Berry curvature generation detected by Nernst responses in ferroelectric Weyl semimetal

The quest for nonmagnetic Weyl semimetals with high tunability of phase has remained a demanding challenge. As the symmetry-breaking control parameter, the ferroelectric order can be steered to turn on/off the Weyl semimetals phase, adjust the band structures around the Fermi level, and enlarge/shrink the momentum separation of Weyl nodes which generate the Berry curvature as the emergent magnetic field. Here, we report the realization of a ferroelectric nonmagnetic Weyl semimetal based on indium-doped Pb_{1- x} Sn _x Te alloy in which the underlying inversion symmetry as well as mirror symmetry are broken with the strength of ferroelectricity adjustable via tuning the indium doping level and Sn/Pb ratio. The transverse thermoelectric effect (i.e., Nernst effect), both for out-of-plane and in-plane magnetic field geometry, is exploited as a Berry curvature-sensitive experimental probe to manifest the generation of Berry curvature via the redistribution of Weyl nodes under magnetic fields. The results demonstrate a clean, nonmagnetic Weyl semimetal coupled with highly tunable ferroelectric order, providing an ideal platform for manipulating the Weyl fermions in nonmagnetic systems.

Noncentrosymmetric Weyl phase and topological phase transition in bulk MoTe

Ideal topological materials are those stable materials with less nontrivial band crossing near the Fermi surface and a long Fermi arc. By means of first-principles calculations, here we present that the 3D monochalcogenide molybdenum telluride (Pm-MoTe) without an inversion center shows a type-II Weyl semimetal (WSM) phase which cannot checked by symmetry index method. A total of eight Weyl points (WPs) are found in different quadrants of the Brillouin zone (BZ) of Pm-MoTe, which guarantee a long Fermi arc. The WSM phase is robust against the spin-orbit coupling (SOC) effect because of mirror symmetry and time reversal symmetry. It is also found that a topological phase transition can be tuned by strain. For different types of strain, the number of WPs can be effectively modulated to a minimum number, and their energies could be closer to Fermi level. These findings propose a promising material candidate that partly satisfies the ideal WSM criteria and extends the potential applications of the tunable topological phase.

It Runs in the BaAl4 Family: Relating the Structure and Properties of Middle Child Ln2Co3Ge5 (Ln = Pr, Nd, and Sm) to its Siblings LnCo2Ge2 and LnCoGe3

The BaAl₄ prototype structure and its derivatives have been identified to host several topological quantum materials and noncentrosymmetric superconductors. Single crystals up to ∼3 mm × 3 mm × 5 mm of Ln₂Co₃Ge₅ (Ln = Pr, Nd, and Sm) are obtained via flux growth utilizing Sn as metallic flux. The crystal structure is isostructural to the Lu₂Co₃Si₅ structure type in the crystallographic space group C2/c. The temperature-dependent magnetization indicates magnetic ordering at 30 K for all three compounds. Pr₂Co₃Ge₅ and Nd₂Co₃Ge₅ exhibit complex magnetic behavior with spin reorientations before ordering antiferromagnetically around 6 K, whereas Sm₂Co₃Ge₅ shows a clear antiferromagnetic behavior at 26 K. The structures and properties of Ln₂Co₃Ge₅ (Ln = Pr, Nd, and Sm) are compared to those of the ThCr₂Si₂ and BaNiSn₃ structure types. Herein, we present the optimized crystal growth, structure, and physical properties of Ln₂Co₃Ge₅ (Ln = Pr, Nd, and Sm).

Magnetic topological quantum chemistry

For over 100 years, the group-theoretic characterization of crystalline solids has provided the foundational language for diverse problems in physics and chemistry. However, the group theory of crystals with commensurate magnetic order has remained incomplete for the past 70 years, due to the complicated symmetries of magnetic crystals. In this work, we complete the 100-year-old problem of crystalline group theory by deriving the small corepresentations, momentum stars, compatibility relations, and magnetic elementary band corepresentations of the 1,421 magnetic space groups (MSGs), which we have made freely accessible through tools on the Bilbao Crystallographic Server. We extend Topological Quantum Chemistry to the MSGs to form a complete, real-space theory of band topology in magnetic and nonmagnetic crystalline solids - Magnetic Topological Quantum Chemistry (MTQC). Using MTQC, we derive the complete set of symmetry-based indicators of electronic band topology, for which we identify symmetry-respecting bulk and anomalous surface and hinge states.

Direct Measurement of Helicoid Surface States in RhSi Using Nonlinear Optics

Despite the fundamental nature of the edge state in topological physics, direct measurement of electronic and optical properties of the Fermi arcs of topological semimetals has posed a significant experimental challenge, as their response is often overwhelmed by the metallic bulk. However, laser-driven currents carried by surface and bulk states can propagate in different directions in nonsymmorphic crystals, allowing for the two components to be easily separated. Motivated by a recent theoretical prediction G. Chang et al., Phys. Rev. Lett. 124, 166404 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.166404, we have measured the linear and circular photogalvanic effect currents deriving from the Fermi arcs of the nonsymmorphic, chiral Weyl semimetal RhSi over the 0.45-1.1 eV incident photon energy range. Our data are in good agreement with the predicted spectral shape of the circular photogalvanic effect as a function of photon energy, although the direction of the surface photocurrent departed from the theoretical expectation over the energy range studied. Surface currents arising from the linear photogalvanic effect were observed as well, with the unexpected result that only two of the six allowed tensor element were required to describe the measurements, suggesting an approximate emergent mirror symmetry inconsistent with the space group of the crystal.

