov and Melik-Barkhudarov formulas for the Ginzburg-Landau coefficients, (iii) the Moskalenko two-band formula for the specific heat jump, (iv) the temperature dependence of the specific heat for the two-band model, applicable to MgB_2, (v) the two-dimensional d-wave model, applicable for YBa_2Cu_3O_{7-delta}, and (vi) the Zhitomirsky and Rice triplet p-wave model with horizontal line nodes for Sr_2RuO_4. The temperature dependence of the penetration depth is illustrated by fitting the general theoretical formula to the experimental data for MgB_2, YBa_2Cu_3O_{7-delta}, and the triplet superconductor Sr_2RuO_4.