Superconducting phase fluctuations and gap-filling phenomenology in the underdoped cuprates

We revisit the role of superconducting phase fluctuations in the cuprates as probed by various spectroscopic methods. We assume that the fluctuations of the phase of the d-wave superconducting order parameter are governed solely by a two-dimensional classical XY model and that no amplitude fluctuations are present. We find that much of the "filling-of-the-gap" phenomenology seen in the cuprates is captured by this simple model. At temperatures below the Kosterlitz-Thouless transition, the system behaves as a spatially uniform d-wave superconductor whose gap is proportional to the modulus of the spatial average of the order parameter. Above the KT transition, the vortex-dominated phase exhibits behavior that becomes more normal-like with increasing temperature. Fermi arcs in the spectral function are present near the KT transition. We also examine the effect of spatial inhomogeneity in the classical XY model and consider how the coexistence of superconducting and pseudogap-like regions seen in the cuprates can be reproduced using this model.