Catalogue of topological electronic materials.

Topological electronic materials such as bismuth selenide, tantalum arsenide and sodium bismuthide show unconventional linear response in the bulk, as well as anomalous gapless states at their boundaries. They are of both fundamental and applied interest, with the potential for use in high-performance electronics and quantum computing. But their detection has so far been hindered by the difficulty of calculating topological invariant properties (or topological nodes), which requires both experience with materials and expertise with advanced theoretical tools. Here we introduce an effective, efficient and fully automated algorithm that diagnoses the nontrivial band topology in a large fraction of nonmagnetic materials. Our algorithm is based on recently developed exhaustive mappings between the symmetry representations of occupied bands and topological invariants. We sweep through a total of 39,519 materials available in a crystal database, and find that as many as 8,056 of them are topologically nontrivial. All results are available and searchable in a database with an interactive user interface.

Observation of unconventional chiral fermions with long Fermi arcs in CoSi.

Chirality-the geometric property of objects that do not coincide with their mirror image-is found in nature, for example, in molecules, crystals, galaxies and life forms. In quantum field theory, the chirality of a massless particle is defined by whether the directions of its spin and motion are parallel or antiparallel. Although massless chiral fermions-Weyl fermions-were predicted 90 years ago, their existence as fundamental particles has not been experimentally confirmed. However, their analogues have been observed as quasiparticles in condensed matter systems. In addition to Weyl fermions1-4, theorists have proposed a number of unconventional (that is, beyond the standard model) chiral fermions in condensed matter systems5-8, but direct experimental evidence of their existence is still lacking. Here, by using angle-resolved photoemission spectroscopy, we reveal two types of unconventional chiral fermion-spin-1 and charge-2 fermions-at the band-crossing points near the Fermi level in CoSi. The projections of these chiral fermions on the (001) surface are connected by giant Fermi arcs traversing the entire surface Brillouin zone. These chiral fermions are enforced at the centre or corner of the bulk Brillouin zone by the crystal symmetries, making CoSi a system with only one pair of chiral nodes with large separation in momentum space and extremely long surface Fermi arcs, in sharp contrast to Weyl semimetals, which have multiple pairs of Weyl nodes with small separation. Our results confirm the existence of unconventional chiral fermions and provide a platform for exploring the physical properties associated with chiral fermions.

Gate-Tunable Multiband Transport in ZrTe5 Thin Devices.

Interest in ZrTe5 has been reinvigorated in recent years owing to its potential for hosting versatile topological electronic states and intriguing experimental discoveries. However, the mechanism of many of its unusual transport behaviors remains controversial: for example, the characteristic peak in the temperature-dependent resistivity and the anomalous Hall effect. Here, through employing a clean dry-transfer fabrication method in an inert environment, we successfully obtain high-quality ZrTe5 thin devices that exhibit clear dual-gate tunability and ambipolar field effects. Such devices allow us to systematically study the resistance peak as well as the Hall effect at various doping densities and temperatures, revealing the contribution from electron-hole asymmetry and multiple-carrier transport. By comparing with theoretical calculations, we suggest a simplified semiclassical two-band model to explain the experimental observations. Our work helps to resolve the longstanding puzzles on ZrTe5 and could potentially pave the way for realizing novel topological states in the two-dimensional limit.

Twist-Induced Modification in the Electronic Structure of Bilayer WSe2.

The recent discovery of strongly correlated phases in twisted transition-metal dichalcogenides (TMDs) highlights the significant impact of twist-induced modifications on electronic structures. In this study, we employed angle-resolved photoemission spectroscopy with submicrometer spatial resolution (µ-ARPES) to investigate these modifications by comparing valence band structures of twisted (5.3°) and nontwisted (AB-stacked) bilayer regions within the same WSe2 device. Relative to the nontwisted region, the twisted area exhibits pronounced moiré bands and ∼90 meV renormalization at the Γ-valley, substantial momentum separation between different layers, and an absence of flat bands at the K-valley. We further simulated the effects of lattice relaxation, which can flatten the Γ-valley edge but not the K-valley edge. Our results provide a direct visualization of twist-induced modifications in the electronic structures of twisted TMDs and elucidate their valley-dependent responses to lattice relaxation.

Flat-Band-Induced Anomalous Anisotropic Charge Transport and Orbital Magnetism in Kagome Metal CoSn.

