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 MnBi$_2$Te$_4$ as a concrete example. \textcolor{blue}{By breaking the parity-time ($\mathcal{PT}$) symmetry of even-layer MnBi$_2$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 $\mathcal{PT}$ symmetry, tetralayer MnBi$_2$Te$_4$ can host a Chern number $\mathcal{C}=-1$. Such spin configuration can be stabilized by pinning the spin orientations of the surfaces. \textcolor{blue}{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 locate at the boundaries of the bottom and top layers. Our work 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.