Effects of Quenched Random Gap Inhomogeneities on the Specific Heat of a Model High-$T_c$ Superconductor

In many cuprate superconductors, scanning tunneling microscopy experiments show that the energy gap has substantial quenched random spatial variations. We have calculated how such gap variations affect the specific heat $C_V$ in a model for the most anisotropic of these materials. The model is based on a Ginzburg-Landau free energy functional in which position- dependent coefficients are used to model quenched inhomogeneity. Using Monte Carlo simulations, we evaluate $C_V$ for different disorder strengths. Near optimal doping, we find that quenched gap disorder substantially broadens the specific heat anomaly near the phase ordering transition $T_c$, compared to that due to thermal fluctuations alone. But for strongly underdoped samples, in which $T_c$ is greatly separated from the pseudogap temperature $T_{c0}$, disorder only slightly increases the broadening beyond the already substantial amount due to thermal fluctuations. We compare these results to recent experiments.