Fermi Gas with 4-Fermion BCS-type Interaction

J. Maćkowiak and P. Tarasewicz Institute of Physics, N. Copernicus University, Grudziądzka 5/7, 87-100 Toruń, Poland

Received: September 2, 1997

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A gas of spin 1/2 fermions with an interaction V + W = - ∑k,k'gkk'b*kb*–kbk'b–k' + ∑kγkb*kbk, where bk=ak+ak– and akσ,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*kb*–k replacing a*k+a*–k–, but because the excitation energies are not simply additive, the trial density matrix ρ0 differs from the BCS one. The expectation values ⟨G|H|G⟩ and Tr(Hρ0) are minimized, revealing the presence of a second-order phase transition, with Tc > Tc(BCS) for appropriately adjusted γk. It is shown that the minimization procedure applied leads to an expression for 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 γk qualitative agreement is found with the temperature dependence of the order parameter of the BSCCO superconductor.

DOI: 10.12693/APhysPolA.93.659 PACS numbers: 74.20.-z, 74.20.Fg