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Besides topological insulators and the integer quantum Hall state, which have a full bulk gap, there are also gapless phases that belong to the broad class of topological materials, such as, e.g., semi-metals with topologically protected Fermi points and nodal superconductors with topologically stable nodal lines. An important class of materials for nodal topological superconductors are noncentrosymmetric superconductors which are characterized by strong spin-orbit coupling and a mixing of spin-singlet and spin-triplet pairing. In this talk, I show that the topology of these nodal superconductors manifests itself in the presence of nondegenerate flat-band zero-energy surface states, which possess an intricate spin structure. This nontrivial spin texture of the surface states can be tested from the absence of large-ky backscattering processes in Fourier-transform scanning tunneling measurements. Another possibility is to probe the spin polarization of the surface states by bringing the superconductor into contact with a ferromagnetic insulator. I demonstrate that a charge current develops in an nodal topological superconductor close to the interface with a ferromagnet. The current is dominated by the response of the flat-band surface states of the superconductor to the exchange field of the ferromagnet, and hence has completely different characteristics for a fully gapped and a nodal topological superconductor. For example, while the current in the fully gapped noncentrosymmetric superconductor is weak and saturates to its zero-temperature value, the presence of nondegenerate flat bands in the nodal noncentrosymmetric superconductor is responsible for an enormous enhancement of the current at low temperatures. This provides a novel test of the topology of noncentrosymmetric superconductors, and in particular of the existence of nondegenerate flat-band states. |
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