Topology and symmetry of circular photogalvanic effect in the chiral multifold semimetals: a review

The circular photogalvanic effect (CPGE) is the only possible quantized signal in chiral Weyl and multifold semimetals with inversion and mirror symmetries broken. Here, we review CPGE in the chiral multifold semimetals in terms of classification of CPGE tensor, the quantization of CPGE fromk⋅peffective model and topological semimetal RhSi family. Firstly, we give complete symmetric analysis of CPGE tensors for all nonmagnetic point groups, and get a table classifying matrix of response tensors. Secondly, the CPGE becomes a quantized response in the noncentrosymmetric topological semimetals, and depends on the Chern number of multifold fermions. Based onk⋅peffective model with linear dispersion, detailed derivations about the quantization of CPGE are given. Finally, according toab initioanalysis for the quantized CPGE based on noninteracting electronic structures, we review previous reports and make new calculations for the chiral topological semimetals in RhSi family, which can be separated into two groups. The first group, including RhSi, PtAl and CoSi, can be the promising candidates to exhibit a quantized CPGE trace, while the second group includes PdGa, PtGa and RhSn without a quantization.

Higher-Order Dirac Sonic Crystals

Discovering new topological phases of matter is a major theme in fundamental physics and materials science. Dirac semimetal provides an exceptional platform for exploring topological phase transitions under symmetry breaking. Recent theoretical studies have revealed that a three-dimensional Dirac semimetal can harbor fascinating hinge states, a higher-order topological manifestation not known before. However, its realization in experiment is yet to be achieved. In this Letter, we propose a minimum model to construct a spinless higher-order Dirac semimetal protected by C_{6v} symmetry. By breaking different symmetries, this parent phase transitions into a variety of novel topological phases including higher-order topological insulator, higher-order Weyl semimetal, and higher-order nodal-ring semimetal. Furthermore, for the first time, we experimentally realize this unprecedented higher-order topological phase in a sonic crystal and present an unambiguous observation of the desired hinge states via momentum-space spectroscopy and real-space visualization. Our findings may offer new opportunities to manipulate classical waves such as sound and light.

Evolving Devil's Staircase Magnetization from Tunable Charge Density Waves in Nonsymmorphic Dirac Semimetals

While several magnetic topological semimetals have been discovered in recent years, their band structures are far from ideal, often obscured by trivial bands at the Fermi energy. Square-net materials with clean, linearly dispersing bands show potential to circumvent this issue. CeSbTe, a square-net material, features multiple magnetic-field-controllable topological phases. Here, it is shown that in this material, even higher degrees of tunability can be achieved by changing the electron count at the square-net motif. Increased electron filling results in structural distortion and formation of charge density waves (CDWs). The modulation wave-vector evolves continuously leading to a region of multiple discrete CDWs and a corresponding complex "Devil's staircase" magnetic ground state. A series of fractionally quantized magnetization plateaus is observed, which implies direct coupling between CDW and a collective spin-excitation. It is further shown that the CDW creates a robust idealized nonsymmorphic Dirac semimetal, thus providing access to topological systems with rich magnetism.

Weyl Semimetal Path to Valley Filtering in Graphene

We propose a device in which a sheet of graphene is coupled to a Weyl semimetal, allowing for the physical access to the study of tunneling from two- to three-dimensional massless Dirac fermions. Because of the reconstructed band structure, we find that this device acts as a robust valley filter for electrons in the graphene sheet. We show that, by appropriate alignment, the Weyl semimetal draws away current in one of the two graphene valleys, while allowing current in the other to pass unimpeded. In contrast to other proposed valley filters, the mechanism of our proposed device occurs in the bulk of the graphene sheet, obviating the need for carefully shaped edges or dimensions.

Anab initiostudy of topological and transport properties of YAuPb

In the last few decades, the study of topological materials has been carried out on an extensive scale. Half-Heusler alloys are well known for their topological behaviours. In this work, we present a detailed study of topological properties of a ternary half-Heusler alloy, YAuPb, using the tight-binding approach. We have calculated some important topological properties which includes-finding nodes and their chiralities, Berry curvature (Ω) and the surface-states. Five pairs of characteristic nodes with equal and opposite chiralities are obtained. Based on the study of these properties, we categorise the material as non-trivial topological semimetal. Besides the topological behaviours, we present a comparative study of temperature dependent transport properties corresponding to the chemical potential (μ) of the Fermi level and the node points. The temperature range chosen for the study is 50-300 K. The results obtained from the calculations of electrical conductivity per unit relaxation time (σ/τ) and the electronic part of thermal conductivity per unit relaxation time (κ₀) indicates the conducting nature of the material to both the heat and electricity. At the Fermi level, the value of Seebeck coefficient (S) is found to be ∼-9.07(-35.95) μV K^-1at 50(300) K. The negative value ofSindicates the n-type behaviour of the compound. The calculated value of electronic specific heat (Pauli magnetic susceptibility) corresponding to Fermi level is ∼0.03(0.18) × 10^-2 J mol^-1 K^-1(∼1.21(1.14) × 10^-10 m³ mol^-1) at 50(300) K. This work suggests that YAuPb is a promising candidate of non-trivial topological semimetals which can be employed in transmission of heat and electricity, and as n-type material within the temperature range of 50-300 K.

Tunable topologically nontrivial states in newly discovered graphyne allotropes: from Dirac nodal grid to Dirac nodal loop

By means of quotient-graph associated crystal prediction method, a new graphyne allotrope with unique Dirac nodal grid state is reported in this work. It is named as 191-E24Y24-1 according to its hexagonal lattice (with P6/mmm symmetry, No. 191) containing 24 sp²-hybridized carbon atoms and 24 sp-hybridized ones. The first-principles results show that the total energy of 191-E24Y24-1 is more favorable than that of recent synthesizedβ-graphdiyne and carbon ene-yne. It is also demonstrated to be dynamically, thermally, and mechanically stable. Interestingly, the 191-E24Y24-1 harbors intrinsic semimetal features showing intriguing hexagonal Dirac nodal grid state in the reciprocal space. Such unique electronic state is stable against small external tensile strains, and it is tunable under compression strains which will transform to new triangle Dirac nodal grid state. Moreover, a new metastable graphyne allotrope named 191-E12Y36-4 with Dirac nodal loop state is also observed in the process of stretching 191-E24Y24-1 with large tensile strains. The results presented in this work reveal two novel graphyne allotropes with exotic electronic properties. These discoveries are not only physical interesting, but also provide potential material candidates for carbon-based high performance electronic nanodevices.

