We propose new topological insulators in cerium filled skutterudite (FS) compounds based on ab initio calculations. We find that two compounds CeOs4As12 and CeOs4Sb12 are zero gap materials with band inversion between Os-d and Ce-f orbitals, which are thus parent compounds of two and three-dimensional topological insulators just like bulk HgTe. At low temperature, both compounds become topological Kondo insulators, which are Kondo insulators in the bulk, but have robust Dirac surface states on the boundary. This new family of topological insulators has two advantages compared to previous ones. First, they can have good proximity effect with other superconducting FS compounds to realize Majarona fermions. Second, the antiferromagnetism of CeOs4Sb12 at low temperature provides a way to realize the massive Dirac fermion with novel topological phenomena.

We study the generic band structures of the five-dimensional (5D) Weyl semimetal, in which the band degeneracies are 2D Weyl surfaces in the momentum space, and may have non-trivial linkings with each other if they carry nonzero second Chern numbers. We prove a number of theorems constraining the topological linking configurations of the Weyl surfaces, which can be viewed as a 5D generalization of the celebrated Doubling Theorem for 3D Weyl semimetal. As a direct physical consequence of these constraints, the 5D Weyl semimetal hosts a rich structure of topological boundary states. We show that on the 4D boundary of the 5D Weyl semimetal, there are 3D chiral Fermi hypersurfaces protected by bulk Weyl surfaces. On top of that, for bulk Weyl surfaces that are linked and carry nonzero second Chern numbers, the associated boundary 3D Fermi hypersurfaces will shrink to singularities at certain energies, which trace out a protected 1D Weyl nodal arc, in analogy to the Fermi arc on the 3D Weyl semimetal surface.

An 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 remained elusive experimentally for a long time. Here we report the experimental realization of thin films of an intrinsic magnetic TI, MnBi2Te4, by alternate growth of a Bi2Te3 quintuple layer and a MnTe bilayer with molecular beam epitaxy. The material shows the archetypical Dirac surface states in angle-resolved photoemission spectroscopy and is demonstrated to be an antiferromagnetic topological insulator with ferromagnetic surfaces by magnetic and transport measurements as well as first-principles calculations. The unique magnetic and topological electronic structures and their interplays enable the material to embody rich quantum phases such as quantum anomalous Hall insulators and axion insulators at higher temperature and in a well-controlled way.

Pure spin currents carry information in quantum spintronics and could play an essential role in the next generation low-energy-consumption electronics. Here, we theoretically predict that the magnetic field can induce a quantum spin current without a concomitant charge current in metals without time reversal symmetry T and inversion symmetry P but respect the combined PT symmetry. It is governed by the magnetic moment of the Bloch states on the Fermi surface, and can be regarded as a spinful generalization of the gyrotropic magnetic effect in P-broken metals. The effect is explicitly studied for a minimal model of an antiferromagnetic Dirac semimetal, where the experimental signature is proposed. We further propose candidate materials, including topological antiferromagnetic Dirac semimetals, Weyl semimetals and tenary Heusler compounds.

Erratum: Experimental Realization of an Intrinsic Magnetic Topological Insulator [Chin. Phys. Lett. 36 (2019) 076801] Yan Gong(龚演), Jingwen Guo(郭景文), Jiaheng Li(李佳恒), Kejing Zhu(朱科静), Menghan Liao(廖孟涵), Xiaozhi Liu(刘效治), Qinghua Zhang(张庆华), Lin Gu(谷林), Lin Tang(唐林), Xiao Feng(冯硝), Ding Zhang(张定), Wei Li(李渭), Canli Song(宋灿立), Lili Wang(王立莉), Pu Yu(于浦), Xi Chen(陈曦), Yayu Wang(王亚愚), Hong Yao(姚宏), Wenhui Duan(段文晖), Yong Xu(徐勇)1,4,6** , Shou-Cheng Zhang(张首晟), Xucun Ma(马旭村), Qi-Kun Xue(薛其坤)1,3,4** , Ke He(何珂)1,3,4** State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 Beijing Academy of Quantum Information Sciences, Beijing 100193 Collaborative Innovation Center of Quantum Matter, Beijing 100084 Institute for Advanced Study, Tsinghua University, Beijing 100084 RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan Stanford Center for Topological Quantum Physics, Department of Physics, Stanford University, Stanford, California 94305-4045, USA

