Thermodynamics of weak coupling anisotropic superconductors with energy dependent electronic density of states

We derive analytical expressions for the gap edge and thermodynamic functions of anisotropic weak coupling superconductors with a model energy dependent electronic density of states N (ε). We choose N (ε) to be a Lorentzian superimposed on a constant background with the Fermi energy at an arbitrary distance from the maximum. Significant modification to the Bardeen–Cooper–Schrieffer (BCS) expressions are found for sharp peaks and for valleys in the density of states when the peak width is on the scale of the Debye energy. In this last case corrections can be very important.