Chern Number Tunable Quantum Anomalous Hall Effect in Compensated Antiferromagnets

We propose to realize the quantum anomalous Hall effect (QAHE) in two-dimensional compensated antiferromagnets without net spin magnetization. We consider antiferromagnetic ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ as a concrete example. By breaking the parity-time ($\mathcal{P}\mathcal{T}$) symmetry of even-layer ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$, we find that the system can host the QAHE with a nonzero Chern number. We show that by controlling the antiferromagnetic spin configuration---for example, down/up/up/down that breaks $\mathcal{P}\mathcal{T}$ symmetry---tetralayer ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ can host a Chern number $|\mathcal{C}|=1$. Such spin configuration can be stabilized by pinning the spin orientations of the surfaces. Furthermore, via tuning the on-site orbital energy and vertical electric fields, we find rich QAHE phases with tunable Chern number of $|\mathcal{C}|=1,2,3$. In addition, we reveal that the edge states are layer selective and primarily located at the boundaries of the bottom and top layers. Our Letter not only proposes a scheme to realize Chern number tunable QAHE in antiferromagnets without net spin magnetization but also provides a platform for layer-selective dissipationless transport devices.