# Stability of the boundary zero modes in one-dimensional topological superconductors

## TL;DR

This paper investigates how zero-energy boundary modes in one-dimensional topological superconductors are affected by time-reversal symmetry-breaking perturbations, revealing their fragility even in topologically nontrivial states.

## Contribution

It provides a detailed analysis of the stability of boundary zero modes under symmetry-breaking fluctuations in Rashba spin-orbit coupled superconductors.

## Key findings

- Zero modes are destroyed by time-reversal symmetry-breaking fluctuations.
- Boundary zero modes are fragile even in topologically nontrivial states.
- The study emphasizes the importance of symmetry protection for topological boundary states.

## Abstract

We calculate the spectrum of the Andreev bound states in a one-dimensional superconductor with a strong Rashba spin-orbit coupling. We focus on the fate of the zero-energy Andreev modes in the presence of time reversal symmetry-breaking perturbations, both at the boundary and in the bulk. It is shown that the zero modes are destroyed by time reversal symmetry-breaking fluctuations, even if the mean-field state of the system is time-reversal invariant and topologically nontrivial.