| By way of examples, I will discuss how quasiparticle edge flatbands and the phase-frustration between two superconducting order parameters provide mechanisms for spontaneous time-reversal symmetry breaking in topological noncentrosymmetric superconductors. First, I will show that a bulk superconducting topological phase transition is masked by a local breaking of time-reversal symmetry at twin boundaries, that are the generic lattice defects in materials without inversion symmetry. As a result, supercurrents flow along the twin boundary an a local magnetization develops. Second, I will discuss possible pairing states for the locally noncentrosymmetric superconductor SrPtAs in the light of recent experiments that revealed a spontaneous breaking of time-reversal symmetry. The two competing scenarios are a chiral d-wave state and an f-wave state. In the former, SrPtAs is a Weyl superconductor that supports dispersing Majorana edge modes on the surface, while the latter state features surface Majorana flatbands. These flatbands can undergo a transition towards a time-reversal symmetry broken surface state. |
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