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.

Quantum anomalous Hall (QAH) effect in magnetic topological insulator (TI) is a novel transport phenomenon in which theThe realization of QAH effect requires that a two-dimensional (2D) material must be FM, topological, and insulating simultaneously 9 . Magnetically doped TIs have been proposed 1, 2, 10-12 and experimentally proved 3-6 to be an ideal material system for fulfilling these stringent requirements. For a 3D TI, the inverted bulk band structure ensures topologically protected metallic surface states (SSs), which become 2D when the film is sufficiently thin 13 . The spontaneous FM order induced by magnetic doping not only leads to the anomalous Hall effect, but also opens an energy gap at the Dirac point. When the Fermi level (E F ) lies within this gap, the only remaining conduction channel is the quasione-dimensional chiral edge state, which gives rise to quantized Hall resistance and vanishing longitudinal resistance at zero magnetic field 3, 14 . Up to date, the QAH effect has been observed in Cr or V doped (Bi,Sb) 2 Te 3 TI thin films with accurately controlled chemical composition and thickness grown by molecular beam epitaxy (MBE) 3-6 .The MBE-grown QAH insulator film studied here has a chemical formula Fig. 1a is a schematic drawing of the transport device, which is similar to that reported previously 3 .The film is manually scratched into a Hall bar geometry, and the SrTiO 3 substrate is used as the bottom gate oxide due to its large dielectric constant at low temperature. The Cr concentration, hence the density of local moment, is higher than that in the sample where the QAH effect was originally discovered 3 . As a result, the FM order forms at a higher Curie temperature T C = 24 K as determined by the temperature dependent anomalous Hall effect (supplementary Fig. S1). Another important consequence of higher Cr doping is that the sample becomes more disordered, which is crucial to the physics that will be discussed in this work.We first demonstrate the existence of QAH effect in this sample. Fig. 1b displays the gate voltage (V g ) dependence of the Hall resistance  yx (blue curve) and longitudinal resistance  xx (red curve) measured at T = 10 mK in a strong magnetic field B = 12 T applied perpendicular to the film. The  yx exhibits a plateau for -10 V < V g < 10 V with its maximum value close to 99.1% of the quantum resistance h/e 2 ~ 25.8 k. In the same V g range  xx shows a pronounced dip with its minimum value close to 0.1 h/e 2 . To show that the apparent Hall quantization in Fig. 1b is due to the QAH effect rather than conventional QH effect in high magnetic field, in Fig. 1c we display the field dependence of  yx measured at V g = -5 V, when  xx reaches a minimum in Fig. 1b. The Hall trace shows an abrupt jump at zero magnetic field, characteristic of the anomalous Hall effect.With increasing magnetic field, the  yx value increases gradually and approaches h/e 2 at 12 T. The  xx shown in Fig. 1d exhibits two sharp peaks at the coercive field H C , and decreases rapidly on b...

With molecular beam epitaxy, we grew uniformly vanadium-doped Bi2Se3 films which exhibit ferromagnetism with perpendicular magnetic anisotropy. A systematic study on the magneto-transport properties of the films revealed the crucial role of topological surface states in ferromagnetic coupling. The enhanced ferromagnetism with reduced carrier density can support quantum anomalous Hall phase in the films, though the anomalous Hall resistance is far from quantization due to high carrier density. The topological surface states of films exhibit a gap of ∼180 meV which is unlikely to be magnetically induced but may significantly influence the quantum anomalous Hall effect in the system.

Quantum anomalous Hall (QAH) effect is a quantum Hall effect that occurs without the need of external magnetic field. A system composed of multiple parallel QAH layers is an effective high Chern number QAH insulator and the key to the applications of the dissipationless chiral edge channels in low energy consumption electronics. Such a QAH multilayer can also be engineered into other exotic topological phases such as a magnetic Weyl semimetal with only one pair of Weyl points. This work reports the first experimental realization of QAH multilayers in the superlattices composed of magnetically doped (Bi,Sb) 2 Te 3 topological insulator and CdSe normal insulator layers grown by molecular beam epitaxy. The obtained multilayer samples show quantized Hall resistance h/Ne 2 , where h is the Planck's constant, e is the elementary charge and N is the number of the magnetic topological insulator layers, resembling a high Chern number QAH insulator. Keywords quantum anomalous Hall effect, multilayer, molecular beam epitaxy, chiral edge state A quantum anomalous Hall (QAH) insulator (or Chern insulator) possesses topologically nontrivial band structure characterized by a non-zero Chern number (C). At each edge of a QAH insulator, there are C dissipationless chiral edge channels which give rise to quantized Hall resistance h/Ce 2 (h is

The quantum anomalous Hall (QAH) effect in magnetic topological insulator (TI) represents a new state of matter originated from the interplay between topology and magnetism. The defining characteristics of the QAH ground state are the quantized Hall resistivity (ρyx) and vanishing longitudinal resistivity (ρxx) in the absence of external magnetic field. A fundamental question concerning the QAH effect is whether it is merely a zero-magnetic-field quantum Hall (QH) effect, or if it can host unique quantum phases and phase transitions that are unavailable elsewhere. The most dramatic departure of the QAH systems from other QH systems lies in the strong magnetic disorders that induce spatially random magnetization. Because disorder and magnetism play pivotal roles in the phase diagram of two-dimensional electron systems, the high degree of magnetic disorders in QAH systems may create novel phases and quantum critical phenomena. In this work, we perform systematic transport studies of a series of magnetic TIs with varied strength of magnetic disorders. We find that the ground state of QAH effect can be categorized into two distinct classes: the QAH insulator and anomalous Hall (AH) insulator phases, as the zero-magnetic-field counterparts of the QH liquid and Hall insulator in the QH systems. In the low disorder limit of the QAH insulator regime, we observe a universal quantized longitudinal resistance ρxx = h/e 2 at the coercive field. In the AH insulator regime, we find that a magnetic field can drive it to the QAH insulator phase through a quantum critical point with distinct scaling behaviors from that in the QH phase transition. We propose that the transmission between chiral edge states at domain boundaries, tunable by disorder and magnetic fields, is the key for determining the QAH ground state.

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We report electromagnetic and thermomagnetic transport studies on a magnetic topological insulator thin film Cr 0.15 (Bi 0.1 Sb 0.9 ) 1.85 Te 3 grown by molecular beam epitaxy. The temperature and gate voltage dependence of the anomalous Hall effect exhibits the typical behavior of a quantum anomalous Hall insulator. The anomalous Nernst effect (ANE) shows a sign reversal when the Fermi level is tuned across the charge neutrality point of the surface Dirac cone. We show that the ambi-polar behavior of the ANE can be explained by the semiclassical Mott relation, in conjunction with the ambi-polar Dirac band structure.

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