Anomalous band-filling dependence of the quasiparticle density of states and the gap ratio 2 Δ 0 / k B T c in strong-coupling superconductors

Within the framework of the Eliashberg theory including the energy-dependent Lorentzian electronic density of states (EDOS), the behavior of the quasiparticle density of states (QDOS) is studied for strong-coupling superconductors. Our numerical calculation shows that when the EDOS has structure it can give an additional structure to the QDOS besides the usual fine structures due to the strong electron-phonon coupling when the carrier concentration has appropriate values. It is also found that the inclusion of the energy-varying EDOS leads to unusual band-filling dependence of the gap ratio 2 Delta 0/k(B)T(c): The calculation with the band-filling n being varied, reveals that the gap ratio does not necessarily take its maximum value at half-filling, but at a value of n far away from half-filling. This may occur as the electron-phonon coupling becomes very strong.