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 with $N = \pm 1$ drives graphene into a quantum anomalous Hall phase, with a band-gap in bulk, a Chern number ${\cal C}=2N$ and chiral edge states with perfect quantization of conductance $G = 2N\frac{e^2}{h}$ . Our findings imply that the topological properties of the Skyrmion lattice can be imprinted in the Dirac electrons of graphene.