Evolution of the Fermi surface of Weyl semimetals in the transition metal pnictide family

Topological phase transition and tunable surface states in YBi

A unique co-existence of extremely large magnetoresistance (XMR) and topological characteristics in non-magnetic rare-earth monopnictides has stimulated intensive research on these materials. Yttrium monobismuthide (YBi) has been reported to exhibit XMR up to 105% but its topological properties still need clarification. Here we use the hybrid density functional theory to probe the structural, electronic, and topological properties of YBi in detail. We observe that YBi is topologically trivial semimetal at ambient pressure which is in accordance with reported experimental results. The topological phase transitions i.e. trivial to non-trivial are obtained with volumetric pressure of 6.5 GPa and 3% of epitaxial strain. These topological phase transitions are well within the structural phase transition of YBi (24.5 GPa). The topological non-trivial state is characterized by band inversions amongY-dband andBi-pband atΓ-andX-pointwhich is further verified with the help of surface band structure along (001) plane. The Z2topological invariants are calculated with the help of product of parities and evolution of Wannier charge centers. The occurrence of non-trivial phase in YBi with a relatively small epitaxial strain, which a thin film geometry can naturally have, make it an ideal candidate to probe inter-relationship between XMR and non-trivial topology.

Efficient Nitrogen Reduction on Weyl Antiferromagnet Mn3 Sn

Topological semimetals have gradually emerged as excellent catalysts owing to their robust surface states. Recently, Mn3 X (X=Sn, Ge, and Ir), which exhibits noncollinear antiferromagnetic phases at room temperature, has been found to possess energy bands that are characteristic of Weyl semimetals. In this study, we demonstrate that the perfect Mn3 Sn (001) surface is favorable for N2 reduction with a low onset potential. According to a theoretical criterion, the catalytic performance of the (001) surface of Mn3 Sn is higher than that of the (001) surfaces of the homologues Cr3 Sn and Mo3 Sn. The construction and catalytic performance of other types of Mn3 Sn surfaces are also investigated. Our findings highlight the feasibility of applying topological Weyl semimetals as electrocatalysts for N2 reduction.

The discovery of three-dimensional Van Hove singularity

Arising from the extreme/saddle point in electronic bands, Van Hove singularity (VHS) manifests divergent density of states (DOS) and induces various new states of matter such as unconventional superconductivity. VHS is believed to exist in one and two dimensions, but rarely found in three dimension (3D). Here, we report the discovery of 3D VHS in a topological magnet EuCd2As2 by magneto-infrared spectroscopy. External magnetic fields effectively control the exchange interaction in EuCd2As2, and shift 3D Weyl bands continuously, leading to the modification of Fermi velocity and energy dispersion. Above the critical field, the 3D VHS forms and is evidenced by the abrupt emergence of inter-band transitions, which can be quantitatively described by the minimal model of Weyl semimetals. Three additional optical transitions are further predicted theoretically and verified in magneto-near-infrared spectra. Our results pave the way to exploring VHS in 3D systems and uncovering the coordination between electronic correlation and the topological phase.

Observing Relative Homotopic Degeneracy Conversions with Circuit Metamaterials

Making nodal lines (NLs) deterministic is quite challenging because directly probing them requires bulk momentum resolution. Here, based on the general scattering theory, we show that the Bloch modes of the circuit metamaterials can be selectively excited with a proper source. Consequently, the transport measurement for characterizing the circuit band structure is momentum resolved. Facilitated by this bulk resolution, we systematically demonstrate the degeneracy conversions ruled by the relative homotopy, including the conversions between Weyl points (WPs) and NLs, and between NLs. It is experimentally shown that two WPs with opposite chirality in a two-band model surprisingly convert into an NL rather than annihilating. And the multiband anomaly (due to the delicate property) in the NL-to-NL conversions is also observed, which in fact is captured by the non-Abelian relative homotopy. Additionally, the physical effects owing to the conversions, like the Fermi arc connecting NLs and the parallel transport of eigenstates, are discussed as well. Other types of degeneracy conversions, such as those induced by spin-orbit coupling or symmetry breaking, are directly amenable to the proposed circuit platform.

