Engineering Corner States from Two-Dimensional Topological Insulators

Abstract

We theoretically demonstrate that the second-order topological insulator with robust corner states can be realized in two-dimensional $\mathbb{Z}_2$ topological insulators by applying an in-plane Zeeman field. The Zeeman field breaks the time-reversal symmetry and thus destroys the $\mathbb{Z}_2$ topological phase. Nevertheless, it respects some crystalline symmetries and thus can protect the higher-order topological phase. By taking the Kane-Mele model as a concrete example, we find that spin-helical edge states along zigzag boundaries are gapped out by the Zeeman field whereas the in-gap corner state at the intersection between two zigzag edges arises, which is independent of the field orientation. In this work, we further show that the corner states are robust against the out-of-plane Zeeman field, staggered sublattice potentials, Rashba spin-orbit coupling, and the buckling of honeycomb lattices, making them experimentally feasible. Similar behaviors can also be found in the well-known Bernevig-Hughes-Zhang model.