Intrinsic magnetic topological insulators in van der Waals layered MnBi2Te4-family materials.

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.

Reversible and selective ion intercalation through the top surface of few-layer MoS2.

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 MoS2 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 MoS2 flakes. Furthermore, we reveal that sealed-edge MoS2 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.

Epitaxial growth of ultraflat stanene with topological band inversion.

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.

Three-Dimensional Chiral Lattice Fermion in Floquet Systems.

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.

Topological quantum computation based on chiral Majorana fermions.

The chiral Majorana fermion is a massless self-conjugate fermion which can arise as the edge state of certain 2D topological matters. It has been theoretically predicted and experimentally observed in a hybrid device of a quantum anomalous Hall insulator and a conventional superconductor. Its closely related cousin, the 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 leads to the same unitary transformation as that in the braiding of Majorana zero modes and propose a platform to perform quantum computation with chiral Majorana fermions. A Corbino ring junction of the hybrid device can use 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.

A three-dimensional photonic topological insulator using a two-dimensional ring resonator lattice with a synthetic frequency dimension.

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.

Conversion Rules for Weyl Points and Nodal Lines in Topological Media.

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.

Learning atoms for materials discovery.

Exciting advances have been made in artificial intelligence (AI) during recent 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 has already beat human world champions convincingly with and without learning from the 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 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.

Wave Function and Emergent SU(2) Symmetry in the ν_{T}=1 Quantum Hall Bilayer.

We propose a trial wave function for the quantum Hall bilayer system of total filling factor ν_{T}=1 at a layer distance d to magnetic length ℓ ratio d/ℓ=κ_{c1}≈1.1, where the lowest charged excitation is known to have a level crossing. The wave function has two-particle correlations, which fit well with those in previous numerical studies, and can be viewed as a Bose-Einstein condensate of free excitons formed by composite bosons and anticomposite bosons in different layers. We show the free nature of these excitons indicating an emergent SU(2) symmetry for the composite bosons at d/ℓ=κ_{c1}, which leads to the level crossing in low-lying charged excitations. We further show the overlap between the trial wave function, and the ground state of a small size exact diagonalization is peaked near d/ℓ=κ_{c1}, which supports our theory.

Spatially controlled doping of two-dimensional SnS2 through intercalation for electronics.

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 interface2,3. Besides, the emergence of two-dimensional (2D) materials enables the realization of atomically thin integrated circuits4-9. 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 SnS2, Cu intercalated bilayer SnS2 obtained by this technique displays a hole field-effect mobility of ~40 cm2 V-1 s-1, and the obtained Co-SnS2 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.

Multiple Types of Topological Fermions in Transition Metal Silicides.

Exotic massless fermionic excitations with nonzero Berry flux, other than the Dirac and Weyl fermions, could exist in condensed matter systems under the protection of crystalline symmetries, such as spin-1 excitations with threefold degeneracy and spin-3/2 Rarita-Schwinger-Weyl fermions. Herein, by using the ab initio density functional theory, we show that these unconventional quasiparticles coexist with type-I and type-II Weyl fermions in a family of transition metal silicides, including CoSi, RhSi, RhGe, and CoGe, when spin-orbit coupling is considered. Their nontrivial topology results in a series of extensive Fermi arcs connecting projections of these bulk excitations on the side surface, which is confirmed by (001) surface electronic spectra of CoSi. In addition, these stable arc states exist within a wide energy window around the Fermi level, which makes them readily accessible in angle-resolved photoemission spectroscopy measurements.

Double Helix Nodal Line Superconductor.

Time-reversal invariant superconductors in three dimensions may contain nodal lines in the Brillouin zone, which behave as Wilson loops of 3D momentum-space Chern-Simons theory of the Berry connection. Here we study the conditions of realizing linked nodal lines (Wilson loops), which yield a topological contribution to the thermal magnetoelectric coefficient that is given by the Chern-Simons action. We find the essential conditions are the existence of torus or higher genus Fermi surfaces and spiral spin textures. We construct such a model with two torus Fermi surfaces, where a generic spin-dependent interaction leads to double-helix-like linked nodal lines as the superconductivity is developed.

Topological states of condensed matter.

Topological states of quantum matter have been investigated intensively in recent years in materials science and condensed matter physics. The field developed explosively largely because of the precise theoretical predictions, well-controlled materials processing, and novel characterization techniques. In this Perspective, we review recent progress in topological insulators, the quantum anomalous Hall effect, chiral topological superconductors, helical topological superconductors and Weyl semimetals.

Topological semimetal in honeycomb lattice LnSI.

Recognized as elementary particles in the standard model, Weyl fermions in condensed matter have received growing attention. However, most of the previously reported Weyl semimetals exhibit rather complicated electronic structures that, in turn, may have raised questions regarding the underlying physics. Here, we report promising topological phases that can be realized in specific honeycomb lattices, including ideal Weyl semimetal structures, 3D strong topological insulators, and nodal-line semimetal configurations. In particular, we highlight a semimetal featuring both Weyl nodes and nodal lines. Guided by this model, we showed that GdSI, the long-perceived ideal Weyl semimetal, has two pairs of Weyl nodes residing at the Fermi level and that LuSI (YSI) is a 3D strong topological insulator with the right-handed helical surface states. Our work provides a mechanism to study topological semimetals and proposes a platform for exploring the physics of Weyl semimetals as well as related device designs.

