Effect of varying the electronic band-filling on the temperature dependence of the superconducting energy gap

In the framework of the Eliashberg theory where the energy dependence of the electronic density of states (EDOS) is taken into account, the temperature dependence of the superconducting energy gap Delta(0)(T) is studied for strong coupling superconductors with the band-filling being varied. It is found that, when the electron-phonon coupling becomes very strong, the inclusion of the energy-dependent EDOS leads to a distinctive behavior of Delta(0)(T) depending on the band-filling. Moreover, the existence of this strong band-filling dependence of the behavior of Delta(0)(T) suggests that the requirement of the number conservation of electrons is a necessary ingredient in these numerical studies, from the results of which we ever discuss the gap feature.