Heat capacity of mesoscopically disordered superconductors: implications for MgB₂

Abstract

The electronic specific heat C as a function of temperature T is calculated for a mesoscopically disordered s-wave superconductor treated as a spatial ensemble of domains with continuously varying superconducting properties. Each domain is characterized by a certain critical temperature Tc0 in the range [0,Tc] and is supposed to have a size L > x, where x is the coherence length. Specific calculations are performed for exponential and Gaussian distributions of Tc₀. For low T, the spatially averaged ‹C(T)› is proportional to T², whereas the anomaly at Tc is substantially smeared even for small dispersions. For narrow gap distributions there exists an intermediate T range, where the curve ‹C(T)› can be well approximated by an exponential Bardeen-Cooper-Schrieffer-like dependence with an effective gap smaller than the weak-coupling value. The results obtained successfully reproduce the salient features of the C(T) data for MgB₂, where a wide superconducting gap distribution has been observed previously in the tunneling, point-contact, photoemission and Raman spectra. The conclusion is reached that the multiple-gap behavior of superconducting MgB₂ is due to the spatial distribution of dissimilar domains. Intrinsic nonstoichiometry of the compound or possible electronic phase separation may be the origin of the mesoscopic inhomogeneities. The same model describes the low-T heat capacity of cuprates, although the sources of inhomogeneity are different from those in MgB₂.