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 were assumed to have sizes L > ξ, where ξ was the coherence length. Each domain was characterized by a certain critical temperature TC0 in the range [0, TC]. Averaging over a broad superconducting gap distribution led to <C(T)>  T2 for low T, whereas the specific heat anomaly at TC was substantially smeared. For narrow gap distributions there exists an intermediate-T range, where the curve <C(T)> could be well approximated by an exponential Bardeen–Cooper–Schrieffer-like dependence with the effective gap smaller than the weak-coupling value. The results were applicable in the general case of inhomogeneous superconductors. The C(T) data for MgB2, where multiple gaps were observed, were considered in more detail.

Heat Capacity of Mesoscopically Disordered Superconductors with Emphasis on MgB2. A.M.Gabovich, M.S.Li, M.Pekala, H.Szymczak, A.I.Voitenko: Journal of Physics - Condensed Matter, 2002, 14, 9621-9