Andreev level spectrum and Josephson current in a superconducting ballistic point contact

Abstract

Using a transfer-matrix method, we study the Josephson current in a normal, clean, one-dimensional quantum channel in contact with two superconducting electrodes characterized by a finite value of the ratio between the gap Δ and the Fermi energy μ. Going beyond the ‘‘Andreev approximation,’’ gaps open up in the quasiparticle level spectrum, the critical current is reduced, and the relationship between current and superconducting phase difference φ becomes more Josephson-like without any discontinuous jump at φ=π. The mechanism behind these effects is the normal reflection at the interfaces due to a finite value of Δ/μ. The gap at φ=π goes to zero only at transmission resonances kFL=(2n+1)π/2.

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