Higher-order topological superconductors based on weak topological insulators

High-order topological phases host robust boundary states at the of boundary, which can be interpreted from their topology. In this work, considering interplay between superconductors and magnetic fields to gap surface three-dimensional weak insulators, we show that second-order (TSCs) featuring helical or chiral Majorana hinge modes third-order TSC corner realized. Remarkably, higher-order TSCs in our models attributed certain boundaries, surfaces, hinges, naturally behave as first-order DIII D symmetry class. Correspondingly, these characterized by invariants, such Chern numbers $Z_2$ invariants for TSCs. Our effectively capture topology iron-based with desired inverted band structures superconducting pairings.