Quasiparticle scattering and current-voltage characteristics of superconductor-normal-superconductor film structures

Abstract

The quasiparticle spectrum of a film with superconducting surface sheaths is calculated for states with energies less than the maximum value $\ensuremath{\Delta}$ of the pair potential. The influence of a magnetic field parallel to the film surface is discussed semiqualitatively. The probability of Andreev scattering (AS) in a surface sheath is found to be limited by ordinary reflection processes to a narrow range of values of momentum perpendicular to the film surface. The "normal" region behaves like a gapless superconductor. When a ground-state current flows in it, in thermal equilibrium quasiparticle states with momenta opposite to the ground-state flow are preferentially populated. Those with high probability of AS continuously transfer momentum to the condensate so that a voltage must appear in order to maintain a stationary current. Current-voltage characteristics are calculated and discussed for various temperatures and film thicknesses. They show step structures due to the spatial quantization of the quasiparticle states. The theory is compared to the experiments on quantized resistances.