Edge-state transport in twisted bilayer graphene

We investigate the electronic structure and transport properties of twisted bilayer graphene (TBLG) at a twist angle of $\ensuremath{\theta}\ensuremath{\approx}1.{696}^{\ensuremath{\circ}}$. Using a combination of molecular dynamics and tight-binding calculations, we find two superlattice gaps in the energy spectrum of the bulk, which emerge close to the Fermi level from the atomic rearrangement of the carbon atoms leading to a corrugation of the graphene sheets. Nanoribbons made from $1.{696}^{\ensuremath{\circ}}$-TBLG show edge-localized states inside the superlattice gaps. Applying the Green's function method, we demonstrate that the edge states carry electronic current with conductance values close to the conductance quantum. The edge states can generate a nonlocal resistance, which is not due to one-way transport at the edges but due to the fact that these states are localized only at certain edges of the system, depending on how the nanoribbon has been cut from the bulk.