Electric Field Control of the Magnetic Weyl Fermion in an Epitaxial SrRuO3 (111) Thin Film

The magnetic Weyl fermion originates from the time reversal symmetry (TRS)-breaking in magnetic crystalline structures, where the topology and magnetism entangle with each other. Therefore, the magnetic Weyl fermion is expected to be effectively tuned by the magnetic field and electrical field, which holds promise for future topologically protected electronics. However, the electrical field control of the magnetic Weyl fermion has rarely been reported, which is prevented by the limited number of identified magnetic Weyl solids. Here, the electric field control of the magnetic Weyl fermion is demonstrated in an epitaxial SrRuO₃ (111) thin film. The magnetic Weyl fermion in the SrRuO₃ films is indicated by the chiral anomaly induced magnetotransport, and is verified by the observed Weyl nodes in the electronic structures characterized by the angle-resolved photoemission spectroscopy (ARPES) and first-principles calculations. Through the ionic-liquid gating experiment, the effective manipulation of the Weyl fermion by electric field is demonstrated, in terms of the sign-change of the ordinary Hall effect, the nonmonotonic tuning of the anomalous Hall effect, and the observation of the linear magnetoresistance under proper gating voltages. The work may stimulate the searching and tuning of Weyl fermions in other magnetic materials, which are promising in energy-efficient electronics.

Double-bowl state in photonic Dirac nodal line semimetal

The past decade has seen a proliferation of topological materials for both insulators and semimetals in electronic systems and classical waves. Topological semimetals exhibit topologically protected band degeneracies, such as nodal points and nodal lines. Dirac nodal line semimetals (DNLS), which own four-fold line degeneracy, have drawn particular attention. DNLSs have been studied in electronic systems but there is no photonic DNLS. Here in this work, we provide a new mechanism, which is unique for photonic systems to investigate a stringent photonic DNLS. When truncated, the photonic DNLS exhibits double-bowl states (DBS), which comprise two sets of perpendicularly polarized surface states. In sharp contrast to nondegenerate surface states in other photonic systems, here the two sets of surface states are almost degenerate over the whole-spectrum range. The DBS and the bulk Dirac nodal ring (DNR) dispersion along the relevant directions, are experimentally resolved.

Transmission properties of microwaves at an optical Weyl point in a three-dimensional chiral photonic crystal

Microwave transmission measurements were performed for a three-dimensional (3D) layer-by-layer chiral photonic crystal (PhC), whose photonic band structure contains 3D singular points, Weyl points. For the frequency and wavevector in the vicinity of a Weyl point, the transmitted intensity was found to be inversely proportional to the square of the propagation length. In addition, the transmitted wave was well-collimated in the plane parallel to the PhC layers, even for point-source incidence. When a plane wave was incident on the PhC containing metal scatters, the planar wavefront was reconstructed after the transmission, indicating a cloaking effect.

Linked Weyl surfaces and Weyl arcs in photonic metamaterials

Generalization of the concept of band topology from lower-dimensional to higher-dimensional (n > 3) physical systems is expected to introduce new bulk and boundary topological effects. However, theoretically predicted topological singularities in five-dimensional systems-Weyl surfaces and Yang monopoles-have either not been demonstrated in realistic physical systems or are limited to purely synthetic dimensions. We constructed a system possessing Yang monopoles and Weyl surfaces based on metamaterials with engineered electromagnetic properties, leading to the observation of several intriguing bulk and surface phenomena, such as linking of Weyl surfaces and surface Weyl arcs, via selected three-dimensional subspaces. The demonstrated photonic Weyl surfaces and Weyl arcs leverage the concept of higher-dimension topology to control the propagation of electromagnetic waves in artificially engineered photonic media.

Tip-induced superconductivity

It is widely believed that topological superconductivity, a hitherto elusive phase of quantum matter, can be achieved by inducing superconductivity in topological materials. In search of such topological superconductors, certain topological insulators (like, Bi₂Se₃) were successfully turned into superconductors by metal-ion (Cu, Pd, Sr, Nb etc) intercalation. Superconductivity could be induced in topological materials through applying pressure as well. For example, a pressure-induced superconducting phase was found in the topological insulator Bi₂Se₃. However, in all such cases, no conclusive signature of topological superconductivity was found. In this review, we will discuss about another novel way of inducing superconductivity in a non-superconducting topological material-by creating a mesoscopic interface on the material with a non-superconducting, normal metallic tip where the mesoscopic interface becomes superconducting. Such a phase is now known as a tip-induced superconducting (TISC) phase. This was first realized on Cd₃As₂in India. Following that, a large number of other topological materials were shown to display TISC. Since the TISC phase emerges only at a confined region under a mesoscopic point contact, traditional bulk tools for characterizing superconductivity cannot be employed to detect/confirm such a phase. On the other hand, such a point contact geometry is ideal for probing the possible existence of a temperature and magnetic field dependent superconducting energy gap and a temperature and magnetic field dependent critical current. We will review the details of the experimental signatures that can be used to prove the existence of superconductivity even when the 'text-book' tests for detecting superconductivity cannot be performed. Then, we will review various systems where a TISC phase could be realized.

Resistance-Chiral Anisotropy of Chiral Mesostructured Half-metallic Fe3 O4 Films

Half-metallic materials are theoretically predicted to be metallic and insulating, which have not been confirmed experimentally, and the predictions are still in doubt. We report the resistance-chiral anisotropy (R-ChA), i.e., chirality-dependent electrical conductivity, in chiral mesostructured Fe₃ O₄ films (CMFFs) grown on the substrates via a hydrothermal method using amino acids as symmetry-breaking agents. Two levels of chirality exist in the CMFFs: primary distortion of the crystal lattice forms twisted nanoflakes, and secondary helical stacking of nanoflakes forms fan-shaped nanoplates. At temperatures below 30 K, the CMFFs exhibited metallic conductivity and insulation for one handedness and the other, respectively. The chirality-dependent effective magnetic fields were speculated to stabilize the opposite spin in the antipodal chiral frame, which led to the free transport of electrons in one handedness of the chiral structure and immobility for the other handedness.

