Temperature dependence of the superconducting energy gap within the Eliashberg theory involving the energy-varying electronic density of states

The temperature dependence of the superconducting energy gap is studied by the Eliashberg theory with inclusion of the energy-varying electronic density of states (EDOS). In order to investigate in what manner the inclusion of the energy-varying EDOS affects the temperature dependence of the energy gap, the numerical analysis is carried out with two typical shapes of the Lorentzian EDOS; one has a peak at the Fermi energy (convex EDOS) and the other has a hollow structure at the Fermi energy (concave EDOS). It is pointed out that the inclusion of the energy variation of the EDOS significantly affects the temperature dependence of the superconducting energy gap when the electron-phonon coupling becomes strong. In the case of the convex EDOS, especially, the curve of the energy gap sometimes lies even below that of the weak-coupling BCS theory.