VARIATIONAL TREATMENT OF RETARDED PHONON-INDUCED ELECTRON PAIRING

To treat the phonon-induced electron pairing in a way which allows for vortex corrections and retardation effects, we develop a method using a canonical transformation involving a variational function. This method is expected to be useful for developing a unified theory for phonon-induced electron pairing ranging between adiabatic and nonadiabatic behavior, or, respectively, between Copper-pair condensation in momentum space and bipolaron condensation in real space. To demonstrate the power of our variational treatment we determine for a model pairing potential, involving a temperature-dependent energy cutoff c(T) as a variational parameter, the thermodynamical properties of the conventional intermediate- and strong-coupling superconductors. Thus, we obtain results which compare well with those obtained by solving the Eliashberg equations.