Quantum spin Hall effect from multi-scale band inversion in twisted bilayer Bi$_2$(Te$_{1-x}$Se$_x$)$_3$

TL;DR

This paper predicts that twisting bilayer Bi$_2$(Te$_{1-x}$Se$_x$)$_3$ induces a Moiré-scale topological phase transition, creating flat bands and edge states that could lead to new quantum materials and devices.

Contribution

It introduces twisted bilayer Bi$_2$(Te$_{1-x}$Se$_x$)$_3$ as a new Moiré material exhibiting Moiré-scale topological states driven by band inversion and edge states.

Findings

Coexistence of topological insulator and normal insulator domains in Moiré structure

Nearly flat bands formed by edge states at domain boundaries

Moiré-scale band inversion leading to topological states

Abstract

Moir\'e materials have become one of the most active fields in material science in recent years due to their high tunability, and their unique properties emerge from the Moir\'e-scale structure modulation. Here, we propose twisted bilayer Bi$_2$(Te$_{1-x}$Se$_x$)$_3$ as a new Moir\'e material where the Moir\'e-scale modulation induces a topological phase transition. We show, in twisted bilayer Bi$_2$(Te$_{1-x}$Se$_x$)$_3$, a topological insulator domain and a normal insulator domain coexist in the Moir\'e lattice structure, and edge states on the domain boundary make nearly flat bands that dominate the material properties. The edge states further contribute to a Moir\'e-scale band inversion, resulting in Moir\'e-scale topological states. There are corresponding Moir\'e-scale edge states and they are so to speak "edge state from edge state", which is a unique feature of twisted bilayer Bi$_2$(Te$_{1-x}$Se$_x$)$_3$. Our result not only proposes novel quantum phases in twisted bilayer Bi$_2$Te$_3$-family, but also suggests the twisting of stacking sensitive topological materials paves an avenue in the search for novel quantum materials and devices.