Gorkov equations for a pseudogapped high-temperature superconductor

A phenomenological theory of superconductivity based on the two-body Cooperon propagator is presented. This theory takes the form of a modified Gorkov equation for the Green's function and allows one to model the effect of local superconducting correlations and long-range phase fluctuations on the spectral properties of high-temperature superconductors, both above and below T_c. A model is proposed for the Cooperon propagator, which provides a simple physical picture of the pseudogap phenomenon, as well as insights into the doping dependence of the spectral properties. Numerical calculations of the density of states and spectral functions based on this model are also presented, and compared with the experimental tunneling (STM) and photoemission (ARPES) data. It is found, in particular, that the sharpness of the peaks in the density of states is related to the strength and the range of the superconducting correlations and that the apparent pseudogap in STM and ARPES can be different, although the underlying model is the same.