Interaction effects along the edge of a topological superconductor

Topological nodal superconductors, such as d_xy-wave and nodal non-centrosymmetric superconductors, exhibit protected zero-energy flat-band edge states. These zero-energy edge modes are protected by time-reversal and translation symmetry and their stability is guaranteed by the conservation of a quantized topological invariant. Here, we study the fate of these flat-band edge states in the presence of interactions. We find that Hubbard interactions lead to spontaneous breaking of time-reversal or translation symmetry at the edge of the system. For the d_xy-wave superconductor in the presence of attractive Hubbard interactions we find that the flat-band states become unstable towards the formation of a charge-density wave state or a state with s-wave type pairing correlations. Repulsive Hubbard interactions, on the other hand, induce ferromagnetic order at the edge of the d_xy-wave superconductor.