Heat capacity of mesoscopically disordered superconductors with emphasis on MgB2

The temperature dependence of the electronic heat capacity C(T) was calculated for a mesoscopically disordered s-wave superconductor treated as a spatial ensemble of domains with continuously varying superconducting properties. The domains are assumed to have sizes L > xi, where xi is the coherence length. Each domain is characterized by a certain critical temperature T-c0 in the range [0, T-c]. The averaging over a broad superconducting gap distribution leads to proportional to T-2 for low T, whereas the specific heat anomaly at Tc is substantially smeared. For narrow gap distributions there exists an intermediate-T range, where the curve can be well approximated by an exponential Bardeen-Cooper-Schrieffer-like dependence with the effective gap smaller than the weak-coupling value. The results are applicable in the general case of inhomogeneous superconductors including, e.g., electron-doped and hole-doped cuprates. The C(T) data for MgB2, where multiple gaps are observed, are discussed in more detail.