Quantum-resistance states of normal-superconducting layered films

We have investigated quantum-resistance states in films composed of alternating layers of superconducting and normal metals, and have found good agreement with the phenomenological model which is based on the momentum quantization of quasiparticles in the normal layer. We have also observed that the formation of quantum-resistance states is inhibited by the introduction of impurities into the normal layer. In films composed of more than one normal layer, the quantum-resistance states of each layer combine in parallel to produce an $I$-$V$ characteristic whose properties are quite different from those due to the series combination of localized voltages.