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A quantum anomalous Hall (QAH) state is a two-dimensional topological insulating state that has a quantized Hall resistance of h /( Ce 2 ) and vanishing longitudinal resistance under zero magnetic field (where h is the Planck constant, e is the elementary charge, and the Chern number C is an integer) 1 , 2 . The QAH effect has been realized in magnetic topological insulators 3 – 9 and magic-angle twisted bilayer graphene 10 , 11 . However, the QAH effect at zero magnetic field has so far been realized only for C  = 1. Here we realize a well quantized QAH effect with tunable Chern number (up to C  = 5) in multilayer structures consisting of alternating magnetic and undoped topological insulator layers, fabricated using molecular beam epitaxy. The Chern number of these QAH insulators is determined by the number of undoped topological insulator layers in the multilayer structure. Moreover, we demonstrate that the Chern number of a given multilayer structure can be tuned by varying either the magnetic doping concentration in the magnetic topological insulator layers or the thickness of the interior magnetic topological insulator layer. We develop a theoretical model to explain our experimental observations and establish phase diagrams for QAH insulators with high, tunable Chern number. The realization of such insulators facilitates the application of dissipationless chiral edge currents in energy-efficient electronic devices, and opens up opportunities for developing multi-channel quantum computing and higher-capacity chiral circuit interconnects. The number of edge channels in quantum anomalous Hall insulators is controlled by varying either the magnetic dopant concentration or the interior spacer layer thickness, yielding Chern numbers up to 5.

The properties of van der Waals (vdW) materials often vary dramatically with the atomic stacking order between layers, but this order can be difficult to control. Trilayer graphene (TLG) stacks in either a semimetallic ABA or a semiconducting ABC configuration with a gate-tunable band gap, but the latter has only been produced by exfoliation. Here we present a chemical vapor deposition approach to TLG growth that yields greatly enhanced fraction and size of ABC domains. The key insight is that substrate curvature can stabilize ABC domains. Controllable ABC yields ~59% were achieved by tailoring substrate curvature levels. ABC fractions remained high after transfer to device substrates, as confirmed by transport measurements revealing the expected tunable ABC band gap. Substrate topography engineering provides a path to large-scale synthesis of epitaxial ABC-TLG and other vdW materials. The semiconducting ABC configuration of trilayer graphene is more challenging to grow on large scales than its semimetallic ABA counterpart. Here, an approach to trilayer growth via chemical vapor deposition is presented that utilizes substrate curvature to yield enhanced fraction and size of ABC domains.

The discovery of Weyl semimetals (WSMs) has fueled tremendous interest in condensed matter physics. The realization of WSMs requires the breaking of either inversion symmetry (IS) or time-reversal symmetry (TRS). WSMs can be categorized into type-I and type-II WSMs, which are characterized by untilted and strongly tilted Weyl cones, respectively. Type-I WSMs with breaking of either IS or TRS and type-II WSMs with solely broken IS have been realized experimentally, but a TRS-breaking type-II WSM still remains elusive. In this article, we report transport evidence for a TRS-breaking type-II WSM observed in the intrinsic antiferromagnetic topological insulatorMn(Bi1−xSbx)2Te4under magnetic fields. This state is manifested by the electronic structure transition caused by the spin-flop transition. The transition results in an intrinsic anomalous Hall effect and negativec-axis longitudinal magnetoresistance attributable to the chiral anomaly in the ferromagnetic phases of lightly hole-doped samples. Our results establish a promising platform for exploring the underlying physics of the long-sought, ideal TRS-breaking type-II WSM.

