Periodic structures of clean, normal, and superconducting material I: the density of states of the normal sections

Abstract

We can calculate the density of states in the normal regions of periodic structures of clean, normal, and superconducting material. A derivation of the energy-momentum relation for sections of different Fermi surfaces is very briefly sketched. The results reduce to formulas with m* and pF taken as uniform throughout, as, for example, in the mixed state of a type-I superconductor. A plot of the density of states N(ε,x) vs. energy E for periodic structures of different cell lengths and normal-metal superconducting sharing widths, as well as [Formula: see text], where νF is the Fermi velocity of the superconducting sections, is presented in the body of this paper. A brief look at the proximity effect is included, as well as a verbal discussion of the self-consistency for our model. The density of states in the superconducting regions is dependent on the parallel coordinate x in an oscillating fashion, which is hard to calculate numerically. This is not the case for the normal sections or for the self-consistency equation.