Controlled Synthesis of MoxW1-xTe2 Atomic Layers with Emergent Quantum States

Recently, new states of matter like superconducting or topological quantum states were found in transition metal dichalcogenides (TMDs) and manifested themselves in a series of exotic physical behaviors. Such phenomena have been demonstrated to exist in a series of transition metal tellurides including MoTe₂, WTe₂, and alloyed Mo_xW_1-xTe_2. However, the behaviors in the alloy system have been rarely addressed due to their difficulty in obtaining atomic layers with controlled composition, albeit the alloy offers a great platform to tune the quantum states. Here, we report a facile CVD method to synthesize the Mo_xW_1-xTe₂ with controllable thickness and chemical composition ratios. The atomic structure of a monolayer Mo_xW_1-xTe₂ alloy was experimentally confirmed by scanning transmission electron microscopy. Importantly, two different transport behaviors including superconducting and Weyl semimetal states were observed in Mo-rich Mo_0.8W_0.2Te₂ and W-rich Mo_0.2W_0.8Te₂ samples, respectively. Our results show that the electrical properties of Mo_xW_1-xTe₂ can be tuned by controlling the chemical composition, demonstrating our controllable CVD growth method is an efficient strategy to manipulate the physical properties of TMDCs. Meanwhile, it provides a perspective on further comprehension and sheds light on the design of devices with topological multicomponent TMDC materials.

Multiple Dirac cones and Lifshitz transition in a two-dimensional Cairo lattice as a Hawking evaporation analogue

The linear energy-momentum dispersion of Dirac cones offers a unique platform for mimicking the fantastical phenomena in high energy physics, such as Dirac fermions and black hole (BH) horizons. Three types of Dirac cones (I, III, and II) with different tilts have been proposed individually in specific materials but lack of integral lattice model. Here, we demonstrated the three types of Dirac cones inherited in aπ-conjugated Cairo lattice of double-degenerated_πandp_zorbitals by means of tight-binding (TB) approach, which paves a way for the design of two-dimensional (2D) Dirac materials. From first-principles calculations, we predicted a candidate material,penta-NiSb₂monolayer, to achieve these multiple Dirac cones and the Lifshitz transition between different Dirac cones driven by external biaxial strain. The coexistence of the three types of Dirac cones renderspenta-NiSb₂monolayer a promising 2D fermionic analogue to simulate the event-horizon evaporation with a high Hawking temperature.

Probing Rotated Weyl Physics on Nonlinear Lithium Niobate-on-Insulator Chips

Topological photonics, featured by stable topological edge states resistant to perturbations, has been utilized to design robust integrated devices. Here, we present a study exploring the intriguing topological rotated Weyl physics in a 3D parameter space based on quaternary waveguide arrays on lithium niobate-on-insulator (LNOI) chips. Unlike previous works that focus on the Fermi arc surface states of a single Weyl structure, we can experimentally construct arbitrary interfaces between two Weyl structures whose orientations can be freely rotated in the synthetic parameter space. This intriguing system was difficult to realize in usual 3D Weyl semimetals due to lattice mismatch. We found whether the interface can host gapless topological interface states or not is determined by the relative rotational directions of the two Weyl structures. In the experiment, we have probed the local characteristics of the TISs through linear optical transmission and nonlinear second harmonic generation. Our study introduces a novel path to explore topological photonics on LNOI chips and various applications in integrated nonlinear and quantum optics.

Delocalization Transition of a Disordered Axion Insulator

The axion insulator is a higher-order topological insulator protected by inversion symmetry. We show that, under quenched disorder respecting inversion symmetry on average, the topology of the axion insulator stays robust, and an intermediate metallic phase in which states are delocalized is unavoidable at the transition from an axion insulator to a trivial insulator. We derive this conclusion from general arguments, from classical percolation theory, and from the numerical study of a 3D quantum network model simulating a disordered axion insulator through a layer construction. We find the localization length critical exponent near the delocalization transition to be ν=1.42±0.12. We further show that this delocalization transition is stable even to weak breaking of the average inversion symmetry, up to a critical strength. We also quantitatively map our quantum network model to an effective Hamiltonian and we find its low-energy k·p expansion.

Band Engineering of Dirac Semimetals Using Charge Density Waves

New developments in the field of topological matter are often driven by materials discovery, including novel topological insulators, Dirac semimetals, and Weyl semimetals. In the last few years, large efforts have been made to classify all known inorganic materials with respect to their topology. Unfortunately, a large number of topological materials suffer from non-ideal band structures. For example, topological bands are frequently convoluted with trivial ones, and band structure features of interest can appear far below the Fermi level. This leaves just a handful of materials that are intensively studied. Finding strategies to design new topological materials is a solution. Here, a new mechanism is introduced, which is based on charge density waves and non-symmorphic symmetry, to design an idealized Dirac semimetal. It is then shown experimentally that the antiferromagnetic compound GdSb_0.46 Te_1.48 is a nearly ideal Dirac semimetal based on the proposed mechanism, meaning that most interfering bands at the Fermi level are suppressed. Its highly unusual transport behavior points to a thus far unknown regime, in which Dirac carriers with Fermi energy very close to the node seem to gradually localize in the presence of lattice and magnetic disorder.

Ideal type-II Weyl points in topological circuits

Weyl points (WPs), nodal degenerate points in three-dimensional (3D) momentum space, are said to be 'ideal' if they are symmetry-related and well-separated, and reside at the same energy and far from nontopological bands. Although type-II WPs have unique spectral characteristics compared with type-I counterparts, ideal type-II WPs have not yet been reported because of a lack of an experimental platform with enough flexibility to produce strongly tilted dispersion bands. Here, we experimentally realize a topological circuit that hosts only topological bands with a minimal number of four ideal type-II WPs. By stacking two-dimensional (2D) layers of inductor-capacitor (LC) resonator dimers with the broken parity inversion symmetry (P), we achieve a strongly tilted band structure with two group velocities in the same direction, and topological surface states in an incomplete bandgap. Our results establish an ideal system for the further study of Weyl physics and other exotic topological phenomena.

