Higher-Order Band Topology in Twisted Bilayer Kagome Lattice

TL;DR

This paper demonstrates that twisted bilayer kagome lattices can host higher-order topological insulator phases with robust corner states, verified through theoretical models and topological invariants, and resilient to disorder and charge density waves.

Contribution

It establishes a connection between higher-order topological insulators and twisted bilayer kagome lattices, revealing a new way to realize and control such phases experimentally.

Findings

Topologically nontrivial bulk band gap arises due to twist-induced intervalley scattering.

Higher-order topological insulator phases are robust against disorder and charge density waves.

Corner states are verified by second Stiefel-Whitney number and fractional charges.

Abstract

Topologically protected corner states serve as a key indicator for two-dimensional higher-order topological insulators, yet they have not been experimentally identified in realistic materials. Here, by utilizing the effective tight-binding model and symmetry arguments, we establish a connection between higher-order topological insulators and twisted bilayer kagome lattices. We find that the topologically nontrivial bulk band gap arises in the twisted bilayer kagome lattice system due to twist-induced intervalley scattering, leading to the emergence of higher-order topological insulators with a range of commensurate twist angles, and the higher-order band topology is verified by the second Stiefel-Whitney number and fractionally quantized corner charges. Moreover, we investigate the influence of disorder and charge density wave order on the stability of higher-order topological insulator phases. The results show that the corner states of twisted bilayer kagome lattice systems are robust with respect to disorder and charge density wave. Our work not only provides a feasible approach to realize the readily controllable higher-order topological insulator phases by employing a simple twist technique, but also demonstrates that the twisted bilayer kagome lattice systems exhibit the robustness of higher-order band topology, making it feasible to check above prediction in experiments.