Quantum Valley and Sub-valley Hall Effect in the Large Angle Twisted Bilayer Graphene

Abstract

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 sub-valley Hall effect, a small deviation from the commensurate angle generates two-dimensional conducting network patterns composed of one-dimensional domain wall conducting channels, which can induce non-Fermi liquid transport behavior within an accessible temperature range. The domain wall modes can be manipulated by using the layer shifting and external electric fields which, in turn, leads to the sub-valley Haldane and Semenoff masses on the domain wall modes. The large-angle twisted bilayer graphene and related materials can be a new setup to harness the quantum valley and sub-valley Hall effect with enhanced tunability.