Pure spin currents carry information in quantum spintronics and could play an essential role in the next generation low-energy-consumption electronics. Here, we theoretically predict that the magnetic field can induce a quantum spin current without a concomitant charge current in metals without time reversal symmetry [Formula: see text] and inversion symmetry [Formula: see text] but respect the combined [Formula: see text] symmetry. It is governed by the magnetic moment of the Bloch states on the Fermi surface, and can be regarded as a spinful generalization of the gyrotropic magnetic effect in [Formula: see text]-broken metals. The effect is explicitly studied for a minimal model of an antiferromagnetic Dirac semimetal, where the experimental signature is proposed. We further propose candidate materials, including topological antiferromagnetic Dirac semimetals, Weyl semimetals and tenary Heusler compounds.

The interplay of magnetism and topology is a key research subject in condensed matter physics, which offers great opportunities to explore emerging new physics, such as the quantum anomalous Hall (QAH) effect, axion electrodynamics, and Majorana fermions. However, these exotic physical effects have rarely been realized experimentally because of the lack of suitable working materials. Here, we predict a series of van der Waals layered MnBi2Te4-related materials that show intralayer ferromagnetic and interlayer antiferromagnetic exchange interactions. We find extremely rich topological quantum states with outstanding characteristics in MnBi2Te4, including an antiferromagnetic topological insulator with the long-sought topological axion states on the surface, a type II magnetic Weyl semimetal with one pair of Weyl points, as well as a collection of intrinsic axion insulators and QAH insulators in even- and odd-layer films, respectively. These notable predictions, if proven experimentally, could profoundly change future research and technology of topological quantum physics.

In the development of topological photonics, achieving three-dimensional topological insulators is of notable interest since it enables the exploration of new topological physics with photons and promises novel photonic devices that are robust against disorders in three dimensions. Previous theoretical proposals toward three-dimensional topological insulators use complex geometries that are challenging to implement. On the basis of the concept of synthetic dimension, we show that a two-dimensional array of ring resonators, which was previously demonstrated to exhibit a two-dimensional topological insulator phase, automatically becomes a three-dimensional topological insulator when the frequency dimension is taken into account. Moreover, by modulating a few of the resonators, a screw dislocation along the frequency axis can be created, which provides robust one-way transport of photons along the frequency axis. Demonstrating the physics of screw dislocation in a topological system has been a substantial challenge in solid-state systems. Our work indicates that the physics of three-dimensional topological insulators can be explored in standard integrated photonic platforms, leading to opportunities for novel devices that control the frequency of light.

We show that the Nielsen-Ninomiya no-go theorem still holds on a Floquet lattice: there is an equal number of right-handed and left-handed Weyl points in a three-dimensional Floquet lattice. However, in the adiabatic limit, where the time evolution of the low-energy subspace is decoupled from the high-energy subspace, we show that the bulk dynamics in the low-energy subspace can be described by Floquet bands with extra left- or right-handed Weyl points, despite the no-go theorem. Assuming adiabatic evolution of two bands, we show that the difference of the number of right-handed and left-handed Weyl points equals twice the winding number of the adiabatic Floquet operator over the Brillouin zone. Based on these findings, we propose a realization of purely left- or right-handed Weyl particles on a 3D lattice using a Hamiltonian obtained through dimensional reduction of a four-dimensional quantum Hall system. We argue that the breakdown of the adiabatic approximation on the surface facilitates unusual closed orbits of wave packets in an applied magnetic field, which traverse alternatively through the low-energy and high-energy sector of the spectrum.

