Josephson effect in a junction coupled to an electron reservoir

Abstract

We extend the scattering theory of the Josephson effect to include a coupling of the Josephson junction to a gapless electron reservoir in the normal state. By opening up the system with a quasiparticle escape rate $1/\tau$, the supercurrent carried at zero temperature by an Andreev level at energy ${\epsilon }_{\mathrm{A}}$ is reduced by a factor $(2/\pi )\arctan (2{\epsilon }_{\mathrm{A}}\tau /\hslash )$ . We make contact with recent work on "non-Hermitian Josephson junctions", by comparing this result to different proposed generalizations of the Josephson effect to non-Hermitian Hamiltonians.

5 pages, 3 figures; contribution to the special issue of APL on "Josephson junctions and related proximity effects"

References in corpus (6)

• Dephasing-enabled triplet Andreev conductance
• Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport
• Josephson-phase-controlled interplay between correlation effects and electron pairing in a three-terminal nanostructure
• Non-Hermitian phase-biased Josephson junctions
• Anomalous Andreev Spectrum and Transport in Non-Hermitian Josephson Junctions
• Voltage staircase in a current-biased quantum-dot Josephson junction

Cited by in corpus (12)

• Non-hermitian topology in multiterminal superconducting junctions
• Non-Hermitian multiterminal phase-biased Josephson junctions
• Interplay between Majorana and Shiba states in a minimal Kitaev chain coupled to a superconductor
• Non-Hermitian minimal Kitaev chains
• Josephson effect and critical currents in trivial and topological full-shell hybrid nanowires
• Andreev non-Hermitian Hamiltonian for open Josephson junctions from Green's functions
• Non-Hermitian superconducting diode effect
• Exceptional Andreev spectrum and supercurrent in p-wave non-Hermitian Josephson junctions
• Signatures of exceptional points in multiterminal superconductor-normal metal junctions
• Non-Hermitian Josephson junctions with four Majorana zero modes
• Supercurrent from the imaginary part of the Andreev levels in non-Hermitian Josephson junctions
• Hexagonal Warping Control of Exceptional Points in Topological Insulator--Ferromagnetic Heterojunctions