Magnetoelectric control of topological phases in graphene

Topological antiferromagnetic (AFM) spintronics is an emerging field of research, which involves the topological electronic states coupled to the AFM order parameter known as the N$acute{rm e}$el vector. The control of these states is envisioned through manipulation of the N$acute{rm e}$el vector by spin-orbit torques driven by electric currents. Here we propose a different approach favorable for low-power AFM spintronics, where the control of the topological states in a two-dimensional material, such as graphene, is performed via the proximity effect by the voltage induced switching of the N$acute{rm e}$el vector in an adjacent magnetoelectric AFM insulator, such as chromia. Mediated by the symmetry protected boundary magnetization and the induced Rashba-type spin-orbit coupling at the interface between graphene and chromia, the emergent topological phases in graphene can be controlled by the N$acute{rm e}$el vector. Using density functional theory and tight-binding Hamiltonian approaches, we model a graphene/Cr2O3 (0001) interface and demonstrate non-trivial band gap openings in the graphene Dirac bands asymmetric between the K and K valleys. This gives rise to an unconventional quantum anomalous Hall effect (QAHE) with a quantized value of $2e^2/h$ and an additional step-like feature at a value close to $e^2/2h$, and the emergence of the spin-polarized valley Hall effect (VHE). Furthermore, depending on the N$acute{rm e}$el vector orientation, we predict the appearance and transformation of different topological phases in graphene across the $180^{circ}$ AFM domain wall, involving the QAHE, the valley-polarized QAHE and the quantum VHE (QVHE), and the emergence of the chiral edge state along the domain wall. These topological properties are controlled by voltage through magnetoelectric switching of the AFM insulator with no need for spin-orbit torques.