Josephson effect of the superconducting quantum point contact

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Abstract
The dc Josephson effect of a constriction in a two-dimensonal superconductor-semiconductor-superconductor junction, i.e., a superconducting quantum point contact, is investigated theoretically for both long and short constriction lengths compared with the superconducting coherence length. It is shown that the critical current of a ballistic superconducting quantum point contact increases stepwise as a function of its width under appropriate conditions. The step height generally depends on both the superconducting energy gap and junction parameters. The effect of normal reflections at the superconductor-semiconductor interface is also examined.