Universal theory of tunable second-order topological corner states induced by interlayer coupling in twist bilayer Chern insulators

TL;DR

This paper develops a universal theoretical framework for tunable second-order topological corner states in bilayer Chern insulators, showing how interlayer coupling and twist angles control their existence and position, enabling design of advanced topological materials.

Contribution

It introduces a universal theory linking twist angles and interlayer coupling to the emergence and control of second-order topological corner states in bilayer Chern insulators.

Findings

Corner states depend on twist angle and normal angles of the sides.

Position of corner states can be precisely controlled by twist angle.

The theory applies broadly to design higher-order topological materials.

Abstract

We propose a universal theory for tunable second-order topological corner states induced by interlayer coupling in bilayer Chern insulators with opposite Chern numbers. We demonstrate that the existence of the topological corner state is determined by the relationship between the twist angle of the bilayer Chern insulators and the normal angles of the two sides of the corner. In addition, the position of these corner states can be sensitively controlled by the twist angle, as confirmed by a rigorous analysis of edge state theory. Our findings serve as a universal theory, opening avenues for the design and realization of higher-order topological materials.