Magnetic Weyl Semimetal in K_{2}Mn_{3}(AsO_{4})_{3} with the Minimum Number of Weyl Points.

The "hydrogen atom" of magnetic Weyl semimetals, with the minimum number of Weyl points, has received growing attention recently due to the possible presence of Weyl-related phenomena. Here, we report a nontrivial electronic structure of the ferromagnetic alluaudite-type compound K_{2}Mn_{3}(AsO_{4})_{3}. It exhibits only a pair of Weyl points constrained in the z direction by the twofold rotation symmetry, leading to extremely long Fermi arc surface states. In addition, the study of its low-energy effective model results in the discovery of various topological superconducting states, such as the hydrogen atom of a Weyl superconductor. Our Letter provides a feasible platform to explore the intrinsic properties related to Weyl points, and the related device applications.

Multiple mobile excitons manifested as sidebands in quasi-one-dimensional metallic TaSe3.

Charge neutrality and their expected itinerant nature makes excitons potential transmitters of information. However, exciton mobility remains inaccessible to traditional optical experiments that only create and detect excitons with negligible momentum. Here, using angle-resolved photoemission spectroscopy, we detect dispersing excitons in the quasi-one-dimensional metallic trichalcogenide, TaSe3. The low density of conduction electrons and the low dimensionality in TaSe3 combined with a polaronic renormalization of the conduction band and the poorly screened interaction between these polarons and photo-induced valence holes leads to various excitonic bound states that we interpret as intrachain and interchain excitons, and possibly trions. The thresholds for the formation of a photo-hole together with an exciton appear as side valence bands with dispersions nearly parallel to the main valence band, but shifted to lower excitation energies. The energy separation between side and main valence bands can be controlled by surface doping, enabling the tuning of certain exciton properties.

Discovery of [Formula: see text] rotation anomaly in topological crystalline insulator SrPb.

Topological crystalline insulators (TCIs) are insulating electronic states with nontrivial topology protected by crystalline symmetries. Recently, theory has proposed new classes of TCIs protected by rotation symmetries [Formula: see text], which have surface rotation anomaly evading the fermion doubling theorem, i.e., n instead of 2n Dirac cones on the surface preserving the rotation symmetry. Here, we report the first realization of the [Formula: see text] rotation anomaly in a binary compound SrPb. Our first-principles calculations reveal two massless Dirac fermions protected by the combination of time-reversal symmetry [Formula: see text] and [Formula: see text] on the (010) surface. Using angle-resolved photoemission spectroscopy, we identify two Dirac surface states inside the bulk band gap of SrPb, confirming the [Formula: see text] rotation anomaly in the new classes of TCIs. The findings enrich the classification of topological phases, which pave the way for exploring exotic behavior of the new classes of TCIs.

Observation and control of the weak topological insulator state in ZrTe5.

A quantum spin Hall (QSH) insulator hosts topological states at the one-dimensional (1D) edge, along which backscattering by nonmagnetic impurities is strictly prohibited. Its 3D analogue, a weak topological insulator (WTI), possesses similar quasi-1D topological states confined at side surfaces. The enhanced confinement could provide a route for dissipationless current and better advantages for applications relative to strong topological insulators (STIs). However, the topological side surface is usually not cleavable and is thus hard to observe. Here, we visualize the topological states of the WTI candidate ZrTe5 by spin and angle-resolved photoemission spectroscopy (ARPES): a quasi-1D band with spin-momentum locking was revealed on the side surface. We further demonstrate that the bulk band gap is controlled by external strain, realizing a more stable WTI state or an ideal Dirac semimetal (DS) state. The highly directional spin-current and the tunable band gap in ZrTe5 will provide an excellent platform for applications.

High-throughput screening for Weyl semimetals with S4 symmetry.