High-Mobility Topological Semimetals as Novel Materials for Huge Magnetoresistance Effect and New Type of Quantum Hall Effect

The quantitative description of electrical and magnetotransport properties of solid-state materials has been a remarkable challenge in materials science over recent decades. Recently, the discovery of a novel class of materials-the topological semimetals-has led to a growing interest in the full understanding of their magnetotransport properties. In this review, the strong interplay among topology, band structure, and carrier mobility in recently discovered high carrier mobility topological semimetals is discussed and their effect on their magnetotransport properties is outlined. Their large magnetoresistance effect, especially in the Hall transverse configuration, and a new version of a three-dimensional quantum Hall effect observed in high-mobility Weyl and Dirac semimetals are reviewed. The possibility of designing novel quantum sensors and devices based on solid-state semimetals is also examined.

SdH Oscillations from the Dirac Surface State in the Fermi-Arc Antiferromagnet NdBi

The recent progress in CuMnAs and Mn3X (X = Sn, Ge, Pt) shows that antiferromagnets (AFMs) provide a promising platform for advanced spintronics device innovations. Most recently, a switchable Fermi-arc is discovered by the ARPES technique in antiferromagnet NdBi, but the knowledge about electron-transport property and the manipulability of the magnetic structure in NdBi is still vacant to date. In this study, SdH oscillations are successfully verified from the Dirac surface states (SSs) with 2-dimensionality and nonzero Berry phase. Particularly, it is observed that the spin-flop transition only appears when the external magnetical field is applied along [001] direction, and features obvious hysteresis for the first time in NdBi, which provides a powerful handle for adjusting the spin texture in NdBi. Crucially, the DFT shows the Dirac cone and the Fermi arc strongly depend on the high-order magnetic structure of NdBi and further reveals the orbital magnetic moment of Nd plays a crucial role in fostering the peculiar SSs, leading to unveil the mystery of the band-splitting effect and to manipulate the electronic transport, high-effectively, in the thin film works in NdBi. It is believed that this study provides important guidance for the development of new antiferromagnet-based spintronics devices based on cutting-edge rare-earth monopnictides.

Surface-independent CO2 and CO reduction on two-dimensional kagome metal KV3Sb5

Two-dimensional kagome metals possess rich band structure characteristics, including Dirac points, flat bands, and van Hove singularities, because of their special geometric structures. Furthermore, kagome metals AV3Sb5 (A = K, Rb, and Cs) have garnered significant attention due to their nontrivial topological electronic structures. In this study, we theoretically demonstrate that the KV3Sb5 (001) surface is conducive to CO2 and CO reduction. The thermodynamic stability and electrochemical states of various surface types are investigated. The reaction paths reveal that the product is identical on different surfaces, and the free energy profiles exhibit low onset potentials. This paper elucidates the effect of two-dimensional topological kagome metals on CO2 and CO reduction.

Assessing Nontrivial Topology in Weyl Semimetals by Dichroic Photoemission

The electronic structure of Weyl semimetals features Berry flux monopoles in the bulk and Fermi arcs at the surface. While angle-resolved photoelectron spectroscopy (ARPES) is successfully used to map the bulk and surface bands, it remains a challenge to explicitly resolve and pinpoint these topological features. Here we combine state-of-the-art photoemission theory and experiments over a wide range of excitation energies for the Weyl semimetals TaAs and TaP. Our results show that simple surface-band-counting schemes, proposed previously to identify nonzero Chern numbers, are ambiguous due to pronounced momentum-dependent spectral weight variations and the pronounced surface-bulk hybridization. Instead, our findings indicate that dichroic ARPES provides an improved approach to identify Fermi arcs but requires an accurate description of the photoelectron final state.

