Microscopic theory of quantum anomalous Hall effect in graphene

We present a microscopic theory to give a physical picture of the formation of the quantum anomalous Hall (QAH) effect in magnetized graphene coupled with Rashba spin-orbit coupling. Based on a continuum model at valley K or K', we show that there exist two distinct physical origins of the QAH effect at two different limits. For large exchange field M, the quantization of Hall conductance in the absence of Landau-level quantization can be regarded as a summation of the topological charges carried by skyrmions from real-spin textures and merons from AB sublattice pseudospin textures, while for strong Rashba spin-orbit coupling lambda(R), the four-band low-energy model Hamiltonian is reduced to a two-band extended Haldane model, giving rise to a nonzero Chern number C = 1 at either K or K'. In the presence of staggered AB sublattice potential U, a topological phase transition occurs at U = M from a QAH phase to a quantum valley Hall phase. We further find that the band gap responses at K and K' are different when lambda(R), M, and U are simultaneously considered. We also show that the QAH phase is robust against weak intrinsic spin-orbit coupling lambda(SO), and it transitions to a trivial phase when lambda(SO) > ( root M-2 + lambda(2)(R) + M)/2. Moreover, we use a tight-binding model to reproduce the ab initio method obtained band structures through doping magnetic atoms on 3 x 3 and 4 x 4 supercells of graphene, and explain the physical mechanisms of opening a nontrivial bulk gap to realize the QAH effect in different supercells of graphene.