The Axial Anomaly in Lorentz Violating Theories: Towards the Electromagnetic Response of Weakly Tilted Weyl Semimetals

Using the path integral formulation in Euclidean space, we extended the calculation of the abelian chiral anomalies in the case of Lorentz violating theories by considering a new fermionic correction term provided by the standard model extension, which arises in the continuous Hamiltonian of a weakly tilted Weyl semimetal, and whose cones have opposite tilting. We found that this anomaly is insensitive to the tilting parameter, retaining its well-known covariant form. This independence on the Lorentz violating parameters is consistent with other findings reported in the literature. The initially imposed gauge invariant regularization was consistently recovered at the end of the calculation by the appearance of highly non-trivial combinations of the covariant derivatives, which ultimately managed to give only terms containing the electromagnetic tensor. We emphasize that the value of the anomaly with an arbitrary parameter is not automatically related to the effective action describing the electromagnetic response of such materials.

Observation of a singular Weyl point surrounded by charged nodal walls in PtGa

Constrained by the Nielsen-Ninomiya no-go theorem, in all so-far experimentally determined Weyl semimetals (WSMs) the Weyl points (WPs) always appear in pairs in the momentum space with no exception. As a consequence, Fermi arcs occur on surfaces which connect the projections of the WPs with opposite chiral charges. However, this situation can be circumvented in the case of unpaired WP, without relevant surface Fermi arc connecting its surface projection, appearing singularly, while its Berry curvature field is absorbed by nontrivial charged nodal walls. Here, combining angle-resolved photoemission spectroscopy with density functional theory calculations, we show experimentally that a singular Weyl point emerges in PtGa at the center of the Brillouin zone (BZ), which is surrounded by closed Weyl nodal walls located at the BZ boundaries and there is no Fermi arc connecting its surface projection. Our results reveal that nontrivial band crossings of different dimensionalities can emerge concomitantly in condensed matter, while their coexistence ensures the net topological charge of different dimensional topological objects to be zero. Our observation extends the applicable range of the original Nielsen-Ninomiya no-go theorem which was derived from zero dimensional paired WPs with opposite chirality.

Direct Synthesis of Nanosheet-Stacked Hierarchical "Honey Stick-like" MFI Zeolites by an Aromatic Heterocyclic Dual-Functional Organic Structure-Directing Agent

Soft template designing is the most promising strategy for the synthesis of zeolite nanosheets. MFI nanosheets directed by soft templates (containing long-chain alkyl groups or aromatic groups as hydrophobic component) can be found frequently; however, so far, MFI nanosheets synthesized by soft templates with aromatic heterocycle groups (e. g., s-triazine groups) are rare. Herein, a nanosheet-stacked hierarchical MFI zeolite (NSHM) has been synthesized by using a triply branched s-triazine-based surfactant as a bifunctional organic structure-directing agent. On the basis of a geometrical match relationship, a formation model has been proposed. Synthesized NSHM had abundant mesopores stacked by nanosheets and exhibited a high surface area (430 m²  ⋅ g^-1 ). The 1 wt% Pd/NSHM attained a significant increase in yield of cyclohexanol/cyclohexanone mixture (from 66 to 85 %) in the oxidation of cyclohexane compared with Silicalite-1 and SBA-15 as supports.

Vortex states in an acoustic Weyl crystal with a topological lattice defect

Crystalline materials can host topological lattice defects that are robust against local deformations, and such defects can interact in interesting ways with the topological features of the underlying band structure. We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital angular momentum locked to the direction of propagation. They span a range of axial wavenumbers defined by the projections of two bulk Weyl points to a one-dimensional subspace, in a manner analogous to the formation of Fermi arc surface states. We use acoustic experiments to probe their dispersion relation, orbital angular momentum locked waveguiding, and ability to emit acoustic vortices into free space. These results point to new possibilities for creating and exploiting topological modes in three-dimensional structures through the interplay between band topology in momentum space and topological lattice defects in real space.

Momentum-space signatures of Berry flux monopoles in the Weyl semimetal TaAs

Since the early days of Dirac flux quantization, magnetic monopoles have been sought after as a potential corollary of quantized electric charge. As opposed to magnetic monopoles embedded into the theory of electromagnetism, Weyl semimetals (WSM) exhibit Berry flux monopoles in reciprocal parameter space. As a function of crystal momentum, such monopoles locate at the crossing point of spin-polarized bands forming the Weyl cone. Here, we report momentum-resolved spectroscopic signatures of Berry flux monopoles in TaAs as a paradigmatic WSM. We carried out angle-resolved photoelectron spectroscopy at bulk-sensitive soft X-ray energies (SX-ARPES) combined with photoelectron spin detection and circular dichroism. The experiments reveal large spin- and orbital-angular-momentum (SAM and OAM) polarizations of the Weyl-fermion states, resulting from the broken crystalline inversion symmetry in TaAs. Supported by first-principles calculations, our measurements image signatures of a topologically non-trivial winding of the OAM at the Weyl nodes and unveil a chirality-dependent SAM of the Weyl bands. Our results provide directly bulk-sensitive spectroscopic support for the non-trivial band topology in the WSM TaAs, promising to have profound implications for the study of quantum-geometric effects in solids.

Weyl semimetals exhibit Berry flux monopoles in momentum-space, but direct experimental evidence has remained elusive. Here, the authors reveal topologically non-trivial winding of the orbital-angular-momentum at the Weyl nodes and a chirality-dependent spin-angular-momentum of the Weyl bands, as a direct signature of the Berry flux monopoles in TaAs.

Systematic Investigation of the Coupling between One-Dimensional Edge States of a Topological Crystalline Insulator

The interaction of spin-polarized one-dimensional (1D) topological edge modes localized along single-atomic steps of the topological crystalline insulator Pb_{0.7}Sn_{0.3}Se(001) has been studied systematically by scanning tunneling spectroscopy. Our results reveal that the coupling of adjacent edge modes sets in at a step-to-step distance d_{ss}≤25  nm, resulting in a characteristic splitting of a single peak at the Dirac point in tunneling spectra. Whereas the energy splitting exponentially increases with decreasing d_{ss} for single-atomic steps running almost parallel, we find no splitting for single-atomic step edges under an angle of 90°. The results are discussed in terms of overlapping wave functions with p_{x}, p_{y} orbital character.

