Anomalous Andreev Spectrum and Transport in Non-Hermitian Josephson Junctions

TL;DR

This paper investigates how non-Hermitian physics influences the Andreev spectrum and transport properties in a phase-biased Josephson junction, revealing unique spectral features and complex supercurrents.

Contribution

It introduces a non-Hermitian Josephson junction model and analyzes its spectral and transport properties using the Lindblad formalism and Bogoliubov-de Gennes equation, highlighting novel spectral features.

Findings

Existence of Josephson gaps with no Andreev bound states

Complex supercurrents from inelastic Cooper pair tunneling

Strong influence of non-Hermitian physics on Josephson effect

Abstract

We propose a phase-biased non-Hermitian Josephson junction (NHJJ) composed of two superconductors mediated by a short non-Hermitian link. Such a NHJJ is described by an effective non-Hermitian Hamiltonian derived based on the Lindblad formalism in the weak coupling regime. By solving the Bogoliubov-de Gennes equation, we find that its Andreev spectrum as a function of phase difference exhibits Josephson gaps, i.e., finite phase windows with no Andreev (quasi)bound states. The complex Andreev spectrum and the presence of Josephson gaps constitute particular spectral features of the NHJJ. Moreover, we propose complex supercurrents arising from inelastic Cooper pair tunneling to characterize the anomalous transport in the NHJJ. Additional numerical simulations complement our analytical predictions. We demonstrate that the Josephson effect is strongly affected by non-Hermitian physics.