Andreev bound states in junctions formed by conventional and $\mathcal{PT}$-symmetric non-Hermitian superconductors

TL;DR

This paper explores the unique Andreev bound states and Majorana zero modes in junctions involving $ ext{PT}$-symmetric non-Hermitian superconductors, revealing discrete phase conditions and time-dependent phenomena.

Contribution

It introduces a theoretical model of junctions with $ ext{PT}$-symmetric non-Hermitian superconductors, highlighting novel bound states and zero modes arising from symmetry and non-Hermitian interactions.

Findings

Discrete phase values yield bound state solutions.

Time-growing and decaying Andreev states at 0 and π.

Majorana zero mode appears at π/2 and 3π/2, enabling unidirectional supercurrent.

Abstract

We study theoretically a junction 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 $0$ and $\pi$, we obtain growing and decaying in time Andreev bound states. For $\pi/2$ and $3\pi/2$, there is a Majorana zero mode penetrating through the junction in only one direction forming a quasiparticle supercurrent.