For solids, the dispersionless flat band has long been recognized as an ideal platform for achieving intriguing quantum phases. However, experimental progress in revealing flat-band physics has so far been achieved mainly in artificially engineered systems represented as magic-angle twisted bilayer graphene. Here, we demonstrate the emergence of flat-band-dominated anomalous transport and magnetic behaviors in CoSn, a paramagnetic kagome-lattice compound. By combination of angle-resolved photoemission spectroscopy measurements and first-principles calculations, we reveal the existence of a kagome-lattice-derived flat band right around the Fermi level. Strikingly, the resistivity within the kagome lattice plane is more than one order of magnitude larger than the interplane one, in sharp contrast with conventional (quasi-) two-dimensional layered materials. Moreover, the magnetic susceptibility under the out-of-plane magnetic field is found to be much smaller as compared with the in-plane case, which is revealed to be arising from the introduction of a unique orbital diamagnetism. Systematic analyses reveal that these anomalous and giant anisotropies can be reasonably attributed to the unique properties of flat-band electrons, including large effective mass and self-localization of wave functions. Our results broaden the already fascinating flat-band physics, and demonstrate the feasibility of exploring them in natural solid-state materials in addition to artificial ones.

Magnetic Semimetals and Quantized Anomalous Hall Effect in EuB_{6}.

Exploration of the novel relationship between magnetic order and topological semimetals has received enormous interest in a wide range of both fundamental and applied research. Here we predict that "soft" ferromagnetic material EuB_{6} can achieve multiple topological semimetal phases by simply tuning the direction of the magnetic moment. Explicitly, EuB_{6} is a topological nodal-line semimetal when the moment is aligned along the [001] direction, and it evolves into a Weyl semimetal with three pairs of Weyl points by rotating the moment to the [111] direction. Interestingly, we identify a composite semimetal phase featuring the coexistence of a nodal line and Weyl points with the moment in the [110] direction. Topological surface states and anomalous Hall conductivity, which are sensitive to the magnetic order, have been computed and are expected to be experimentally observable. Large-Chern-number quantum anomalous Hall effect can be realized in its [111]-oriented quantum-well structures.

Magnetization-Induced Band Shift in Ferromagnetic Weyl Semimetal Co_{3}Sn_{2}S_{2}.

The discovery of magnetic Weyl semimetal (magnetic WSM) in Co_{3}Sn_{2}S_{2} has triggered great interest for abundant fascinating phenomena induced by band topology conspiring with the magnetism. Understanding how the magnetization affects the band structure can give us a deeper comprehension of the magnetic WSMs and guide us for the innovation in applications. Here, we systematically study the temperature-dependent optical spectra of ferromagnetic WSM Co_{3}Sn_{2}S_{2} experimentally and simulated by first-principles calculations. Our results indicate that the many-body correlation effect due to Co 3d electrons leads to the renormalization of electronic kinetic energy by a factor about 0.43, which is moderate, and the description within density functional theory is suitable. As the temperature drops down, the magnetic phase transition happens, and the magnetization drives the band shift through exchange splitting. The optical spectra can well detect these changes, including the transitions sensitive and insensitive to the magnetization, and those from the bands around the Weyl nodes. The results support that, in magnetic WSM Co_{3}Sn_{2}S_{2}, the bands that contain Weyl nodes can be tuned by magnetization with temperature change.

Inelastic Electron Tunneling in 2H-Ta_{x}Nb_{1-x}Se_{2} Evidenced by Scanning Tunneling Spectroscopy.

We report a detailed study of tunneling spectra measured on 2H-Ta_{x}Nb_{1-x}Se_{2} (x=0∼0.1) single crystals using a low-temperature scanning tunneling microscope. The prominent gaplike feature, which has not been understood for a long time, was found to be accompanied by some "in-gap" fine structures. By investigating the second-derivative spectra and their temperature and magnetic field dependencies, we were able to prove that inelastic electron tunneling is the origin of these features and obtain the Eliashberg function of 2H-Ta_{x}Nb_{1-x}Se_{2} at an atomic scale, providing a potential way to study the local Eliashberg function and the phonon spectra of the related transition-metal dichalcogenides.

Higher-Order Topology of the Axion Insulator EuIn_{2}As_{2}.

