Heat capacity of mesoscopically inhomogeneous superconductors:: theory and applications to MgB2

Electronic specific heat C as a function of temperature T was calculated for a mesoscopically disordered s-wave superconductor treated as a spatial ensemble of domains with continuously varying superconducting properties. Domains are supposed to have sizes L > xi, where xi is the coherence length. Specific calculations were performed for an exponential and Gaussian distributions of domain critical temperatures T-c0's. It is shown that the spatially averaged <C(T)> is proportional to T-2 for low T, whereas the anomaly at T-c is substantially smeared even for small dispersions. For narrow gap distributions there exists an intermediate T range, where the curve (C(T)) can be relatively well approximated by an exponential Bardeen-Cooper-Schrieffer-like dependence with the 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 previously seen in tunnel, point-contact, photoemission and Raman spectra. The observed anomalously low ratio Delta(0)/T-c, where Delta(0) is the superconducting energy gap at T = 0, can be also understood in the framework of our theory. After an analysis of the available experimental evidence a conclusion is made that the multiple-gap behavior of superconducting MgB2 is due to the spatial intrinsic non-homogeneities. Possible origins of the latter are discussed. (C) 2004 Published by Elsevier B.V.