FERMI GAS WITH 4-FERMION BCS-TYPE INTERACTION

摘要

A gas of spin 1/2 fermions with an interaction V + W = - ∑_(k,k′) g_(kk′)b_k~*b_(-k)~*b_(k′)b_(-k′), + ∑_k γkb_k~*b_k, where b_k = a_(k+)a_(k-) and a_(kσ), a_(k′σ′)~* satisfy Fermi anticommutation relations, is investigated. The trial ground state |G > is similar in form to the BCS ground state, with b_k~*b_(-k)~* replacing a_(k+)~*a_(-k-)~*, but because the excitation energies are not simply additive, the trial density matrix ρ_0 differs from the BCS one. The expectation values < G|H|G >and Tr(H ρ_0 ) are minimized, revealing the presence of a second-order phase transition, with T_c > T_(C(BCS)) for appropriately adjusted γ_k. It is shown that the minimization procedure applied leads to an expression tor the free energy density of H, which is asymptotically exact in the infinite-volume limit. Comparison with experimental data on high-temperature superconductors is made and for a particular choice of γ_k qualitative agreement is found with the temperature dependence of the order parameter of the BSCCO superconductor.