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We discuss the stability of highly degenerate zero-energy states tha appearat the surface of a nodal superconductor preserving time-reversal symmetry. Theexistence of such surface states is a direct consequence of the nontrivialtopological numbers defined in the restricted Brillouin zones in the cleanlimit. In experiments, however, potential disorder is inevitable near thesurface of a real superconductor, which may lift the high degeneracy at zeroenergy. We show that an index defined in terms of the chiral eigenvalues of thezero-energy states can be used to measure the degree of degeneracy at zeroenergy in the presence of potential disorder. We also discuss the relationshipbetween the index and the topological numbers.

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