Model of a superconducting singular Fermi liquid with a first-order phase transition

Model of s-wave and d-wave superconductivity in a singular Fermi liquid with a divergent scattering amplitude for particles with the same quasi-momenta and opposite spins is formulated and presented with regard to a narrow, nearly half-filled conduction band. The ground state and other eigenstates for the superconducting phase are found. Thermodynamic functions are obtained by the use of the Bogolubov method. The gap equation along with the equation for the chemical potential is derived in a general form and solved in a self-consistent manner for s-wave pairing. Above a certain temperature there are two solutions of the gap equation, however only for the greater one the superconducting phase remains stable. It is shown that the system undergoes a first-order phase transition between the superconducting and the normal phase. The critical temperature and the heat of the transition are found. The temperature dependence of the entropy and the specific heat of the system is also presented. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.