Microscopic theory of quantum anomalous Hall effect in graphene

Zhenhua Qiao; Hua Jiang; Xiao Li; Yugui Yao; Qian Niu

doi:10.1103/PhysRevB.85.115439

paper

Microscopic theory of quantum anomalous Hall effect in graphene

arXiv:1201.0543 · doi:10.1103/PhysRevB.85.115439

Abstract

We present a microscopic theory to give a physical picture of the formation of quantum anomalous Hall (QAH) effect in graphene due to a joint effect of Rashba spin-orbit coupling $λ_{R}$ and exchange field $M$ . Based on a continuum model at valley $K$ or $K^{'}$ , we show that there exist two distinct physical origins of QAH effect at two different limits. For $M / λ_{R} ≫ 1$ , 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 \emph{AB} sublattice pseudo-spin textures; while for $λ_{R} / M ≫ 1$ , the four-band low-energy model Hamiltonian is reduced to a two-band extended Haldane's model, giving rise to a nonzero Chern number $C = 1$ at either $K$ or $K^{'}$ . In the presence of staggered \emph{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 $λ_{R}$ , $M$ , and $U$ are simultaneously considered. We also show that the QAH phase is robust against weak intrinsic spin-orbit coupling $λ_{S O}$ , and it transitions a trivial phase when $λ_{S O} > (M^{2} + λ_{R}^{2} + M) /2$ . Moreover, we use a tight-binding model to reproduce the ab-initio method obtained band structures through doping magnetic atoms on $3 \times 3$ and $4 \times 4$ supercells of graphene, and explain the physical mechanisms of opening a nontrivial bulk gap to realize the QAH effect in different supercells of graphene.

10pages, ten figures

Microscopic theory of quantum anomalous Hall effect in graphene

Abstract

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