Andreev bound states in junctions formed by conventional and PT -symmetric non-Hermitian superconductors

Abstract

We study theoretically a junction composed of a $\mathcal{PT}$-symmetric non-Hermitian superconductor (PTS) placed between two conventional superconductors. We show that due to non-Hermitian electron-electron interaction in the PTS region and the combination of symmetries, only discrete values of phases of the conventional superconductors yield solutions for Andreev bound states. Remarkably, in the case of phases 0 and $\ensuremath{\pi}$, we obtain Andreev bound states that are growing and decaying in time. For $\ensuremath{\pi}/2$ and $3\ensuremath{\pi}/2$, there is a Majorana zero mode penetrating through the junction in only one direction forming a quasiparticle supercurrent.