Helical networks in twisted bilayer graphene under interlayer bias

A twisted graphene bilayer exhibits a triangular Moire pattern in the local stacking, that smoothly alternates between the three basic types AA', AB', and BA'. Under an interlayer bias U, the latter two types develop a spectral gap, characterizsed by opposite valley Chern numbers. We show that for large enough Moire periods and bias, these regions become depleted electronically, and topologically protected helical modes appear at their boundaries. This gives rise to a delocalized topological network of the Chalker-Coddington type, composed of valley current vortices. This network can be tailored by controlled deposition of valley-mixing adsorbates, which block transmission in selected links, thus opening the possibility of custom topological nanoelectronics.