Based on irreducible representations (or symmetry eigenvalues) and compatibility relations (CR), a material can be predicted to be a topological/trivial insulator (satisfying CR) or a topological semimetal (violating CR). However, Weyl semimetals (WSMs) usually go beyond this symmetry-based strategy. In other words, Weyl nodes could emerge in a material, no matter if its occupied bands satisfy CR, or if the symmetry indicators are zero. In this work, we propose a new topological invariant χ for the systems with S4 symmetry (i.e., the improper rotation S4(≡IC4z) is a proper fourfold rotation (C4z) followed by inversion (I)), which can be used to diagnose the WSM phase. Moreover, χ can be easily computed through the one-dimensional Wilson-loop technique. By applying this method to the high-throughput screening in our first-principles calculations, we predict a lot of WSMs in both nonmagnetic and magnetic compounds. Various interesting properties (e.g., magnetic frustration effects, superconductivity and spin-glass order, etc.) are found in predicted WSMs, which provide realistic platforms for future experimental study of the interplay between Weyl fermions and other exotic states.

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.

Emergence of Nontrivial Low-Energy Dirac Fermions in Antiferromagnetic EuCd2 As2.

Parity-time symmetry plays an essential role for the formation of Dirac states in Dirac semimetals. So far, all of the experimentally identified topologically nontrivial Dirac semimetals (DSMs) possess both parity and time reversal symmetry. The realization of magnetic topological DSMs remains a major issue in topological material research. Here, combining angle-resolved photoemission spectroscopy with density functional theory calculations, it is ascertained that band inversion induces a topologically nontrivial ground state in EuCd2 As2 . As a result, ideal magnetic Dirac fermions with simplest double cone structure near the Fermi level emerge in the antiferromagnetic (AFM) phase. The magnetic order breaks time reversal symmetry, but preserves inversion symmetry. The double degeneracy of the Dirac bands is protected by a combination of inversion, time-reversal, and an additional translation operation. Moreover, the calculations show that a deviation of the magnetic moments from the c-axis leads to the breaking of C3 rotation symmetry, and thus, a small bandgap opens at the Dirac point in the bulk. In this case, the system hosts a novel state containing three different types of topological insulator: axion insulator, AFM topological crystalline insulator (TCI), and higher order topological insulator. The results provide an enlarged platform for the quest of topological Dirac fermions in a magnetic system.

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.

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.

Experimental evidence of hourglass fermion in the candidate nonsymmorphic topological insulator KHgSb.

Topological insulators (TIs) host novel states of quantum matter characterized by nontrivial conducting boundary states connecting valence and conduction bulk bands. All TIs discovered experimentally so far rely on either time-reversal or mirror crystal symmorphic symmetry to protect massless Dirac-like boundary states. Several materials were recently proposed to be TIs with nonsymmorphic symmetry, where a glide mirror protects exotic surface fermions with hourglass-shaped dispersion. However, an experimental confirmation of this new fermion is missing. Using angle-resolved photoemission spectroscopy, we provide experimental evidence of hourglass fermions on the (010) surface of crystalline KHgSb, whereas the (001) surface has no boundary state, in agreement with first-principles calculations. Our study will stimulate further research activities of topological properties of nonsymmorphic materials.

Electronic evidence of temperature-induced Lifshitz transition and topological nature in ZrTe5.

The topological materials have attracted much attention for their unique electronic structure and peculiar physical properties. ZrTe5 has host a long-standing puzzle on its anomalous transport properties manifested by its unusual resistivity peak and the reversal of the charge carrier type. It is also predicted that single-layer ZrTe5 is a two-dimensional topological insulator and there is possibly a topological phase transition in bulk ZrTe5. Here we report high-resolution laser-based angle-resolved photoemission measurements on the electronic structure and its detailed temperature evolution of ZrTe5. Our results provide direct electronic evidence on the temperature-induced Lifshitz transition, which gives a natural understanding on underlying origin of the resistivity anomaly in ZrTe5. In addition, we observe one-dimensional-like electronic features from the edges of the cracked ZrTe5 samples. Our observations indicate that ZrTe5 is a weak topological insulator and it exhibits a tendency to become a strong topological insulator when the layer distance is reduced.

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.

Spontaneous Formation of a Superconductor-Topological Insulator-Normal Metal Layered Heterostructure.

2D materials with heterolayered structures beyond graphene are explored. A theoretically predicted superconductor-topological insulator-normal metal heterolayered structure is realized experimentally. The generated hybrid structure HfTe3 /HfTe5 /Hf has potential applications in both quantum-spin Hall effect-based and Majorana-based devices.