An axion insulator is a three-dimensional (3D) topological insulator (TI), in which the bulk maintains the time-reversal symmetry or inversion symmetry but the surface states are gapped by surface magnetization. The axion insulator state has been observed in molecular beam epitaxy (MBE)-grown magnetically doped TI sandwiches and exfoliated intrinsic magnetic TI MnBi 2 Te 4 flakes with an even number layer. All these samples have a thickness of ~ 10 nm, near the 2D-to-3D boundary. The coupling between the top and bottom surface states in thin samples may hinder the observation of quantized topological magnetoelectric response. Here, we employ MBE to synthesize magnetic TI sandwich heterostructures and find that the axion insulator state persists in a 3D sample with a thickness of ~ 106 nm. Our transport results show that the axion insulator state starts to emerge when the thickness of the middle undoped TI layer is greater than ~ 3 nm. The 3D hundred-nanometer-thick axion insulator provides a promising platform for the exploration of the topological magnetoelectric effect and other emergent magnetic topological states, such as the high-order TI phase. A zero Hall conductance plateau has been taken as evidence of the axion insulator state in magnetically doped topological insulator heterostructures, but it can also originate from surface state hybridization. Here the authors establish such a state in a ~106 nm thick sample, where hybridization is negligible.

Rare-earth monopnictides are a family of materials simultaneously displaying complex magnetism, strong electronic correlation, and topological band structure. The recently discovered emergent arc-like surface states in these materials have been attributed to the multi-wave-vector antiferromagnetic order, yet the direct experimental evidence has been elusive. Here we report observation of non-collinear antiferromagnetic order with multiple modulations using spin-polarized scanning tunneling microscopy. Moreover, we discover a hidden spin-rotation transition of single-to-multiple modulations 2 K below the Néel temperature. The hidden transition coincides with the onset of the surface states splitting observed by our angle-resolved photoemission spectroscopy measurements. Single modulation gives rise to a band inversion with induced topological surface states in a local momentum region while the full Brillouin zone carries trivial topological indices, and multiple modulation further splits the surface bands via non-collinear spin tilting, as revealed by our calculations. The direct evidence of the non-collinear spin order in NdSb not only clarifies the mechanism of the emergent topological surface states, but also opens up a new paradigm of control and manipulation of band topology with magnetism. Several recent experimental studies have found disconnected Fermi surface arcs emerging below the Neel temperature in several rare-earth mono-pnictides. While these electronic states have been attributed to a non-collinear antiferromagnetic order, experimental evidence of this has been lacking. Here Huang et al demonstrate the emergence of non-collinear antiferromagnetic order using spin-polarized scanning tunnelling microscopy.

Dirac and Weyl semimetals are a central topic of contemporary condensed matter physics, and the discovery of new compounds with Dirac/Weyl electronic states is crucial to the advancement of topological materials and quantum technologies. Here we show a widely applicable strategy that uses high configuration entropy to engineer relativistic electronic states. We take the A MnSb 2 ( A = Ba, Sr, Ca, Eu, and Yb) Dirac material family as an example and demonstrate that mixing of Ba, Sr, Ca, Eu and Yb at the A site generates the compound (Ba 0.38 Sr 0.14 Ca 0.16 Eu 0.16 Yb 0.16 )MnSb 2 (denoted as A 5 MnSb 2 ), giving access to a polar structure with a space group that is not present in any of the parent compounds. A 5 MnSb 2 is an entropy-stabilized phase that preserves its linear band dispersion despite considerable lattice disorder. Although both A 5 MnSb 2 and A MnSb 2 have quasi-two-dimensional crystal structures, the two-dimensional Dirac states in the pristine A MnSb 2 evolve into a highly anisotropic quasi-three-dimensional Dirac state triggered by local structure distortions in the high-entropy phase, which is revealed by Shubnikov–de Haas oscillations measurements. Manipulating the electronic properties of topological semimetals is a central goal of modern condensed matter physics research. Here, the authors demonstrate how a high-entropy engineering approach allows for the tuning of the crystal structure and the electronic states in a Dirac semimetal.

