Abstract
The quasiparticle spectra and the densities of states of superconducting-normal-superconducting junctions are computed from the WKBJ transformed Bogoliubov-de Gennes Equations (BdGE), which are solved by Picard iteration and numerical integration. It is shown that the influence of the proximity effect on the bound states can be modeled by a rectangular pair potential well of effective normal layer thickness 2a*=∫ L−L [1−Δ(z)/Δ]dz, where Δ(z) is the pair potential of the junction, Δ is its asymptotic constant value, and 2L is the total length of the sample. The density of states exhibits a subgap peak at energies less than Δ besides the BCS peak atE=Δ; forE>Δ there are geometrical resonances which are due to electron-hole interferences in finiteS layers of thicknessL-a*.
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Plehn, H., Gunsenheimer, U. & Kümmel, R. Subgap peak and Tomash-McMillan-Anderson oscillations in the density of states of SNS Bridges. J Low Temp Phys 83, 71–88 (1991). https://doi.org/10.1007/BF00683504
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DOI: https://doi.org/10.1007/BF00683504