Metallic network of topological domain walls

We study the electronic and transport properties of a network of domain walls between insulating domains with opposite valley Chern numbers. We find that the network is semimetallic with Dirac dispersion near the charge neutrality point and the corresponding electronic states distribute along the domain walls. Near the charge neutrality point, we find quantized conductance in a nanoribbon with sawtooth domain wall edges that propagates along the boundaries and is robust against weak disorder. For a trident edged ribbon, we find a small energy gap due to the finite-size effect making the nanoribbon an insulator. When the Fermi energy is away from the charge neutrality point, all domain walls contribute to the conduction of current. Our results provide a comprehensive analysis of the electronic transport properties in a topological domain wall network that not only agrees qualitatively with experiments on marginally twisted bilayer graphene under a perpendicular electric field, but also can provide useful insights for designing low-power topological quantum devices.