Quantum spin Hall effect from multiscale band inversion in twisted bilayer Bi2(Te1-xSex)3

Moire 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 moire-scale structure modulation. Here, we propose twisted bilayer Bi2(Te1-xSex)3 as a moire material where the moire-scale modulation induces a topological phase transition. We show, in twisted bilayer Bi2(Te1-xSex)3, a topological insulator domain and a normal insulator domain coexist in the moire 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 moire-scale band inversion, resulting in moire-scale topological states. There are corresponding moire-scale edge states and they are so to speak "edge state from edge state," which is a unique feature of twisted bilayer Bi2(Te1-xSex)3. Our result not only proposes characteristic quantum phases in twisted bilayer Bi2Te3 family, but also suggests the twisting of stacking-sensitive topological materials paves an avenue in the search for novel quantum materials and devices.