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Types of topological surface states in nodal noncentrosymmetric superconductors

Nodal noncentrosymmetric superconductors have topologically nontrivial properties manifested by protected zero-energy surface states. Specifically, it was recently found that zero-energy surface flat bands of topological origin appear at their surface. We show that the presence of certain inversion-type lattice symmetries can give rise to additional topological features of the gap nodes, resulting in surface states forming one-dimensional arcs connecting the projections of two nodal rings. In addition, we demonstrate that Majorana surface states can appear at time-reversal-invariant momenta of the surface Brillouin zone, even when the system is not fully gapped in the bulk. Within a continuum theory we derive the topological invariants that protect these different types of zero-energy surface states. We independently derive general conditions for the existence of zero-energy surface bound states using the complementary quasiclassical scattering theory, explicitly taking into account the effects of spin-orbit splitting of the bands. We compute surface bound-state spectra for various crystal point-group symmetries and orbital-angular-momentum pairing states. Finally, we examine the signatures of the arc surface states and of the zero-energy surface flat bands in tunneling-conductance spectra and discuss how topological phase transitions in noncentrosymmetric superconductors could be observed in experiments.