Second-order Dirac superconductors and magnetic field induced Majorana hinge modes

Higher-order topological superconductors (HOTSCs) are a new class of topological materials that in three dimensions are characterized by gapped bulk and surface states and gapless hinge modes. Here, the authors identify two new groups of HOTSCs: (i) second-order Dirac superconductors, which have both topologically protected Dirac cones at the surface and topologically protected dispersionless Majorana states at the hinges; (ii) three-dimensional magnetic field-induced HOTSCs with helical Majorana hinge states, which are located at only two (or one) of the corners. The authors show that, using the sign of the magnetic field and the mirror-diagonal symmetry-breaking perturbation, the Majorana pairs can be tuned to be at a specific corner, leading to a highly tunable setup for realization and detection of helical Majorana states.