Symmetry-driven anisotropic coupling effect in antiferromagnetic topological insulator: Mechanism for high-Chern-number quantum anomalous Hall state

Abstract: Antiferromagnetic (AFM) topological insulators (TIs), which host magnetically gapped Dirac-cone surface states and exhibit many exotic physical phenomena, have attracted great attention. Here, we find that the coupled surface states can be intertwined to give birth to a set of $2n$ unique new Dirac cones, dubbed intertwined Dirac cones, through the anisotropic coupling enforced by crystalline $n$-fold ($n=2, 3, 4, 6$) rotation symmetry $C_{nz}$ in the presence of a $PT$-symmetry breaking potential, for example, an electric field. Interestingly, we also find that the warping effect further drives the intertwined Dirac-cone state into a quantum anomalous Hall phase with a high Chern number ($C=n$). Then, based on first-principles calculations, we have explicitly demonstrated six intertwined Dirac cones and a Chern insulating phase with a high Chern number ($C=3$) in MnBi$2$Te$_4$$/$(Bi$_2$Te$_3$)${\mathrm{m}}/$MnBi$_2$Te$_4$ heterostructures, as well as the $C=2$ and $C=4$ phases in HgS and $\alpha$-Ag$_2$Te films, respectively. This work discovers the intertwined Dirac-cone state in AFM TI thin films, which reveals a mechanism for designing the quantum anomalous Hall state with a high Chern number and also paves a way for studying highly tunable high-Chen-number flat bands of twistronics.