Thermodynamic transitions in inhomogeneous d -wave superconductors

We study the spectral and thermodynamic properties of inhomogeneous d -wave superconductors within a model where the inhomogeneity originates from atomic-scale pair disorder. This assumption has been shown to be consistent with the small charge and large gap modulations observed by scanning tunneling spectroscopy on Bi₂Sr₂CaCu₂O_8+x . Here we calculate the specific heat within the same model, and show that it gives a transition width comparable to those found in experiments on this material. This suggests that nanoscale inhomogeneity is a bulk property of the Bi₂Sr₂CaCu₂O_8+x materials.