Quantum valley and subvalley Hall effect in large-angle twisted bilayer graphene

We study the quantum valley Hall effect and related domain wall modes in twisted bilayer graphene at a large commensurate angle. Due to the quantum valley and subvalley Hall effect, a small deviation from the commensurate angle generates two-dimensional conducting network patterns composed of one-dimensional domain walls, which can host non-Fermi-liquid behavior within an accessible temperature range. The domain wall modes can be manipulated using an external electric field and layer shifting, manifesting the physics of the celebrated Haldane and Semenoff models for the subvalley Dirac cones, living on the domain walls. These findings open up an alternative direction towards realizing the emergence and manipulation of topological quantum valley and subvalley Hall states and possible applications in valleytronics. Our theory can be generalized to many twisted bilayer systems, including twisted graphene, twisted $\ensuremath{\alpha}$-graphene, and twisted kagome bilayers at large-angle rotation.