Anomalous Andreev spectrum and transport in non-Hermitian Josephson junctions

Abstract

We propose a phase-biased non-Hermitian Josephson junction composed of two superconductors connected by a short non-Hermitian link. Solving the Bogoliubov–de Gennes equation reveals Josephson gaps, finite phase windows without Andreev bound states, and a complex Andreev spectrum. We further propose complex supercurrents from inelastic Cooper-pair tunneling as signatures of anomalous transport and show how non-Hermitian physics strongly affects the Josephson effect.