BCS superconductivity inf-d andp-d systems

We study the Fröhlich Hamiltonian for two hybridized bands which describe states with equal or opposite parity of their Wannier functions. The phononic degrees of freedom are eliminated through a canonical transformation. The resulting Hamiltonian, which can take also exchange-like interactions into account, is treated using a generalized Bogoliubov transformation. We find that for some values of the parameters, excitations of arbitrary small energy could be present. In this case the low temperature properties should deviate from the usual BCS behaviour.