# Topological Phase Transition driven by Infinitesimal Instability: Majorana Fermions in Non-Hermitian Spintronics

## TL;DR

This paper uncovers a novel topological quantum phase transition in non-Hermitian superconducting nanowires driven by infinitesimal instability, revealing Majorana states and a unique bulk-boundary correspondence with potential experimental realization.

## Contribution

It introduces a new type of topological phase transition caused by cascade instability in non-Hermitian systems, with a novel bulk-boundary correspondence and experimental proposal.

## Key findings

- Infinitesimal magnetic field suppresses non-Hermitian skin effect.
- Topological phase with Majorana boundary states identified.
- Non-Hermitian bulk-boundary correspondence established.

## Abstract

Quantum phase transitions are intriguing and fundamental cooperative phenomena in physics. Analyzing a superconducting nanowire with spin-dependent non-Hermitian hopping, we discover a topological quantum phase transition driven by infinitesimal cascade instability. The anomalous phase transition is complementary to the universal non-Bloch wave behavior of non-Hermitian systems. We show that an infinite small magnetic field drastically suppresses the non-Hermitian skin effect, inducing a topological phase with Majorana boundary states. Furthermore, by identifying the bulk topological invariant, we establish the non-Hermitian bulk-boundary correspondence that does not have a Hermitian counterpart. We also discuss an experimental realization of the system by using the spin-current injection to a quantum wire.