Quantum Hall effect in gapped graphene heterojunctions

We model the quantum Hall effect in heterostructures made of two gapped graphene stripes with different gaps, Δ1 and Δ2. We consider two main situations, Δ1=0,Δ2≠0, and Δ1=−Δ2. They are different in a fundamental aspect: only the latter features kink states that, when intervalley coupling is absent, are protected against backscattering. We compute the two-terminal conductance of heterostructures with channel length up to 430 nm, in two transport configurations, parallel and perpendicular to the interface. By studying the effect of disorder on the transport along the boundary, we quantify the robustness of kink states with respect to backscattering. Transport perpendicular to the boundary shows how interface states open a backscattering channel for the conducting edge states, spoiling the perfect conductance quantization featured by the homogeneously gapped graphene Hall bars. Our results can be relevant for the study of graphene deposited on hexagonal boron-nitride, as well as to model graphene with an interaction-driven gapped phase with two equivalent phases separated by a domain wall.

Quantum anomalous Hall effect in graphene coupled to skyrmions

Skyrmions are topologically protected spin textures, characterized by a topological winding number N, that occur spontaneously in some magnetic materials. Recent experiments have demonstrated the capability to grow graphene on top Fe/Ir, a system that exhibits a two-dimensional skyrmion lattice. Here we show that a weak exchange coupling between the Dirac electrons in graphene and a two-dimensional skyrmion lattice withN = ±1 drives graphene into a quantum anomalous Hall phase, with a band gap in bulk, a Chern number C = 2N, and chiral edge states with perfect quantization of conductance G = 2N e2 h . Our findings imply that the topological properties of the skyrmion lattice can be imprinted in the Dirac electrons of graphene.

Edge states in graphene-like systems

The edges of graphene and graphene like systems can host localized states with evanescent wave function with properties radically different from those of the Dirac electrons in bulk. This happens in a variety of situations, that are reviewed here. First, zigzag edges host a set of localized non-dispersive state at the Dirac energy. At half filling, it is expected that these states are prone to ferromagnetic instability, causing a very interesting type of edge ferromagnetism. Second, graphene under the influence of external perturbations can host a variety of topological insulating phases, including the conventional quantum Hall effect, the quantum anomalous Hall (QAH) and the quantum spin Hall phase, in all of which phases conduction can only take place through topologically protected edge states. Here we provide an unified vision of the properties of all these edge states, examined under the light of the same one orbital tight-binding model. We consider the combined action of interactions, spin–orbit coupling and magnetic field, which produces a wealth of different physical phenomena. We briefly address what has been actually observed experimentally.