Based on first-principles calculations and symmetry analysis, we propose that EuIn_{2}As_{2} is a long-awaited axion insulator with antiferromagnetic (AFM) long-range order. Characterized by the parity-based invariant Z_{4}=2, the topological magnetoelectric effect is quantized with θ=π in the bulk, with a band gap as large as 0.1 eV. When the staggered magnetic moments of the AFM phase are along the a or b axis, it is also a topological crystalline insulator phase with gapless surface states emerging on (100), (010), and (001) surfaces. When the magnetic moments are along the c axis, both the (100) and (001) surfaces are gapped, and the material can also be viewed as a high-order topological insulator with one-dimensional chiral states existing on the hinges between those gapped surfaces. We have calculated both the topological surface states and the hinge state in different phases of the system, respectively, which can be detected by angle-resolved photoemission spectroscopy or STM experiments.

Topological Nodal-Net Semimetal in a Graphene Network Structure.

Topological semimetals are characterized by the nodal points in their electronic structure near the Fermi level, either discrete or forming a continuous line or ring, which are responsible for exotic properties related to the topology of bulk bands. Here we identify by ab initio calculations a distinct topological semimetal that exhibits nodal nets comprising multiple interconnected nodal lines in bulk and have two coupled drumheadlike flat bands around the Fermi level on its surface. This nodal net semimetal state is proposed to be realized in a graphene network structure that can be constructed by inserting a benzene ring into each C─C bond in the bct-C_{4} lattice or by a crystalline modification of the (5,5) carbon nanotube. These results expand the realm of nodal manifolds in topological semimetals, offering a new platform for exploring novel physics in these fascinating materials.

Double-Weyl Phonons in Transition-Metal Monosilicides.

We employed ab initio calculations to identify a class of crystalline materials of MSi (M=Fe, Co, Mn, Re, Ru) having double-Weyl points in both their acoustic and optical phonon spectra. They exhibit novel topological points termed "spin-1 Weyl point" at the Brillouin zone center and "charge-2 Dirac point" at the zone corner. The corresponding gapless surface phonon dispersions are two helicoidal sheets whose isofrequency contours form a single noncontractible loop in the surface Brillouin zone. In addition, the global structure of the surface bands can be analytically expressed as double-periodic Weierstrass elliptic functions.

From Nodal Chain Semimetal to Weyl Semimetal in HfC.

Based on first-principles calculations and effective model analysis, we propose that the WC-type HfC, in the absence of spin-orbit coupling (SOC), can host a three-dimensional nodal chain semimetal state. Distinguished from the previous material IrF_{4} [T. Bzdusek et al., Nature 538, 75 (2016)], the nodal chain here is protected by mirror reflection symmetries of a simple space group, while in IrF_{4} the nonsymmorphic space group with a glide plane is a necessity. Moreover, in the presence of SOC, the nodal chain in WC-type HfC evolves into Weyl points. In the Brillouin zone, a total of 30 pairs of Weyl points in three types are obtained through the first-principles calculations. Besides, the surface states and the pattern of the surface Fermi arcs connecting these Weyl points are studied, which may be measured by future experiments.

Noncollinear Magnetic Structure and Multipolar Order in Eu_{2}Ir_{2}O_{7}.

The magnetic properties of the pyrochlore iridate material Eu_{2}Ir_{2}O_{7} (5d^{5}) have been studied based on first principles calculations, where the crystal field splitting Δ, spin-orbit coupling (SOC) λ, and Coulomb interaction U within Ir 5d orbitals all play significant roles. The ground state phase diagram has been obtained with respect to the strength of SOC and Coulomb interaction U, where a stable antiferromagnetic ground state with all-in-all-out (AIAO) spin structure has been found. In addition, another antiferromagnetic state with energy close to AIAO has also been found to be stable. The calculated nonlinear magnetization of the two stable states both have the d-wave pattern but with a π/4 phase difference, which can perfectly explain the experimentally observed nonlinear magnetization pattern. Compared with the results of the nondistorted structure, it turns out that the trigonal lattice distortion is crucial for stabilizing the AIAO state in Eu_{2}Ir_{2}O_{7}. Furthermore, besides large dipolar moments, we also find considerable octupolar moments in the magnetic states.

Body-Centered Orthorhombic C_{16}: A Novel Topological Node-Line Semimetal.

We identify by ab initio calculations a novel topological semimetal carbon phase in all-sp^{2} bonding networks with a 16-atom body-centered orthorhombic unit cell, termed bco-C_{16}. Total-energy calculations show that bco-C_{16} is comparable to solid fcc-C_{60} in energetic stability, and phonon and molecular dynamics simulations confirm its dynamical stability. This all-sp^{2} carbon allotrope can be regarded as a three-dimensional modification of graphite, and its simulated x-ray diffraction (XRD) pattern matches well a previously unexplained diffraction peak in measured XRD spectra of detonation and chimney soot, indicating its presence in the specimen. Electronic band structure calculations reveal that bco-C_{16} is a topological node-line semimetal with a single nodal ring. These findings establish a novel carbon phase with intriguing structural and electronic properties of fundamental significance and practical interest.

