Stability of flat-band edge states in topological superconductors without inversion center

Nodal superconductors without inversion symmetry exhibit nontrivial topological properties, manifested by topologically protected flat-band edge states. Herewe study the effects of edge roughness and strong edge disorder on the flat-band states using large-scale numerical simulations. We show that the bulk-edge correspondence remains valid for rough edges and demonstrate that midgap states generically appear at the boundary of nodal noncentrosymmetric superconductors, for almost all edge orientations. Moderately strong nonmagnetic disorder shifts some of the edge states away from zero energy, but does not change their total number. Strong spin-independent edge disorder, on the other hand, leads to the appearance of new weakly disordered midgap states in the layers adjacent to the disordered edge, i.e., at the interface between the bulk topological superconductor and the one-dimensional Anderson insulator formed by the strongly disordered edge layers. Furthermore, we show that magnetic impurities, which lift the time-reversal symmetry protection of the flat-band states, lead to a rapid decrease of the number of edge states with increasing disorder strength.