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 Z_{2} topological insulators by applying an in-plane Zeeman field. The Zeeman field breaks the time-reversal symmetry and thus destroys the 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. 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.