Temperature dependence of specific heat and penetration depth of anisotropic-gap Bardeen-Cooper-Schrieffer superconductors for a factorizable pairing potential

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 Tc and the low-temperature behavior for T⪡Tc. 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 MgB2; (v) the two-dimensional d-wave model, applicable for YBa2Cu3O7−δ; and (vi) the Zhitomirsky and Rice triplet p-wave model with horizontal line nodes for Sr2RuO4. The temperature dependence of the penetration depth is illustrated by fitting the general theoretical formula to the experimental data for MgB2, YBa2Cu3O7−δ, and the triplet superconductor Sr2RuO4.

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