Quantum Anomalous Hall Effect in Low-buckled Honeycomb Lattice with In-plane Magnetization

With out-of-plane magnetization, the quantum anomalous Hall effect has been extensively studied in quantum wells and two-dimensional atomic crystal layers [1]. Here, we investigate the possibility of realizing quantum anomalous Hall effect (QAHE) in honeycomb lattices with in-plane magnetization. We show that the QAHE can only occur in low-buckled honeycomb lattice where both intrinsic and intrinsic Rashba spin-orbit coupling appear spontaneously. The extrinsic Rashba spin-orbit coupling is detrimental to this phase. In contrast to the out-of-plane magnetization induced QAHE, the QAHE from in-plane magnetization is achieved in the vicinity of the time reversal symmetric momenta at $M$ points rather than Dirac points. In monolayer case, the QAHE can be characterized by Chern number $\mathcal{C}=\pm 1$ whereas additional phases with Chern number $\mathcal{C}=\pm 2$ appear in chiral stacked bilayer system. The Chern number strongly depends on the orientation of the magnetization. The bilayer system also provides additional tunability via out-of-plane electric field, which can reduce the critical magnetization strength required to induce QAHE. It can also lead to topological phase transitions from $\mathcal{C}=\pm 2$ to $\pm1$ and finally to $0$. [1] Review article: arXiv:1509.09016