# Stability of flat zero-energy states at the dirty surface of a nodal superconductor

## TL;DR

This paper investigates the robustness of zero-energy surface states in nodal superconductors against potential disorder, linking topological invariants to observable degeneracy in realistic conditions.

## Contribution

It introduces an index based on chiral eigenvalues to quantify degeneracy stability under disorder and relates it to topological numbers.

## Key findings

- Zero-energy states' degeneracy can be characterized by a chiral eigenvalue index.
- Potential disorder can lift degeneracy, but the index remains a measure of stability.
- The index correlates with topological invariants, indicating topological protection.

## Abstract

We discuss the stability of highly degenerate zero-energy states tha appear at the surface of a nodal superconductor preserving time-reversal symmetry. The existence of such surface states is a direct consequence of the nontrivial topological numbers defined in the restricted Brillouin zones in the clean limit. In experiments, however, potential disorder is inevitable near the surface of a real superconductor, which may lift the high degeneracy at zero energy. We show that an index defined in terms of the chiral eigenvalues of the zero-energy states can be used to measure the degree of degeneracy at zero energy in the presence of potential disorder. We also discuss the relationship between the index and the topological numbers.