dc Josephson current in a long multichannel quantum wire

Domenico Giuliano and Ian Affleck
Phys. Rev. B 90, 045133 – Published 25 July 2014

Abstract

The dc Josephson current across a multichannel superconductor–normal-superconductor (SNS) junction is computed by summing contributions from subgap Andreev bound states, as well as from continuum states propagating within the superconducting leads. We show that, in a long multichannel SNS junction, at low temperatures, all these contributions add up, so that the current can be entirely expressed in terms of single-particle normal and Andreev reflection amplitudes at the Fermi level at both SN interfaces. Our derivation applies to a generic number of channels in the normal region and/or in the superconducting leads, without assumptions about scattering processes at the SN interfaces: if the channels within the central region have the same dispersion relation, it leads to simple analytical formulas for the current at low temperatures; if the channels within the central region have different dispersion relations, it allows for expressing the current in terms of a simple integral involving only scattering amplitudes at the Fermi level. Our result motivates using a low-energy effective boundary Hamiltonian formalism for computing the current, which is crucial for treating Luttinger liquid interaction effects.

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  • Received 25 May 2014
  • Revised 5 July 2014

DOI:https://doi.org/10.1103/PhysRevB.90.045133

©2014 American Physical Society

Authors & Affiliations

Domenico Giuliano1,2 and Ian Affleck3

  • 1Dipartimento di Fisica, Università della Calabria Arcavacata di Rende, I-87036 Cosenza, Italy and I.N.F.N., Gruppo Collegato di Cosenza, Arcavacata di Rende, I-87036 Cosenza, Italy
  • 2CNR-SPIN, Monte S. Angelo via Cinthia, I-80126 Napoli, Italy
  • 3Department of Physics and Astronomy, University of British Columbia, Vancouver, B.C., Canada V6T 1Z1

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Issue

Vol. 90, Iss. 4 — 15 July 2014

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