Magnetic quantum phase transition in Cr-doped Bi2(SexTe1-x)3 driven by the Stark effect.

The recent experimental observation of the quantum anomalous Hall effect has cast significant attention on magnetic topological insulators. In these magnetic counterparts of conventional topological insulators such as Bi2Te3, a long-range ferromagnetic state can be established by chemical doping with transition-metal elements. However, a much richer electronic phase diagram can emerge and, in the specific case of Cr-doped Bi2(SexTe1-x)3, a magnetic quantum phase transition tuned by the actual chemical composition has been reported. From an application-oriented perspective, the relevance of these results hinges on the possibility to manipulate magnetism and electronic band topology by external perturbations such as an electric field generated by gate electrodes-similar to what has been achieved in conventional diluted magnetic semiconductors. Here, we investigate the magneto-transport properties of Cr-doped Bi2(SexTe1-x)3 with different compositions under the effect of a gate voltage. The electric field has a negligible effect on magnetic order for all investigated compositions, with the remarkable exception of the sample close to the topological quantum critical point, where the gate voltage reversibly drives a ferromagnetic-to-paramagnetic phase transition. Theoretical calculations show that a perpendicular electric field causes a shift in the electronic energy levels due to the Stark effect, which induces a topological quantum phase transition and, in turn, a magnetic phase transition.

RETRACTED: Chiral Majorana fermion modes in a quantum anomalous Hall insulator-superconductor structure.

Majorana fermion is a hypothetical particle that is its own antiparticle. We report transport measurements that suggest the existence of one-dimensional chiral Majorana fermion modes in the hybrid system of a quantum anomalous Hall insulator thin film coupled with a superconductor. As the external magnetic field is swept, half-integer quantized conductance plateaus are observed at the locations of magnetization reversals, giving a distinct signature of the Majorana fermion modes. This transport signature is reproducible over many magnetic field sweeps and appears at different temperatures. This finding may open up an avenue to control Majorana fermions for implementing robust topological quantum computing.

Buckled two-dimensional Xene sheets.

Silicene, germanene and stanene are part of a monoelemental class of two-dimensional (2D) crystals termed 2D-Xenes (X = Si, Ge, Sn and so on) which, together with their ligand-functionalized derivatives referred to as Xanes, are comprised of group IVA atoms arranged in a honeycomb lattice - similar to graphene but with varying degrees of buckling. Their electronic structure ranges from trivial insulators, to semiconductors with tunable gaps, to semi-metallic, depending on the substrate, chemical functionalization and strain. More than a dozen different topological insulator states are predicted to emerge, including the quantum spin Hall state at room temperature, which, if realized, would enable new classes of nanoelectronic and spintronic devices, such as the topological field-effect transistor. The electronic structure can be tuned, for example, by changing the group IVA element, the degree of spin-orbit coupling, the functionalization chemistry or the substrate, making the 2D-Xene systems promising multifunctional 2D materials for nanotechnology. This Perspective highlights the current state of the art and future opportunities in the manipulation and stability of these materials, their functions and applications, and novel device concepts.

Topological Superconductivity on the Surface of Fe-Based Superconductors.

As one of the simplest systems for realizing Majorana fermions, the topological superconductor plays an important role in both condensed matter physics and quantum computations. Based on ab initio calculations and the analysis of an effective 8-band model with superconducting pairing, we demonstrate that the three-dimensional extended s-wave Fe-based superconductors such as Fe_{1+y}Se_{0.5}Te_{0.5} have a metallic topologically nontrivial band structure, and exhibit a normal-topological-normal superconductivity phase transition on the (001) surface by tuning the bulk carrier doping level. In the topological superconductivity (TSC) phase, a Majorana zero mode is trapped at the end of a magnetic vortex line. We further show that the surface TSC phase only exists up to a certain bulk pairing gap, and there is a normal-topological phase transition driven by the temperature, which has not been discussed before. These results pave an effective way to realize the TSC and Majorana fermions in a large class of superconductors.

Ideal Weyl Semimetals in the Chalcopyrites CuTlSe_{2}, AgTlTe_{2}, AuTlTe_{2}, and ZnPbAs_{2}.

Weyl semimetals are new states of matter which feature novel Fermi arcs and exotic transport phenomena. Based on first-principles calculations, we report that the chalcopyrites CuTlSe_{2}, AgTlTe_{2}, AuTlTe_{2}, and ZnPbAs_{2} are ideal Weyl semimetals, having largely separated Weyl points (∼0.05 Å^{-1}) and uncovered Fermi arcs that are amenable to experimental detections. We also construct a minimal effective model to capture the low-energy physics of this class of Weyl semimetals. Our discovery is a major step toward a perfect playground of intriguing Weyl semimetals and potential applications for low-power and high-speed electronics.

Thickness Dependence of the Quantum Anomalous Hall Effect in Magnetic Topological Insulator Films.

The evolution of the quantum anomalous Hall effect with the thickness of Cr-doped (Bi,Sb)2 Te3 magnetic topological insulator films is studied, revealing how the effect is caused by the interplay of the surface states, band-bending, and ferromagnetic exchange energy. Homogeneity in ferromagnetism is found to be the key to high-temperature quantum anomalous Hall material.