Inhomogeneity, Fluctuations, and Gap Filling in Disordered Overdoped Cuprates

Recent experiments have challenged the notion that overdoped cuprates neatly approach the Landau-BCS paradigm at large hole doping.  We show, via mean-field Bogoliubov-de Gennes (BdG) calculations, that key features of the observed low-T tunneling spectra in Bi-2212 and Bi-2201 are reproduced when the pairing interaction is strongly inhomogeneous on nanometer length scales.  Most notably, the low-T spectra are highly inhomogeneous and exhibit a low-energy spectral shoulder with broad coherence peaks, as seen in tunneling experiments.  However, as T is raised towards T_c, the calculated spectral gap becomes homogeneous,  in contrast to experiments.  We then discuss whether the discrepancies can be explained by thermal order-parameter fluctuations. In this case, time-dependent Ginzburg-Landau (TDGL) calculations show that the superconducting transition to the normal state occurs when global phase coherence is lost at a broadened Berezinski-Kosterlitz-Thouless (BKT) transition.  Because of the inhomogeneous pairing interaction, however, robust phase-coherent superconducting islands persist well above T_BKT.  We use the order parameters generated by the TDGL simulations to obtain fluctuation-averaged densities of states.  We find that the spectral gaps fill, rather than close, with increasing T and that small-gap regions are more strongly affected by fluctuations than large-gap regions.  Consequently, the local spectrum remains inhomogeneous at T_c: the local density of states is predominantly that of the normal state, but with isolated superconducting islands characterized by a spectral pseudogap.