Quantum Transport of the 2D Surface State in a Nonsymmorphic Semimetal

In a topological semimetal with Dirac or Weyl points, the bulk-boundary correspondence principle predicts a gapless edge mode if the essential symmetry is still preserved at the surface. The detection of such topological surface state has been considered as the fingerprint prove for crystals with nontrivial topological bulk band. On the contrary, it has been proposed that even with symmetry broken at the surface, a new surface band can emerge in nonsymmorphic topological semimetals. The symmetry reduction at the surface lifts the bulk band degeneracies and produces an unusual "floating" surface band with trivial topology. Here, we first report quantum transport probing to ZrSiSe thin flakes and directly reveal transport signatures of this new surface state. Remarkably, though topologically trivial, such a surface band exhibits substantial two-dimensional Shubnikov-de Haas quantum oscillations with high mobility, which signifies a new protection mechanism and may open applications for quantum computing and spintronic devices.

Observation of Negative Terahertz Photoconductivity in Large Area Type-II Dirac Semimetal PtTe_{2}

As a newly emergent type-II Dirac semimetal, platinum telluride (PtTe_{2}) stands out from other two dimensional noble-transition-metal dichalcogenides for the unique band structure and novel physical properties, and has been studied extensively. However, the ultrafast response of low energy quasiparticle excitation in terahertz frequency remains nearly unexplored yet. Herein, we employ optical pump-terahertz probe (OPTP) spectroscopy to systematically study the photocarrier dynamics of PtTe_{2} thin films with varying pump fluence, temperature, and film thickness. Upon photoexcitation the terahertz photoconductivity (PC) of PtTe_{2} films shows abrupt increase initially, while the terahertz PC changes into negative value in a subpicosecond timescale, followed by a prolonged recovery process that lasted a few nanoseconds. The magnitude of both positive and negative terahertz PC response shows strongly pump fluence dependence. We assign the unusual negative terahertz PC to the formation of small polaron due to the strong electron-phonon (e-ph) coupling, which is further substantiated by temperature and film thickness dependent measurements. Moreover, our investigations give a subpicosecond timescale of simultaneous carrier cooling and polaron formation. The present study provides deep insights into the underlying dynamics evolution mechanisms of photocarrier in type-II Dirac semimetal upon photoexcitation, which is of crucial importance for designing PtTe_{2}-based optoelectronic devices.

Correlated Magnetic Weyl Semimetal State in Strained Pr2 Ir2 O7

Correlated topological phases (CTPs) with interplay between topology and electronic correlations have attracted tremendous interest in condensed matter physics. Therein, correlated Weyl semimetals (WSMs) are rare in nature and, thus, have so far been less investigated experimentally. In particular, the experimental realization of the interacting WSM state with logarithmic Fermi velocity renormalization has not been achieved yet. Here, experimental evidence of a correlated magnetic WSM state with logarithmic renormalization in strained pyrochlore iridate Pr₂ Ir₂ O₇ (PIO) which is a paramagnetic Luttinger semimetal in bulk, is reported. Benefitting from epitaxial strain, "bulk-absent" all-in-all-out antiferromagnetic ordering can be stabilized in PIO film, which breaks time-reversal symmetry and leads to a magnetic WSM state. With further analysis of the experimental data and renormalization group calculations, an interacting Weyl liquid state with logarithmically renormalized Fermi velocity, similar to that in graphene, is found, dressed by long-range Coulomb interactions. This work highlights the interplay of strain, magnetism, and topology with electronic correlations, and paves the way for strain-engineering of CTPs in pyrochlore iridates.

The Emergence and Evolution of Borophene

Neighboring carbon and sandwiched between non-metals and metals in the periodic table of the elements, boron is one of the most chemically and physically versatile elements, and can be manipulated to form dimensionally low planar structures (borophene) with intriguing properties. Herein, the theoretical research and experimental developments in the synthesis of borophene, as well as its excellent properties and application in many fields, are reviewed. The decade-long effort toward understanding the size-dependent structures of boron clusters and the theory-directed synthesis of borophene, including bottom-up approaches based on different foundations, as well as up-down approaches with different exfoliation modes, and the key factors influencing the synthetic effects, are comprehensively summarized. Owing to its excellent chemical, electronic, mechanical, and thermal properties, borophene has shown great promise in supercapacitor, battery, hydrogen-storage, and biomedical applications. Furthermore, borophene nanoplatforms used in various biomedical applications, such as bioimaging, drug delivery, and photonic therapy, are highlighted. Finally, research progress, challenges, and perspectives for the future development of borophene in large-scale production and other prospective applications are discussed.

Kramers nodal line metals

Recently, it was pointed out that all chiral crystals with spin-orbit coupling (SOC) can be Kramers Weyl semimetals (KWSs) which possess Weyl points pinned at time-reversal invariant momenta. In this work, we show that all achiral non-centrosymmetric materials with SOC can be a new class of topological materials, which we term Kramers nodal line metals (KNLMs). In KNLMs, there are doubly degenerate lines, which we call Kramers nodal lines (KNLs), connecting time-reversal invariant momenta. The KNLs create two types of Fermi surfaces, namely, the spindle torus type and the octdong type. Interestingly, all the electrons on octdong Fermi surfaces are described by two-dimensional massless Dirac Hamiltonians. These materials support quantized optical conductance in thin films. We further show that KNLMs can be regarded as parent states of KWSs. Therefore, we conclude that all non-centrosymmetric metals with SOC are topological, as they can be either KWSs or KNLMs.

Triple-Point Fermions in Ferroelectric GeTe

Ferroelectric α-GeTe is unveiled to exhibit an intriguing multiple nontrivial topology of the electronic band structure due to the existence of triple-point and type-II Weyl fermions, which goes well beyond the giant Rashba spin splitting controlled by external fields as previously reported. Using spin- and angle-resolved photoemission spectroscopy combined with ab initio density functional theory, the unique spin texture around the triple point caused by the crossing of one spin-degenerate and two spin-split bands along the ferroelectric crystal axis is derived. This consistently reveals spin winding numbers that are coupled with time-reversal symmetry and Lorentz invariance, which are found to be equal for both triple-point pairs in the Brillouin zone. The rich manifold of effects opens up promising perspectives for studying nontrivial phenomena and multicomponent fermions in condensed matter systems.

