Diversity of the isotope effect due to the energy-varying electronic density of states on strong-coupling superconductors

We study superconducting critical temperatures within the strong-coupling Migdal-Eliashberg theory to clarify how the isotope effect is affected by the energy dependence of the electronic density of states (EDOS). In the computational procedure, we determine self-consistently both the electron self-energy in the normal state and the shift of the chemical potential. These quantities reflect asymmetry of energy dependence of the EDOS around the Fermi energy. As a result, we find that the energy dependence of the EDOS can reduce or enhance the isotope effect, and in some cases, it can make the isotope effect almost zero.