Higher-order topological superconductors based on weak topological insulators

TL;DR

This paper demonstrates the realization of higher-order topological superconductors from weak topological insulators by manipulating boundary states with superconductivity and magnetic fields, revealing new boundary modes and topological invariants.

Contribution

It introduces models for higher-order topological superconductors based on weak topological insulators, highlighting their boundary behaviors and topological invariants, with relevance to iron-based superconductors.

Findings

Higher-order TSCs with Majorana hinge and corner modes identified.

Boundary states can be characterized by surface Chern numbers and Z2 invariants.

Models effectively capture topology of iron-based superconductors.

Abstract

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