A modified BCS theory of heavy fermion superconductivity

In this paper we derive an expression for the superconducting gap equation for U and Ce based heavy fermion (HF) systems within a modified weak coupling theory of superconductivity. The calculated gap equation presents a mixture of pairing amplitudes of two different quasi-particle bands alpha and beta. These two gap equations are solved numerically and self-consistently within the cut-off energy which arises due to the Kondo energy. It is found that the energy dependence of the enhanced density of states for the HF systems clearly manifests itself in the theory and the Kondo energy naturally takes the role of cut-off energy (omega (C) ), as long as the effective cut-off energy is large in comparison with the Kondo energy. The numerical analysis confirms this result and shows that superconducting transition temperature is independent of effective cut-off energy employed within this approach. The temperature dependence of gap equations are studied by varying the model parameters like position of f-level, hybridization and coupling constants of the HF systems.