An extension of the Bardeen-Cooper-Schrieffer model of superconductivity

An extension of the BCS Hamiltonian of H-BCS the form H = H-BCS + W + V, where W = Sigma k gamma knk = nk -, V = -\Lambda\(-1) X Sigma(k,k')g(k,k')b(k)*b*(-k)b(-k')b(k'), n(k sigma) = a(k sigma)* a(k sigma), b(k) = a(k) (+) a(k) are fermion creation and annihilation operators, is investigated. It is shown that H represents a solvable mean-field model in the thermodynamic limit. H exhibits a 2nd-order phase transition if W is sufficiently strongly attractive and the low-temperature phase, characterized by two order parameters, contains two Condensates: a condensate of BCS-type fermion pairs and a condensate of fermion quadruples with momenta and spins (p,sigma) equal {(p,sigma),(- p,sigma), (p,- sigma), (- p, - sigma)}. If gamma(k), < 0, a pseudogap is present in the excitation spectrum in the normal phase. (C) 2000 Elsevier Science B.V. All rights reserved.