We have confirmed the quantization of the critical current in a superconducting quantum point contact consisting of a split-gate superconductor-(two-dimensional electron gas)-superconductor junction. The critical current and conductance show stepwise changes as a function of the gate voltage. We also observed resonant structure resulting from quantum interference of quasiparticles at the step edge.
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Takayanagi et al. (1995) studied this question.
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