Boundary topological superconductors
Bo-Xuan Li, Zhongbo Yan
Abstract
For strongly anisotropic time-reversal invariant (TRI) insulators in two and three dimensions, the band inversion can occur, respectively, at all TRI momenta of a high symmetry axis and plane. Although these classes of materials are topologically trivial as their strong and weak ${Z}_{2}$ indices are all trivial, they can host an even number of helical gapless edge states or surface Dirac cones on some boundaries. We show in this paper that when the gapless boundary states are gapped by ${s}_{\ifmmode\pm\else\textpm\fi{}}$-wave superconductivity, a boundary time-reversal invariant topological superconductor (BTRITSC) characterized by a ${Z}_{2}$ invariant can be realized on the corresponding boundary. Since the dimension of the BTRITSC is lower than the bulk by one, the whole system is a TRI second-order topological superconductor. When the boundary of the BTRITSC is further cut open, Majorana Kramers pairs and helical gapless Majorana modes will, respectively, appear at the corners and hinges of the considered sample in two and three dimensions. Furthermore, a magnetic field can gap the helical Majorana hinge modes of the three-dimensional TRI second-order topological superconductor and lead to the realization of a third-order topological superconductor with Majorana corner modes. Our proposal can potentially be realized in insulator-superconductor heterostructures and iron-based superconductors whose normal states take the desired inverted band structures.