Quantum Valley Hall Effect, Orbital Magnetism, and Anomalous Hall Effect in Twisted Multilayer Graphene Systems

We study the electronic structures and topological properties of (M+N)-layer twisted graphene systems. We consider the generic situation that N-layer graphene is placed on top of the other M-layer graphene and is twisted with respect to each other by an angle θ. In such twisted multilayer graphene systems, we find that there exist two low-energy flat bands for each valley emerging from the interface between the M layers and the N layers. These two low-energy bands in the twisted multilayer graphene system possess valley Chern numbers that are dependent on both the number of layers and the stacking chiralities. In particular, when the stacking chiralities of the M layers and N layers are opposite, the total Chern number of the two low-energy bands for each valley equals ±(M+N-2) (per spin). If the stacking chiralities of the M layers and the N layers are the same, then the total Chern number of the two low-energy bands for each valley is ±(M-N) (per spin). The valley Chern numbers of the low-energy bands are associated with large, valley-contrasting orbital magnetizations, suggesting the possible existence of orbital ferromagnetism and anomalous Hall effect once the valley degeneracy is lifted either externally by a weak magnetic field or internally by Coulomb interaction through spontaneous symmetry breaking. Such an orbital ferromagnetic state is characterized by chiral current loops circulating around the AA region of the moiré pattern, which can be experimentally detected.