Electrochemical intercalation of ions into the van der Waals gap of two-dimensional (2D) layered materials is a promising low-temperature synthesis strategy to tune their physical and chemical properties. It is widely believed that ions prefer intercalation into the van der Waals gap through the edges of the 2D flake, which generally causes wrinkling and distortion. Here we demonstrate that the ions can also intercalate through the top surface of few-layer MoS 2 and this type of intercalation is more reversible and stable compared to the intercalation through the edges. Density functional theory calculations show that this intercalation is enabled by the existence of natural defects in exfoliated MoS 2 flakes. Furthermore, we reveal that sealed-edge MoS 2 allows intercalation of small alkali metal ions ( e.g ., Li + and Na + ) and rejects large ions (e.g., K + ). These findings imply potential applications in developing functional 2D-material-based devices with high tunability and ion selectivity.

Doped semiconductors are the most important building elements for modern electronic devices 1 . In silicon-based integrated circuits, facile and controllable fabrication and integration of these materials can be realized without introducing a high-resistance interface 2 , 3 . Besides, the emergence of two-dimensional (2D) materials enables the realization of atomically thin integrated circuits 4 – 9 . However, the 2D nature of these materials precludes the use of traditional ion implantation techniques for carrier doping and further hinders device development 10 . Here, we demonstrate a solvent-based intercalation method to achieve p-type, n-type and degenerately doped semiconductors in the same parent material at the atomically thin limit. In contrast to naturally grown n-type S-vacancy SnS 2 , Cu intercalated bilayer SnS 2 obtained by this technique displays a hole field-effect mobility of ~40 cm 2 V −1 s −1 , and the obtained Co-SnS 2 exhibits a metal-like behaviour with sheet resistance comparable to that of few-layer graphene 5 . Combining this intercalation technique with lithography, an atomically seamless p–n–metal junction could be further realized with precise size and spatial control, which makes in-plane heterostructures practically applicable for integrated devices and other 2D materials. Therefore, the presented intercalation method can open a new avenue connecting the previously disparate worlds of integrated circuits and atomically thin materials.

Exciting advances have been made in artificial intelligence (AI) during the past decades. Among them, applications of machine learning (ML) and deep learning techniques brought human-competitive performances in various tasks of fields, including image recognition, speech recognition and natural language understanding. Even in Go, the ancient game of profound complexity, the AI player already beat human world champions convincingly with and without learning from human. In this work, we show that our unsupervised machines (Atom2Vec) can learn the basic properties of atoms by themselves from the extensive database of known compounds and materials. These learned properties are represented in terms of high dimensional vectors, and clustering of atoms in vector space classifies them into meaningful groups in consistent with human knowledge. We use the atom vectors as basic input units for neural networks and other ML models designed and trained to predict materials properties, which demonstrate significant accuracy.

Chiral Majorana fermion is a massless self-conjugate fermion which can arise as the edge state of certain two-dimensonal topological matters. It has been theoretically predicted and experimentally observed in a hybrid device of quantum anomalous Hall insulator and a conventional superconductor. Its closely related cousin, Majorana zero mode in the bulk of the corresponding topological matter, is known to be applicable in topological quantum computations. Here we show that the propagation of chiral Majorana fermions lead to the same unitary transformation as that in the braiding of Majorana zero modes, and propose a new platform to perform quantum computation with chiral Majorana fermions. A Corbino ring junction of the hybrid device can utilize quantum coherent chiral Majorana fermions to implement the Hadamard gate and the phase gate, and the junction conductance yields a natural readout for the qubit state.

Freestanding single bilayer Bi(111) is a two-dimensional topological insulator with edge states propagating along its perimeter. Given the interlayer coupling experimentally, the topological nature of Bi(111) thin films and the impact of the supporting substrate on the topmost Bi bilayer are still under debate. Here, combined with scanning tunneling microscopy and first-principles calculations, we systematically study the electronic properties of Bi(111) thin films grown on a NbSe2 substrate. Two types of nonmagnetic edge structures, i.e., a conventional zigzag edge and a 2 x 1 reconstructed edge, coexist alternately at the boundaries of single bilayer islands, the topological edge states of which exhibit remarkably different energy and spatial distributions. Prominent edge states are persistently visualized at the edges of both single and double bilayer Bi islands, regardless of the underlying thickness of Bi(111) thin films. We provide an explanation for the topological origin of the observed edge states that is verified with first-principles calculations. Our paper clarifies the long-standing controversy regarding the topology of Bi(111) thin films and reveals the tunability of topological edge states via edge modifications.

