The dc Josephson current in a long multi-channel quantum wire

Abstract

The dc Josephson current across a multi-channel SNS junction is computed by summing contributions from sub-gap Andreev bound states, as well as from continuum states propagating within the superconducting leads. We show that, in a long multi-channel 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.

25 pages, 4 .eps figures

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Cited by in corpus (9)

• Spin Orbit coupling and Anomalous Josephson effect in Nanowires
• Anomalous Josephson Effect in S/SO/F/S heterostructures
• Transfer matrix approach to the persistent current in hybrid normal-superconducting rings
• Tunable Kondo screening length at a Y-junction of three inhomogenous spin chains
• Dual fermionic variables and renormalization group approach to junctions of strongly interacting quantum wires
• Green's Function Approach to Josephson Dot Dynamics and Application to Quantum Mpemba Effects
• Andreev non-Hermitian Hamiltonian for open Josephson junctions from Green's functions
• Many-body quantum dynamics of spin-orbit coupled Andreev states in a Zeeman field
• Effect of Disorder on the Conductance of (non-) Topological SN Junctions