Over the last decade, the possibility of realizing topological superconductivity (TSC) has generated much excitement. TSC can be created in electronic systems where the topological and superconducting orders coexist, motivating the continued exploration of candidate material platforms to this end. Here, we use molecular beam epitaxy (MBE) to synthesize heterostructures that host emergent interfacial superconductivity when a non-superconducting antiferromagnet (FeTe) is interfaced with a topological insulator (TI) (Bi, Sb) 2 Te 3 . By performing in-vacuo angle-resolved photoemission spectroscopy (ARPES) and ex-situ electrical transport measurements, we find that the superconducting transition temperature and the upper critical magnetic field are suppressed when the chemical potential approaches the Dirac point. We provide evidence to show that the observed interfacial superconductivity and its chemical potential dependence is the result of the competition between the Ruderman-Kittel-Kasuya-Yosida-type ferromagnetic coupling mediated by Dirac surface states and antiferromagnetic exchange couplings that generate the bicollinear antiferromagnetic order in the FeTe layer. The authors study (Bi,Sb) 2 Te 3 /FeTe bilayers, which feature emergent superconductivity at the interface with T c  ~ 12 K. Through angle-resolved photoemission spectroscopy and electrical transport measurements, they argue that the Dirac-fermion-mediated Ruderman-Kittel-Kasuya-Yosida-type interaction weakens antiferromagnetic order in FeTe layer, allowing for superconductivity.

We use circular dichroism (CD) in time- and angle-resolved photoemission spectroscopy (trARPES) to measure the femtosecond charge dynamics in the topological insulator (TI) Bi 2 Te 3 . We detect clear CD signatures from topological surface states (TSS) and surface resonance (SR) states. In time-resolved measurements, independently from the pump polarization or intensity, the CD shows a dynamics which provides access to the unexplored electronic evolution in unoccupied states of Bi 2 Te 3 . In particular, we are able to disentangle the unpolarized electron dynamics in the bulk states from the spin-textured TSS and SR states on the femtosecond timescale. Our study demonstrates that photoexcitation mainly involves the bulk states and is followed by sub-picosecond transport to the surface. This provides essential details on intra- and interband scattering in the relaxation process of TSS and SR states. Our results reveal the significant role of SRs in the subtle ultrafast interaction between bulk and surface states of TIs.

Topological insulators represent a new quantum state of matter that are insulating in the bulk but metallic on the edge or surface. In the Dirac surface state, it is well-established that the electron spin is locked with the crystal momentum. Here we report a new phenomenon of the spin texture locking with the orbital texture in a topological insulator Bi 2 Se 3 . We observe light-polarization-dependent spin texture of both the upper and lower Dirac cones that constitutes strong evidence of the orbital-dependent spin texture in Bi 2 Se 3 . The different spin texture detected in variable polarization geometry is the manifestation of the spin-orbital texture in the initial state combined with the photoemission matrix element effects. Our observations provide a new orbital degree of freedom and a new way of light manipulation in controlling the spin structure of the topological insulators that are important for their future applications in spin-related technologies. Topological insulators like bismuth selenide exhibit Dirac surface states in which the electron spin is locked with the crystal momentum. Using spin- and angle-resolved photoemission spectroscopy, the authors observe a new kind of coupling between the spin and orbital texture of the Dirac cones.

The Dirac materials, such as graphene and three-dimensional topological insulators, have attracted much attention because they exhibit novel quantum phenomena with their low energy electrons governed by the relativistic Dirac equations. One particular interest is to generate Dirac cone anisotropy so that the electrons can propagate differently from one direction to the other, creating an additional tunability for new properties and applications. While various theoretical approaches have been proposed to make the isotropic Dirac cones of graphene into anisotropic ones, it has not yet been met with success. There are also some theoretical predictions and/or experimental indications of anisotropic Dirac cone in novel topological insulators and AMnBi 2 (A = Sr and Ca) but more experimental investigations are needed. Here we report systematic high resolution angle-resolved photoemission measurements that have provided direct evidence on the existence of strongly anisotropic Dirac cones in SrMnBi 2 and CaMnBi 2 . Distinct behaviors of the Dirac cones between SrMnBi 2 and CaMnBi 2 are also observed. These results have provided important information on the strong anisotropy of the Dirac cones in AMnBi 2 system that can be governed by the spin-orbital coupling and the local environment surrounding the Bi square net.