Critical Field and Specific Heat of Strong Coupling Superconductors

Abstract

Expressions for thermal quantities such as the critical field, entropy, and specific heat are derived for strong coupling superconductors without making a quasiparticle approximation for electron motions. The contributions from the ion motions are also taken into account semiphenomenologically. Nambu's Green's-function formalism at finite temperature is used as well as a relation, derived by Chester, between the differences of the thermal averages of the total Hamiltonian and the ion kinetic energy between the normal and the superconducting phases. Assuming the simple isotope effect, where the transition temperature is proportional to the inverse square root of the ionic mass, the phase transition is shown to be of the second order. The thermal quantities are given in terms of a single function of the temperature and its derivatives, which can be obtained from the energy-gap function and the renormalization factor of the electron Green's function. These expressions lead to the BCS results in the appropriate limit. A new expression for the jump in specific heat is also derived. For strong coupling superconductors it is likely to give better agreement with experiments than the BCS expression. Present theory does not apply to superconductors with isotope effect not simple as above. A possible reason is discussed.