Abstract
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 or , we show that there exist two distinct physical origins of the QAH effect at two different limits. For large exchange field , 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 , the four-band low-energy model Hamiltonian is reduced to a two-band extended Haldane model, giving rise to a nonzero Chern number at either or . In the presence of staggered AB sublattice potential , a topological phase transition occurs at from a QAH phase to a quantum valley Hall phase. We further find that the band gap responses at and are different when , , and are simultaneously considered. We also show that the QAH phase is robust against weak intrinsic spin-orbit coupling , and it transitions to a trivial phase when . Moreover, we use a tight-binding model to reproduce the ab initio method obtained band structures through doping magnetic atoms on and supercells of graphene, and explain the physical mechanisms of opening a nontrivial bulk gap to realize the QAH effect in different supercells of graphene.
3 More- Received 2 January 2012
DOI:https://doi.org/10.1103/PhysRevB.85.115439
©2012 American Physical Society