Topologically Protected Wormholes in Type-III Weyl Semimetal Co3In2X2 (X = S, Se)

The observation of wormholes has proven to be difficult in the field of astrophysics. However, with the discovery of novel topological quantum materials, it is possible to observe astrophysical and particle physics effects in condensed matter physics. It is proposed in this work that wormholes can exist in a type-III Weyl phase. In addition, these wormholes are topologically protected, making them feasible to create and measure in condensed matter systems. Finally, Co3In2X2 (X = S, Se) are identified as ideal type-III Weyl semimetals and experiments are put forward to confirm the existence of a type-III Weyl phase.

Experimental Observation and Spin Texture of Dirac Node Arcs in Tetradymite Topological Metals

We report the observation of a nontrivial spin texture in Dirac node arcs, i.e., novel topological objects formed when Dirac cones of massless particles extend along an open one-dimensional line in momentum space. We find that such states are present in all the compounds of the tetradymite M_{2}Te_{2}X family (M=Ti, Zr, or Hf and X=P or As) regardless of the weak or strong character of the topological invariant. The Dirac node arcs in tetradymites are thus the simplest possible textbook example of a type-I Dirac system with a single spin-polarized node arc.

Hard x-ray photoelectron spectroscopy: a snapshot of the state-of-the-art in 2020

Hard x-ray photoelectron spectroscopy (HAXPES) is establishing itself as an essential technique for the characterisation of materials. The number of specialised photoelectron spectroscopy techniques making use of hard x-rays is steadily increasing and ever more complex experimental designs enable truly transformative insights into the chemical, electronic, magnetic, and structural nature of materials. This paper begins with a short historic perspective of HAXPES and spans from developments in the early days of photoelectron spectroscopy to provide an understanding of the origin and initial development of the technique to state-of-the-art instrumentation and experimental capabilities. The main motivation for and focus of this paper is to provide a picture of the technique in 2020, including a detailed overview of available experimental systems worldwide and insights into a range of specific measurement modi and approaches. We also aim to provide a glimpse into the future of the technique including possible developments and opportunities.

Chiral Anomaly in Interacting Condensed Matter Systems

The chiral anomaly is a fundamental quantum mechanical phenomenon which is of great importance to both particle physics and condensed matter physics alike. In the context of QED, it manifests as the breaking of chiral symmetry in the presence of electromagnetic fields. It is also known that anomalous chiral symmetry breaking can occur through interactions alone, as is the case for interacting one-dimensional systems. In this Letter, we investigate the interplay between these two modes of anomalous chiral symmetry breaking in the context of interacting Weyl semimetals. Using Fujikawa's path integral method, we show that the chiral charge continuity equation is modified by the presence of interactions which can be viewed as including the effect of the electric and magnetic fields generated by the interacting quantum matter. This can be understood further using dimensional reduction and a Luttinger liquid description of the lowest Landau level. These effects manifest themselves in the nonlinear response of the system. In particular, we find an interaction-dependent density response due to a change in the magnetic field as well as a contribution to the nonequilibrium and inhomogeneous anomalous Hall response while preserving its equilibrium value.

Fast nuclear spin relaxation rates in tilted cone Weyl semimetals: redshift factors from Korringa relation

Spin lattice relaxation rate is investigated for 3D tilted cone Weyl semimetals (TCWSMs). The nuclear spin relaxation rate is presented as a function of temperature and tilt parameter. We find that the relaxation rate behaves as(1-ζ2)-αwithα≈ 9 where 0 ⩽ζ< 1 is the tilt parameter. We demonstrate that such a strong enhancement forζ≲ 1 that gives rise to very fast relaxation rates, is contributed by a new hyperfine interactions arising from the tilt itself. This can be attributed to the combination of anisotropy of the Fermi surface and an additional part related to the structure of the spacetime: extracting an effective density of states (DOS)ρ̃from the Korringa relation, we show that it is related to the DOSρof the tilted cone dispersion by the 'redshift factor' asρ̃=ρ/1-ζ2. We interpret this relation as NMR manifestation of an emergent underlying spacetime structure in TCWSMs.

Large Fermi-Energy Shift and Suppression of Trivial Surface States in NbP Weyl Semimetal Thin Films

Weyl semimetals, a class of 3D topological materials, exhibit a unique electronic structure featuring linear band crossings and disjoint surface states (Fermi-arcs). While first demonstrations of topologically driven phenomena have been realized in bulk crystals, efficient routes to control the electronic structure have remained largely unexplored. Here, a dramatic modification of the electronic structure in epitaxially grown NbP Weyl semimetal thin films is reported, using in situ surface engineering and chemical doping strategies that do not alter the NbP lattice structure and symmetry, retaining its topological nature. Through the preparation of a dangling-bond-free, P-terminated surface which manifests in a surface reconstruction, all the well-known trivial surface states of NbP are fully suppressed, resulting in a purely topological Fermi-arc dispersion. In addition, a substantial Fermi-energy shift from -0.2 to 0.3 eV across the Weyl points is achieved by surface chemical doping, unlocking access to the hitherto unexplored n-type region of the Weyl spectrum. These findings constitute a milestone toward surface-state and Fermi-level engineering of topological bands in Weyl semimetals, and, while there are still challenges in minimizing doping-driven disorder and grain boundary density in the films, they do represent a major advance to realize device heterostructures based on Weyl physics.

Defect induced ferromagnetic ordering and room temperature negative magnetoresistance in MoTeP

The magneto-transport, magnetization and theoretical electronic-structure have been investigated on type-II Weyl semimetallic MoTeP. The ferromagnetic ordering is observed in the studied sample and it has been shown that the observed magnetic ordering is due to the defect states. It has also been demonstrated that the presence of ferromagnetic ordering in effect suppresses the magnetoresistance (MR) significantly. Interestingly, a change-over from positive to negative MR is observed at higher temperature which has been attributed to the dominance of spin scattering suppression.

