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

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 N-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 N-ZES not equal 0. Our results show that N-ZES not equal 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 N-ZES not equal 0.