Boundary topological superconductors

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 plane. Although these classes materials are topologically trivial as strong weak $Z_{2}$ indices trivial, they host an even number unprotected helical gapless edge states or surface Dirac cones on some boundaries. We show this work that when boundary gapped by $s_{\pm}$-wave superconductivity, topological superconductor (BTRITSC) characterized be realized corresponding boundary. Since dimension BTRITSC is lower than bulk one, whole system second-order superconductor. When further cut open, Majorana Kramers pairs modes will appear corners hinges considered sample dimensions. Furthermore, magnetic field gap hinge three-dimensional lead to realization third-order with corner modes. Our proposal potentially insulator-superconductor heterostructures iron-based superconductors whose normal take desired inverted structures.