The quantum anomalous Hall (QAH) state is a two-dimensional topological insulating state that has quantized Hall resistance of h/Ce 2 and vanishing longitudinal resistance under zero magnetic field, where C is called the Chern number 1,2 . The QAH effect has been realized in magnetic topological insulators (TIs) 3-9 and magic-angle twisted bilayer graphene 10,11 . Despite considerable experimental efforts, the zero magnetic field QAH effect has so far been realized only for C = 1. Here we used molecular beam epitaxy to fabricate magnetic TI multilayers and realized the QAH effect with tunable Chern number C up to 5. The Chern number of these QAH insulators is tuned by varying the magnetic doping concentration or the thickness of the interior magnetic TI layers in the multilayer samples. A theoretical model is developed to understand our experimental observations and establish phase diagrams for QAH insulators with tunable Chern numbers. The realization of QAH insulators with high tunable Chern numbers facilitates the potential applications of dissipationless chiral edge currents in energy-

Recently, MnBi 2 Te 4 has been demonstrated to be an intrinsic magnetic topological insulator and the quantum anomalous Hall (QAH) effect was observed in exfoliated MnBi 2 Te 4 flakes. Here, we used molecular beam epitaxy (MBE) to grow MnBi 2 Te 4 films with thickness down to 1 septuple layer (SL) and performed thickness-dependent transport measurements. We observed a nonsquare hysteresis loop in the antiferromagnetic state for films with thickness greater than 2 SL. The hysteresis loop can be separated into two AH components. We demonstrated that one AH component with the larger coercive field is from the dominant MnBi 2 Te 4 phase, whereas the other AH component with the smaller coercive field is from the minor Mn-doped Bi 2 Te 3 phase. The extracted AH component of the MnBi 2 Te 4 phase shows a clear even− odd layer-dependent behavior. Our studies reveal insights on how to optimize the MBE growth conditions to improve the quality of MnBi 2 Te 4 films.

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Engineering magnetic orders in topological insulators is critical to the realization of topological quantum phenomena such as the axion insulator state and the quantum anomalous Hall insulator state. Here we establish MnBi6Te10 as a tunable topological material platform where ferromagnetism and antiferromagnetism can be selectively obtained. We conduct a comprehensive measurement of ferromagnetic MnBi6Te10 bulk crystals via laser-based angle-resolved photoemission spectroscopy, and compare the results with those from their antiferromagnetic counterparts. For ferromagnetic MnBi6Te10, we observe a magnetically driven broken-symmetry gap of 15 meV at the topological surface state on the MnBi2Te4 termination, which disappears when the temperature is raised above the Curie temperature. In contrast, antiferromagnetic MnBi6Te10 exhibits gapless topological surface states on all terminations. We consider disorder in the form of Mn migration from MnBi2Te4 layers to the neighboring Bi2Te3 layers as a possible driving force for the delicate ferromagnetism. Our spectroscopic study establishes MnBi6Te10 as the first bulk MnBi2nTe3n+1 compound to host tunable topological orders due to its highly variable electronic and magnetic structures.