Effect of the operator nature of the superconducting order parameter in the presence of an added quasiparticle

Abstract

I investigate corrections to the mean-field approximation for a superconductor at zero temperature using a single-band Hubbard model with an on-site attractive interaction U. These corrections arise from treating the order parameter as an operator rather than as a number. The quasiparticle spectra may be characterized by a renormalized gap and an effective mass that fall rapidly as ‖k-${\mathit{k}}_{\mathit{F}}$‖ increases. For ${\mathrm{\Delta }}_0$∼${10}^{\mathrm{-}2}$ of the bandwidth, which estimates suggest is the appropriate range of values for the high-temperature superconductors, one finds that ${\mathrm{\Delta }}_0$ is reduced by ∼20% both for a parabolic band and for the tight-binding band structure at half-filling. This is comparable to the magnitude of renormalization found for pairing bags.