The quantized version of the anomalous Hall effect has been predicted to occur in magnetic topological insulators, but the experimental realization has been challenging. Here, we report the observation of the quantum anomalous Hall (QAH) effect in thin films of chromium-doped (Bi,Sb)2Te3, a magnetic topological insulator. At zero magnetic field, the gate-tuned anomalous Hall resistance reaches the predicted quantized value of h/e(2), accompanied by a considerable drop in the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes, whereas the Hall resistance remains at the quantized value. The realization of the QAH effect may lead to the development of low-power-consumption electronics.

Topological insulators (TIs) are quantum materials with insulating bulk and topologically protected metallic surfaces with Dirac-like band structure. The most challenging problem faced by current investigations of these materials is the existence of signifi cant bulk conduction. Here we show how the band structure of topological insulators can be engineered by molecular beam epitaxy growth of (Bi 1 − x Sb x ) 2 Te 3 ternary compounds. The topological surface states are shown to exist over the entire composition range of (Bi 1 − x Sb x ) 2 Te 3 , indicating the robustness of bulk Z 2 topology. Most remarkably, the band engineering leads to ideal TIs with truly insulating bulk and tunable surface states across the Dirac point that behave like one-quarter of graphene. This work demonstrates a new route to achieving intrinsic quantum transport of the topological surface states and designing conceptually new topologically insulating devices based on wellestablished semiconductor technology.

Intrinsic magnetic topological insulator (TI) is a stoichiometric magnetic compound possessing both inherent magnetic order and topological electronic states. Such a material can provide a shortcut to various novel topological quantum effects but remains elusive experimentally so far. Here, we report the experimental realization of high-quality thin films of an intrinsic magnetic TI-MnBi2Te4-by alternate growth of a Bi2Te3 quintuple-layer and a MnTe

The breaking of time reversal symmetry in topological insulators may create previously unknown quantum effects. We observed a magnetic quantum phase transition in Cr-doped Bi2(SexTe1-x)3 topological insulator films grown by means of molecular beam epitaxy. Across the critical point, a topological quantum phase transition is revealed through both angle-resolved photoemission measurements and density functional theory calculations. We present strong evidence that the bulk band topology is the fundamental driving force for the magnetic quantum phase transition. The tunable topological and magnetic properties in this system are well suited for realizing the exotic topological quantum phenomena in magnetic topological insulators.

Topological insulators (TI) are a new class of quantum materials with insulating bulk enclosed by topologically protected metallic boundaries 1-3 . The surface states of three-dimensional TIs have spin helical Dirac structure 4-6 , and are robust against time reversal invariant perturbations. This extraordinary property is notably exemplified by the absence of backscattering by nonmagnetic impurities 7-9 and the weak antilocalization (WAL) of Dirac fermions 10-12 . Breaking the time reversal symmetry (TRS) by magnetic element doping is predicted to create a variety of exotic topological magnetoelectric effects 13-18 . Here we report transport studies on magnetically doped TI Cr-Bi 2 Se 3 . With increasing Cr concentration, the low temperature electrical conduction exhibits a characteristic crossover from WAL to weak localization (WL). In the heavily doped regime where WL dominates at the ground state, WAL reenters as temperature rises, but can be driven back to WL by strong magnetic field. These complex phenomena can be explained by a unified picture involving the evolution of Berry phase with the energy gap opened by magnetic impurities. This work demonstrates an effective way to manipulate the topological transport properties of the TI surface states by TRS-breaking perturbations.Bi 2 Se 3 is an ideal three-dimensional TI due to its large bulk energy gap (~ 300meV) and a Dirac point located well outside the bulk bands 19,20 . On the surface of magnetically doped Bi 2 Se 3 single crystals, Angle-resolved photoemission spectroscopy (ARPES) has revealed the opening of an energy gap at the Dirac point 21 and the creation of odd multiples of Dirac

Thin films of magnetically doped topological insulators Cr(0.22) (Bi(x) Sb(1-x) )(1.78) Te(3) are found to possess carrier-independent long-range ferromagnetic order with perpendicular magnetic anisotropy. The anomalous Hall resistance is greatly enhanced, up to one quarter of quantum Hall resistance, by depletion of the carriers. The results demonstrate this material as a promising system to realize the quantized anomalous Hall effect.

The stability of metal−organic frameworks (MOFs) typically decreases with an increasing number of defects, limiting the number of defects that can be created and limiting catalytic and other applications. Herein, we use a hemilabile (Hl) linker to create up to a maximum of six defects per cluster in UiO-66. We synthesized hemilabile UiO-66 (Hl-UiO-66) using benzene dicarboxylate (BDC) as linker and 4-sulfonatobenzoate (PSBA) as the hemilabile linker. The PSBA acts not only as a modulator to create defects but also as a coligand that enhances the stability of the resulting defective framework. Furthermore, upon a postsynthetic treatment in H 2 SO 4 , the average number of defects increases to the optimum of six missing BDC linkers per cluster (three per formula unit), leaving the Zr-nodes on average sixfold coordinated. Remarkably, the thermal stability of the materials further increases upon this treatment. Periodic density functional theory calculations confirm that the hemilabile ligands strengthen this highly defective structure by several stabilizing interactions. Finally, the catalytic activity of the obtained materials is evaluated in the acid-catalyzed isomerization of α-pinene oxide. This reaction is particularly sensitive to the Brønsted or Lewis acid sites in the catalyst. In comparison to the pristine UiO-66, which mainly possesses Brønsted acid sites, the Hl-UiO-66 and the postsynthetically treated Hl-UiO-66 structures exhibited a higher Lewis acidity and an enhanced activity and selectivity. This is further explored by CD 3 CN spectroscopic sorption experiments. We have shown that by tuning the number of defects in UiO-66 using PSBA as the hemilabile linker, one can achieve highly defective and stable MOFs and easily control the Brønsted to Lewis acid ratio in the materials and thus their catalytic activity and selectivity.

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...