Interlayer Coupling Induced Topological Phase Transition to Higher Order

TL;DR

This paper demonstrates how interlayer coupling between $ ext{Z}_2$ topological insulators can induce a transition to higher-order topological phases with corner states, using theoretical models like Kane-Mele and BHZ.

Contribution

It introduces a universal method to engineer higher-order topological insulators via interlayer coupling of $ ext{Z}_2$ topological phases, supported by effective models and examples.

Findings

Corner states can be engineered by coupling $ ext{Z}_2$ topological insulators.

Interlayer coupling drives transition to higher-order topological phases.

Corner states can be realized in various topological systems, including quantum anomalous Hall systems.

Abstract

We theoretically find that the second-order topological insulator, i.e., corner states, can be engineered by coupling two copies of two-dimensional $\mathbb{Z}_2$ topological insulators with opposite spin-helicities. As concrete examples, we utilize Kane-Mele models (i.e., graphene with intrinsic spin-orbit coupling) to realize the corner states by setting the respective graphenes to be $\mathbb{Z}_2$ topological insulators with opposite intrinsic spin-orbit couplings. To exhibit its universality, we generalize our findings to other representative $\mathbb{Z}_2$ topological insulators, e.g., the Bernevig-Hughes-Zhang model. An effective model is presented to reveal the physical origin of corner states. We further show that the corner states can also be designed in other topological systems, e.g., by coupling quantum anomalous Hall systems with opposite Chern numbers. Our work suggests that interlayer coupling can be treated as a simple and efficient strategy to drive lower-order topological insulators to the higher-order ones.