Symmetry conditions of a nodal superconductor for generating robust flat-band Andreev bound states at its dirty surface

TL;DR

This paper analyzes the symmetry conditions under which nodal superconductors can host robust flat-band zero-energy states at their surfaces, even in the presence of disorder, highlighting topological classes and specific Hamiltonians.

Contribution

It generalizes the theory of zero-energy states in nodal superconductors, identifying symmetry conditions and topological classes that support robust surface states.

Findings

Zero-energy states are robust in topological BDI and CII class superconductors.

Two realistic Hamiltonians exhibiting non-zero topological index ${ m N}_{ m ZES}$.

Conditions for superconductor surface states to remain stable under disorder.

Abstract

We discuss the symmetry property of a nodal superconductor that hosts robust flat-band zero-energy states at its surface under potential disorder. Such robust zero-energy states are known to induce the anomalous proximity effect in a dirty normal metal attached to a superconductor. A recent study has shown that a topological index ${\cal N}_\mathrm{ZES}$ describes the number of zero-energy states at the dirty surface of a $p$-wave superconductor. We generalize the theory to clarify the conditions required for a superconductor that enables ${\cal N}_\mathrm{ZES}\neq 0$. Our results show that ${\cal N}_\mathrm{ZES}\neq 0$ is realized in a topological material that belongs to either the BDI or CII class. We also present two realistic Hamiltonians that result in ${\cal N}_\mathrm{ZES}\neq 0$.