The ground state and the thermodynamics of an extended BCS model of superconductivity

Abstract

The thermodynamics of an extended BCS model of superconductivity is investigated. A physical system is described by a Hamiltonian containing the BCS interaction and an attractive four-fermion interaction. The four-fermion potential is caused by attractions between Cooper pairs mediated by the phonon field. The weakness of this potential allows the use of perturbation theory. The perturbation expansion was restricted to the first order because in the ground state the second order terms are not larger than 0.5 percent of first order correction for parameters used for calculations. The BCS Hamiltonian is an unperturbed one. The ground state and the thermal properties are examined. As a result the jump in the specific heat is higher than that in the BCS case. Moreover, the squared critical field is larger than the corresponding one in the BCS theory. Additionally, we show connections with the Bogolyubov's mean field approach used earlier in order to investigate general physical consequences of the model.