Superconducting Pseudogap in a Boson–Fermion Model

Abstract

A boson–fermion (BF) quantum-statistical binary gas mixture model consisting of positive-energy resonant bosonic Cooper electron pairs (CPs) in chemical and thermal equilibrium with single unpaired electrons is presented. Two-time retarded Green functions are shown to conveniently cope and deal with nonzero center-of-mass momentum (CMM) CPs. They yield an analytic expression for a dimensionless-coupling (λ)- and temperature ( T )-dependent generalized energy gap E g (λ, T ) in the single-electron spectrum of a superconductor. This generalized gap vanishes above a specific (“depairing” or “pseudogap”) temperature T * > T c , where T c is the critical Bose–Einstein condensation (BEC) singularity associated with the BF binary mixture, but is nonzero for all T below T * due initially to the formation of “preformed” pairs. Within the present BF model the generalized gap E g (λ, T ) is not restricted to the underdoped high-temperature superconductors as we illustrate with BSCCO, but is also applicable in optimally-doped and even overdoped compounds for which T * and T c virtually coincide as in BCS theory where nonzero-CMM CPs are neglected.