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

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 ${\mathrm{Bi}}_{2}{({\mathrm{Te}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x})}_{3}$ as a moir\'e material where the moir\'e-scale modulation induces a topological phase transition. We show, in twisted bilayer ${\mathrm{Bi}}_{2}{({\mathrm{Te}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x})}_{3}$, 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 ${\mathrm{Bi}}_{2}{({\mathrm{Te}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x})}_{3}$. Our result not only proposes characteristic quantum phases in twisted bilayer ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ family, but also suggests the twisting of stacking-sensitive topological materials paves an avenue in the search for novel quantum materials and devices.