Quantum spin Hall and quantum anomalous Hall states in magnetic Ti2Te2O single layer

Magnetic topological insulators, such as MnBi₂Te₄have attracted great attention recently due to their application to the quantum anomalous Hall (QAH) effect. However, the magnetic quantum spin Hall (QSH) effect in two-dimensional (2D) materials has not yet been reported. Here based on first-principle calculations we find that Ti₂Te₂O, a van der Waals layered compound, can cherish both the QAH and QSH states, depending on the magnetic order in its single layer. If the single layer was in a chessboard antiferromagnetic (FM) state, it is a QSH insulator which carries two counterpropagating helical edge states. The spin-orbit-couplings induced bulk band gap can approach as large as 0.31 eV. On the other hand, if the monolayer becomes FM, exchange interactions would push one pair of bands away from the Fermi energy and leave only one chiral edge state remaining, which turns the compound into a Chern insulator (precisely, it is semimetallic with a topologically direct band gap). Both magnetic orders explicitly break the time reversal symmetry and split the energy bands of different spin orientations. To our knowledge, Ti₂Te₂O is the first compound that predicted to possess both intrinsic QSH and QAH effects. Our works provide new possibilities to reach a controllable phase transition between two topological nontrivial phases through magnetism tailoring.

Longitudinal magnetoconductivity of tilted type-I Weyl semimetals from semiclassical to ultra-quantum regime

Weyl semimetals (WSMs) display many unusual magnetotransport phenomena. Here, based on the Landau quantization and Boltzmann equation, we theoretically study the longitudinal magnetoconductivity for tilted type-I WSMs from weak to strong magnetic field within a unified framework. It is found that, in semiclassical (weak magnetic field) regime, the conductivity has an angular dependentB-linear term besides theB-quadratic term common to isotropic nodes. In ultra-quantum (strong magnetic field) regime, the magnetoconductivity shows a linear dependence onB, and this dependence is affected by the tilt. In the intermediate regime, magnetoconductivity shows a tilt-modified quantum oscillation behavior due to the oscillation in the density of state. These findings recover the results for isotropic nodes without tilt, and suggest a possible way to identify the tilt axis of tilted WSMs through magnetotransport experiment.

Novel electric field effects on magneto-optical conductivity in eight-Pmmnborophene

We theoretically study the Landau levels and the magneto-optical conductivity of eight-Pmmnborophene in the presence of a perpendicular magnetic field and an inplane electric field. We find that in the absence of the inplane electric field, the magneto-optical conductivity of eight-Pmmnborophene presents a series of striking single resonance peaks as functions of the frequencyω, and the longitudinal conductivities are found to be anisotropic due to its anisotropic tilted Dirac cones. In the presence of the inplane electric field, some novel effects are predicted on the Landau levels and the magneto-optical conductivity. The Landau level spacings in the two tilted Dirac cones are different, which lifts the degeneracy of the twofold valley, and the magneto-optical conductivity appears a double peak structure. We also discuss the influence of the chemical potential between different Landau levels on the double peak of the magneto-optical response. The valley related magneto-optical properties in the anisotropic structure may make eight-Pmmnborophene a candidate for the new optical devices.

Omnipresence of Weak Antilocalization (WAL) in Bi2Se3 Thin Films: A Review on Its Origin

Topological insulators are materials with time-reversal symmetric states of matter in which an insulating bulk is surrounded by protected Dirac-like edge or surface states. Among topological insulators, Bi2Se3 has attracted special attention due to its simple surface band structure and its relatively large band gap that should enhance the contribution of its surface to transport, which is usually masked by the appearance of defects. In order to avoid this difficulty, several features characteristic of topological insulators in the quantum regime, such as the weak-antilocalization effect, can be explored through magnetotransport experiments carried out on thin films of this material. Here, we review the existing literature on the magnetotransport properties of Bi2Se3 thin films, paying thorough attention to the weak-antilocalization effect, which is omnipresent no matter the film quality. We carefully follow the different situations found in reported experiments, from the most ideal situations, with a strong surface contribution, towards more realistic cases where the bulk contribution dominates. We have compared the transport data found in literature to shed light on the intrinsic properties of Bi2Se3, finding a clear relationship between the mobility and the phase coherence length of the films that could trigger further experiments on transport in topological systems.

Realization of an ideal Weyl semimetal band in a quantum gas with 3D spin-orbit coupling

Weyl semimetals are three-dimensional (3D) gapless topological phases with Weyl cones in the bulk band. According to lattice theory, Weyl cones must come in pairs, with the minimum number of cones being two. A semimetal with only two Weyl cones is an ideal Weyl semimetal (IWSM). Here we report the experimental realization of an IWSM band by engineering 3D spin-orbit coupling for ultracold atoms. The topological Weyl points are clearly measured via the virtual slicing imaging technique in equilibrium and are further resolved in the quench dynamics. The realization of an IWSM band opens an avenue to investigate various exotic phenomena that are difficult to access in solids.

Ultrafast dynamical Lifshitz transition

Fermi surface is at the heart of our understanding of metals and strongly correlated many-body systems. An abrupt change in the Fermi surface topology, also called Lifshitz transition, can lead to the emergence of fascinating phenomena like colossal magnetoresistance and superconductivity. While Lifshitz transitions have been demonstrated for a broad range of materials by equilibrium tuning of macroscopic parameters such as strain, doping, pressure, and temperature, a nonequilibrium dynamical route toward ultrafast modification of the Fermi surface topology has not been experimentally demonstrated. Combining time-resolved multidimensional photoemission spectroscopy with state-of-the-art TDDFT+U simulations, we introduce a scheme for driving an ultrafast Lifshitz transition in the correlated type-II Weyl semimetal T _d-MoTe₂ We demonstrate that this nonequilibrium topological electronic transition finds its microscopic origin in the dynamical modification of the effective electronic correlations. These results shed light on a previously unexplored ultrafast scheme for controlling the Fermi surface topology in correlated quantum materials.