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

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 Cnz 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 MnBi2Te4/(Bi2Te3)m/MnBi2Te4 heterostructures, as well as the C=2 and C=4 phases in HgS and α-Ag2Te 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.