Spectrum of superconducting films with quantized resistances

Abstract

The lowest-lying quasiparticle states in a superconducting-normal-superconducting layer structure are calculated in the presence of a ground-state current flow parallel to the phase boundaries and an applied magnetic field $H$ parallel to the film surface. Particle-hole scattering at the phase boundaries as well as ordinary reflection processes at the outer film surfaces and at the pair-potential walls are taken into account. Quasiparticle energy and momentum normal to the phase boundaries are obtained as linear functions of a field-dependent parameter $\alpha \mathrm{}\left(H\right)\mathrm{}$, $0<\mathrm{}\alpha \mathrm{}\left(H\right)<\frac{1}{2}$, which has been found previously in the experiments on quantized resistances. The relevance of the results with respect to the hypothesis that the bound quasiparticle states are involved in the formation of the observed quantized resistances is discussed.