The exploration of intriguing topological quantum physics in stanene has attracted enormous interest but is challenged by lacking desirable material samples. The successful fabrication of monolayer stanene on PbTe(111) films with low-temperature molecular beam epitaxy and thorough characterizations of its atomic and electronic structures are reported here. In situ angle-resolved photoemission spectroscopy together with first-principles calculations identify two hole bands of p xy orbital with a spin-orbit coupling induced band splitting and meanwhile reveal an automatic passivation of p z orbital of stanene. Importantly, material properties are tuned by substrate engineering, realizing a decorated stanene sample with truly insulating bulk on Sr-doped PbTe. This finding paves a road for studies of stanene-based topological quantum effects and electronics.

Two-dimensional (2D) topological materials, including quantum spin/anomalous Hall insulators, have attracted intense research efforts owing to their promise for applications ranging from low-power electronics and high-performance thermoelectrics to fault-tolerant quantum computation. One key challenge is to fabricate topological materials with a large energy gap for room-temperature use. Stanene-the tin counterpart of graphene-is a promising material candidate distinguished by its tunable topological states and sizeable bandgap. Recent experiments have successfully fabricated stanene, but none of them have yet observed topological states. Here we demonstrate the growth of high-quality stanene on Cu(111) by low-temperature molecular beam epitaxy. Importantly, we discovered an unusually ultraflat stanene showing an in-plane s-p band inversion together with a spin-orbit-coupling-induced topological gap (~0.3 eV) at the Γ point, which represents a foremost group-IV ultraflat graphene-like material displaying topological features in experiment. The finding of ultraflat stanene opens opportunities for exploring two-dimensional topological physics and device applications.

A single atomic slice of α-tin—stanene—has been predicted to host the quantum spin Hall effect at room temperature, offering an ideal platform to study low-dimensional and topological physics. Although recent research has focused on monolayer stanene, the quantum size effect in few-layer stanene could profoundly change material properties, but remains unexplored. By exploring the layer degree of freedom, we discover superconductivity in few-layer stanene down to a bilayer grown on PbTe, while bulk α-tin is not superconductive. Through substrate engineering, we further realize a transition from a single-band to a two-band superconductor with a doubling of the transition temperature. In situ angle-resolved photoemission spectroscopy (ARPES) together with first-principles calculations elucidate the corresponding band structure. The theory also indicates the existence of a topologically non-trivial band. Our experimental findings open up novel strategies for constructing two-dimensional topological superconductors. Stanene is a single sheet of tin atoms. Here, it is shown that a few stacked layers of stanene can be a superconductor. Changing the thickness of the substrate modifies the form of superconductivity and critical temperature.

According to a widely held paradigm, a pair of Weyl points with opposite chirality mutually annihilate when brought together. In contrast, we show that such a process is strictly forbidden for Weyl points related by a mirror symmetry, provided that an effective two-band description exists in terms of orbitals with opposite mirror eigenvalue. Instead, such a pair of Weyl points convert into a nodal loop inside a symmetric plane upon the collision. Similar constraints are identified for systems with multiple mirrors, facilitating previously unreported nodal-line and nodal-chain semimetals that exhibit both Fermi-arc and drumhead surface states. We further find that Weyl points in systems symmetric under a π rotation composed with time reversal are characterized by an additional integer charge that we call helicity. A pair of Weyl points with opposite chirality can annihilate only if their helicities also cancel out. We base our predictions on topological crystalline invariants derived from relative homotopy theory, and we test our predictions on simple tight-binding models. The outlined homotopy description can be directly generalized to systems with multiple bands and other choices of symmetry.