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

Abstract

An extension of the BCS Hamiltonian of H BCS, the form H= H BCS+ W+ V, where W=∑ k γ k n k + n k −, V=−| Λ| −1∑ k , k ′ g k , k ′ b k * b − k * b − k ′ b k ′ , n k σ = a k σ * a k σ , b k = a k + a k − and a k σ *, a k σ 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 , σ) equal {( p , σ),(− p , σ), ( p ,− σ), (− p ,− σ)}. If γ k <0, a pseudogap is present in the excitation spectrum in the normal phase.