Predicted Quantum Topological Hall Effect and Noncoplanar Antiferromagnetism in K_{0.5}RhO_{2}.

The quantum anomalous Hall (QAH) phase is a two-dimensional bulk ferromagnetic insulator with a nonzero Chern number in the presence of spin-orbit coupling (SOC) but in the absence of applied magnetic fields. Associated metallic chiral edge states host dissipationless current transport in electronic devices. This intriguing QAH phase has recently been observed in magnetic impurity-doped topological insulators, albeit, at extremely low temperatures. Based on first-principles density functional calculations, here we predict that layered rhodium oxide K_{0.5}RhO_{2} in the noncoplanar chiral antiferromagnetic state is an unconventional three-dimensional QAH insulator with a large band gap and a Néel temperature of a few tens of Kelvins. Furthermore, this unconventional QAH phase is revealed to be the exotic quantum topological Hall effect caused by nonzero scalar spin chirality due to the topological spin structure in the system and without the need of net magnetization and SOC.

Topological Node-Line Semimetal and Dirac Semimetal State in Antiperovskite Cu3PdN.

Based on first-principles calculation and effective model analysis, we propose that the cubic antiperovskite material Cu3PdN can host a three-dimensional (3D) topological node-line semimetal state when spin-orbit coupling (SOC) is ignored, which is protected by the coexistence of time-reversal and inversion symmetry. There are three node-line circles in total due to the cubic symmetry. Drumheadlike surface flat bands are also derived. When SOC is included, each node line evolves into a pair of stable 3D Dirac points as protected by C4 crystal symmetry. This is remarkably distinguished from the Dirac semimetals known so far, such as Na3Bi and Cd3As2, both having only one pair of Dirac points. Once C4 symmetry is broken, the Dirac points are gapped and the system becomes a strong topological insulator with (1;111) Z2 indices.

Evidence for Half-Metallicity in n-type HgCr2Se4.

High quality HgCr2Se4 single crystals have been investigated by magnetization, electron transport, and Andreev reflection spectroscopy. In the ferromagnetic ground state, the saturation magnetic moment of each unit cell corresponds to an integer number of electron spins (3 µB/Cr3+), and the Hall effect measurements suggest n-type charge carriers. Spin polarizations as high as 97% were obtained from fits of the differential conductance spectra of HgCr2Se4/Pb junctions with the modified Blonder-Tinkham-Klapwijk theory. The temperature and bias-voltage dependencies of the subgap conductance are consistent with recent theoretical calculations based on spin active scatterings at a superconductor-half-metal interface. Our results suggest that n-HgCr2Se4 is a half-metal, in agreement with theoretical calculations that also predict undoped HgCr2Se4 is a magnetic Weyl semimetal.

Robustness of topological order and formation of quantum well states in topological insulators exposed to ambient environment.

The physical property investigation (like transport measurements) and ultimate application of the topological insulators usually involve surfaces that are exposed to ambient environment (1 atm and room temperature). One critical issue is how the topological surface state will behave under such ambient conditions. We report high resolution angle-resolved photoemission measurements to directly probe the surface state of the prototypical topological insulators, Bi(2)Se(3) and Bi(2)Te(3), upon exposing to various environments. We find that the topological order is robust even when the surface is exposed to air at room temperature. However, the surface state is strongly modified after such an exposure. Particularly, we have observed the formation of two-dimensional quantum well states near the exposed surface of the topological insulators. These findings provide key information in understanding the surface properties of the topological insulators under ambient environment and in engineering the topological surface state for applications.

Topological crystalline Kondo insulator in mixed valence ytterbium borides.

The electronic structures of two mixed valence insulators YbB6 and YbB12 are studied by using the local density approximation supplemented with the Gutzwiller method and dynamic mean field theory. YbB6 is found to be a moderately correlated Z2 topological insulator, similar to SmB6 but having much larger bulk band gap. Notably, YbB12 is revealed to be in a new novel quantum state, strongly correlated topological crystalline Kondo insulator, which is characterized by its nonzero mirror Chern number. The surface calculations find an odd (three) and an even (four) number of Dirac cones for YbB6 and YbB12, respectively.