Higher-order topological superconductors based on weak topological insulators

Higher-order topological phases host robust boundary states at the boundary of the boundary, which can be interpreted from their boundary topology. In this work, we show that based on the surface states of a weak topological insulator, the interplay between superconductors and magnetic fields can lead to the various helical or chiral Majorana hinge modes and even corner modes. Particularly, the obtained higher-order topological superconductors (TSCs) can be attributed to their certain boundaries, surfaces, or hinges, which naturally behave as a TSC in DIII or D symmetry class. Correspondingly, these higher-order TSCs can be characterized by the boundary topological invariants, such as surface Chern numbers or surface Z2 topological invariants for surface TSCs. Remarkably, some chiral hinge states naturally form the Majorana interference loop without complicated heterostructure, revealing the exceptional property of higher-order TSCs. Our models not only can be realized in iron-based superconductors with desired inverted band structures and superconducting pairings, but also pave the way to the implementation of quantum interference device from the higher-order topological matters.