Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors

Over the last few years, the study on node structures in SCs has received renewed interest due to the fact that they are a kind of topological objects. In this context, a line node in time-reversal (TR) invariant SCs is protected by a one-dimensional (1D) topological number and induces a Majorana flat band (MFB) in a surface. The MFBs exhibit a zero-bias conductance peak through the tunneling measurement for TR invariant SCs such as high-Tc SCs and non-centrosymmetric SCs, which gives a conclusive evidence for the bulk topological line nodes.

In this talk, we discuss topology of crystal symmetry protected line nodes in unconventional SCs. We introduced the 1D and 0D topological numbers associated with line nodes, each of which ensures the existence of MFBs and stability of line nodes, respectively. Establishing a relationship between them, we clarified that MFBs are classified into three classes of SCs [1]: (i) odd-parity SCs, (ii) even-parity SCs with pure TR symmetry, and (ii) even-parity SCs with a magnetic translation. These classes are distinguishable through surface sensitive experiments.

[1] S. Kobayashi, S. Sumita, Y. Yanase, and M. Sato, Phys. Rev. B 97, 180504(R) (2018)