Quasiparticle Properties of the Superconducting State of the Two   Dimensional Hubbard Model
  Cluster dynamical mean field methods are used to calculate the normal and anomalous components of the electron self energy of the two dimensional Hubbard model. From these the evolution of the superconducting gap and the momentum dependent photoemission and inverse photoemission spectra across the phase diagram are determined. In the pseudogap regime, decreasing the temperature into the superconducting state leads to a decrease in the energy gap and the formation of a `peak-dip-hump' structure in the electronic density of states. The peak feature disperses very weakly. The calculated spectral functions are in good qualitative agreement with published data. The mathematical origin of the behavior is found to be the effect of the superconductivity on the pole structure giving rise to the normal state pseudogap. In particular the "hump" feature is found to arise from a zero crossing of the real part of the electron self energy rather than from an onset of scattering. The effect of superconductivity on the zone diagonal spectra is presented. 
Emanuel Gull and Andrew J. Millis
cond-mat.str-el