Electronic Density of States of a Superconductor with a Spatially Varying Gap and Phase Fluctuations: A Monte Carlo Simulation

Recent experiments have shown that the superconducting energy gap in some high-T$_c$ superconductors is spatially inhomogeneous. Motivated by these experiments, and using exact diagonalization of a model d-wave Hamiltonian (T. Eckl et al. PRB 66 140510), combined with Monte Carlo simulations of a Ginzburg-Landau free energy functional, we have calculated the electronic density of states $n(E)$ of a model high-T$_c$ superconductor with an inhomogeneous gap. The free energy functional incorporates both phase and amplitude fluctuations together with quenched disorder. It leads to a superconducting transition temperature $T_c$ well below the pseudogap temperature $T_{c0}$, and has a spatially varying gap at very low $T$, both consistent with experiments in underdoped Bi2212. Our calculated $n(E)$ shows coherence peaks for $T < T_c$, which disappear for $T > T_c$. We will also present calculated results for both the global and local $n(E)$ as a function of temperature and disorder.