The intricate interplay between non-trivial topology and magnetism in two-dimensional materials can lead to the emergence of interesting phenomena such as the quantum anomalous Hall effect. Here we investigate the quantum transport of both bulk crystal and exfoliated MnBi 2 Te 4 flakes in a field-effect transistor geometry. For the six septuple-layer device tuned into the insulating regime, we observe a large longitudinal resistance and zero Hall plateau, which are characteristics of an axion insulator state. The robust axion insulator state occurs in zero magnetic field, over a wide magnetic-field range and at relatively high temperatures. Moreover, a moderate magnetic field drives a quantum phase transition from the axion insulator phase to a Chern insulator phase with zero longitudinal resistance and quantized Hall resistance h/e 2 , where h is Planck's constant and e is electron charge. Our results pave the way for using even-number septuple-layer MnBi 2 Te 4 to realize the quantized topological magnetoelectric effect and axion electrodynamics in condensed matter systems. Finding novel topological quantum matter and topological phase transitions has been a central theme in modern physics and mate rial science. An outstanding example is the quantum anomalous Hall (QAH) effect, which was realized in magnetically doped topo logical insulators (TIs) in the absence of magnetic field 1-6. The axion insulator is another exotic topological phase that has zero Chern number but a finite topological Chern-Simons term 7. It was put forward as a promising platform for exploring the Majorana edge modes, quantized topological magnetoelectric coupling and axion electrodynamics in condensed matter 7-12. Previous attempts to con struct the axion insulator phase were mainly based on fabricating heterostructures of QAH films with different coercive fields 13-15 , which require complex epitaxial growth of magnetically doped TIs, and transport measurements at ultralow temperatures and finite magnetic fields. There is an urgent need for finding a stoichiometric material that can achieve a robust axion insulator state in zero magnetic field and high temperatures. Recently, the layered van der Waals compound MnBi 2 Te 4 has been theoretically predicted and experimentally verified to be a TI with interlayer antiferromagnetic (AFM) order 16-26. It is a rare stoichiometric material with coexisting topology and mag netism, and thus represents a perfect building block for complex topological-magnetic structures. Interestingly, it naturally fulfils

We report transport studies of Mn-doped Bi_{2}Te_{3} topological insulator (TI) films with an accurately controlled thickness grown by molecular beam epitaxy. We find that films thicker than five quintuple layers (QLs) exhibit the usual anomalous Hall effect for magnetic TIs. When the thickness is reduced to four QLs, however, characteristic features associated with the topological Hall effect (THE) emerge. More surprisingly, the THE vanishes again when the film thickness is further reduced to three QLs. Theoretical calculations demonstrate that the coupling between the top and bottom surface states at the dimensional crossover regime stabilizes the magnetic Skyrmion structure that is responsible for the THE.

The quantum anomalous Hall (QAH) effect, which has been realized in magnetic topological insulators (TIs), is the key to applications of dissipationless quantum Hall edge states in electronic devices. However, investigations and utilizations of the QAH effect are limited by the ultralow temperatures needed to reach full quantization-usually below 100 mK in either Cr- or V-doped (Bi,Sb) Te of the two experimentally confirmed QAH materials. Here it is shown that by codoping Cr and V magnetic elements in (Bi,Sb) Te TI, the temperature of the QAH effect can be significantly increased such that full quantization is achieved at 300 mK, and zero-field Hall resistance of 0.97 h/e is observed at 1.5 K. A systematic transport study of the codoped (Bi,Sb) Te films with varied Cr/V ratios reveals that magnetic codoping improves the homogeneity of ferromagnetism and modulates the surface band structure. This work demonstrates magnetic codoping to be an effective strategy for achieving high-temperature QAH effect in TIs.

The quantum anomalous Hall (QAH) systems are of great fundamental interest and of potential application because of dissipationless conduction without external magnetic field 1-9 . The QAH effect has been realized in magnetically doped topological insulator thin films 10-14 . However, full quantization requires extremely low temperature (T < 50 mK) in the initial works, though it was significantly improved with modulation doping or co-doping of magnetic elements 15,16 . Improved ferromagnetism was indicated in these thin films, yet a direct evidence of long-range ferromagnetic order is lacking. Herein, we present direct visualization of long-range ferromagnetic order in thin films of Cr and V co-doped (Bi,Sb) 2 Te 3 using low-temperature magnetic force microscopy with in-situ transport. The magnetization reversal process reveals a typical ferromagnetic domain behavior, i.e., domain nucleation and domain wall propagation, in contrast to much weaker magnetic signals observed in the end members, possibly due to superparamagnetic behavior [17][18][19] . The gate dependence of magnetic reversal indicates a significant role of bulk carrier-mediated exchange interactions. The observed long-range ferromagnetic order resolves one of the major challenges in QAH systems, and paves the way to high-temperature dissipationless conduction by exploring magnetic topological insulators. a)

The intrinsic antiferromagnetic topological insulator MnBi2Te4 provides an ideal platform for exploring exotic topological quantum phenomena. Recently, the Chern insulator and axion insulator phases have been realized in few-layer MnBi2Te4 devices at low magnetic field regime. However, the fate of MnBi2Te4 in high magnetic field has never been explored in experiment. In this work, we report transport studies of exfoliated MnBi2Te4 flakes in pulsed magnetic fields up to 61.5 T. In the high-field limit, the Chern insulator phase with Chern number C = −1 evolves into a robust zero Hall resistance plateau state. Nonlocal transport measurements and theoretical calculations demonstrate that the charge transport in the zero Hall plateau state is conducted by two counter-propagating edge states that arise from the combined effects of Landau levels and large Zeeman effect in strong magnetic fields. Our result demonstrates the intricate interplay among intrinsic magnetic order, external magnetic field, and nontrivial band topology in MnBi2Te4.