Effects of energy dependence in the electronic density of states on some superconducting properties

Abstract

We study the influence of energy dependence in the electronic density of states (EDOS) on the single particle tunneling characteristics into a superconductor. The Migdal–Eliashberg equations generalized to the case of a nonconstant EDOS are derived. Three equations are involved, one for the gap, another for the renormalization function, and a new one for the chemical potential shift which does not appear in the conventional formulation. Numerical solutions of these equations are obtained, from which current voltage characteristics are calculated for a model EDOS. The "inversion" of the calculated tunneling conductance shows that the effects of the peaks in the EDOS, on the scale of several Debye energies are important and cannot necessarily be reproduced within the usual Eliashberg theory by working with some effective value of electron–phonon spectral density α2(ω)F(ω) and/or Coulomb parameter μ* without introducing unphysical features to these parameters.