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Fermi Gas with 4-Fermion BCS-type Interaction

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Maćkowiak J., Tarasewicz P.

Acta Physica Polonica A

1998

vol. 93

issue 4

659-675

A gas of spin 1/2 fermions with an interaction V + W = - Σ_{k,k'}g_{kk'}b*_{k} b*_{-k}b_{k'}b_{-k'} + Σ_{k} γ_{k}b*_{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 \rho_0 differs from the BCS one. The expectation values 〈G|H|G〉 and Tr(Hρ_{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 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 \gamma_k qualitative agreement is found with the temperature dependence of the order parameter of the BSCCO superconductor.

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1 Acta Physica Polonica A

1 1998

1 Maćkowiak J.

1 Tarasewicz P.

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Fermi Gas with 4-Fermion BCS-type Interaction