Superconductivity in the Fröhlich two-dimensional model with an arbitrary carrier concentration

Using the Fröhlich Hamiltonian, we obtain self-consistent equations for the energy gap and the chemical potential. Using these equations, we can analyze the superconductivity properties of the system for an arbitrary carrier concentration. We consider weak, intermediate, and strong interactions between fermions and observe the transition from the Cooper coupling to the local-pair regime in the indirect-interaction model.