Superfluid density and specific heat within a self-consistent scheme for a two-band superconductor

Abstract

The two gaps in a two-band clean $s$-wave superconductor are evaluated self-consistently within the quasiclassical Eilenberger weak-coupling formalism with two in-band and one interband pairing potentials. Superfluid density, free energy, and specific heat are given in the form amenable for fitting the experimental data. Well-known two-band ${\text{MgB}}_{2}$ and ${\text{V}}_{3}\text{Si}$ superconductors are used to test the developed approach. The pairing potentials obtained from the fit of the superfluid density data in ${\text{MgB}}_{2}$ crystal were used to calculate temperature-dependent specific heat $C(T)$. The calculated $C(T)$ compares well with the experimental data. Advantages and validity of this, which we call the ``$\ensuremath{\gamma}$ model,'' are discussed and compared with the commonly used empirical (and not self-consistent) ``$\ensuremath{\alpha}$ model.'' Correlation between the sign of the interband coupling and the signs of the two order parameters is discussed. Suppression of the critical temperature by the interband scattering is evaluated and shown to be severe for the interband repulsion as compared to the attraction. The data on a strong ${T}_{c}$ suppression in ${\text{MgB}}_{2}$ crystals by impurities suggest that the order parameters on two effective bands of this material may have opposite signs, i.e., may have the ${s}_{\ifmmode\pm\else\textpm\fi{}}$ structure similar to proposals for iron-based pnictide superconductors.