Pair phase fluctuations and the pseudogap

The single-particle density of states and the tunneling conductance are studied for a two-dimensional BCS-like Hamiltonian with a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-gap and phase fluctuations. The latter are treated by a classical Monte Carlo simulation of an $\mathrm{XY}$ model. Comparison of our results with recent scanning tunneling spectra of Bi-based high-${T}_{c}$ cuprates supports the idea that the pseudogap behavior observed in these experiments can be understood as arising from phase fluctuations of a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing gap whose amplitude forms on an energy scale set by ${T}_{c}^{\mathrm{MF}}$ well above the actual superconducting transition.