Fermi surface of the chiral topological semimetal PtGa

PtGa is a topological semimetal with giant spin-split Fermi arcs. Here, we report on angular-dependent de Haas-van Alphen (dHvA) measurements combined with band-structure calculations to elucidate the details of the bulk Fermi surface of PtGa. The strong spin-orbit coupling leads to eight bands crossing the Fermi energy that form a multitude of Fermi surfaces with closed extremal orbits and results in very rich dHvA spectra. The large number of experimentally observed dHvA frequencies make the assignment to the equally large number of calculated dHvA orbits challenging. Nevertheless, we find consistency between experiment and calculations verifying the topological character with maximal Chern number of the spin-split Fermi surface.

Selective CO2 reduction on topological Chern magnet TbMn6Sn6

As a new type of topological magnet, TbMn₆Sn₆ has a planar Mn kagome lattice with out-of-plane magnetic moments. Previous studies have found spin-polarized Chern gapped Dirac fermions in TbMn₆Sn₆, which are advantageous to topological catalysis. In this study, we theoretically demonstrate that the TbMn₆Sn₆ (001) surface is favorable for CO₂ reduction. The stability of different surface types is investigated, and then the reaction paths of CO₂ reduction on the surfaces are revealed to prove that the product is selective. This work reveals the effect of magnetic topological materials on CO₂ reduction.

Pressure-Quenched Superconductivity in Weyl Semimetal NbP Induced by Electronic Phase Transitions under Pressure

The TaAs family (NbAs, TaAs, NbP, TaP) are kinds of Weyl semimetals with lots of novel properties, thus attracting considerable attention in recent years. Here, we systematically studied the Weyl semimetal NbP up to 72 GPa through the resistivity, Raman spectra, X-ray diffraction measurements, and first-principles density functional theory (DFT) calculations. A pressure-induced semimetal-metal transition was observed at ∼36 GPa, which was further confirmed by the DFT calculations. With further compression up to 52 GPa, a superconducting state was observed. Interestingly, the T_c increases significantly upon decompression and shows a dome-shaped trend as a function of pressure. Surprisingly, the pressure-induced superconductivity can be quenched to ambient pressure, and all transitions under pressure do not involve any structural change. Our work not only depicts a phase diagram of the NbP system under high pressure but also provides a new experimental insight for superconductivity in Weyl semimetals.

Network analysis of Weyl semimetal photogalvanic systems

We develop a general methodology capable of analyzing the response of Weyl semimetal (WSM) photogalvanic networks. Both single-port and multiport configurations are investigated via extended versions of Norton's theorem. An equivalent circuit model is provided where the photogalvanic currents induced in these gapless topological materials can be treated as polarization-dependent sources. To illustrate our approach, we carry out transport simulations in arbitrarily shaped configurations involving pertinent WSMs. Our analysis indicates that the photogalvanic currents collected in a multi-electrode system directly depend on the geometry of the structure as well as on the excitation and polarization pattern of the incident light. Our results could be helpful in designing novel optoelectronic systems that make use of the intriguing features associated with WSMs.

An ideal Weyl nodal ring with a large drumhead surface state in the orthorhombic compound TiS2

Topological metals or semimetals have attracted great research attention and interest in condensed matter physics and chemistry due to their exotic properties. Different from the conventional topological insulators, topological metals or semimetals are characterized by distinct topological surface states, such as a Fermi arc or a drumhead surface state, which are often used in experiments to verify the corresponding topological properties. However, the current study in this field is strongly limited in the experimental characterization because of the extreme lack of perfect material candidates with a clean band structure and clear surface states. In this work, based on theoretical calculations, we propose a new topological semimetal TiS₂, which has an orthorhombic structure and exhibits excellent stability. Calculated electronic band structures reveal that there is a single Weyl nodal ring in the k_y = 0 plane. A detailed symmetry analysis is provided and the corresponding surface state is calculated, which exhibits both a large energy variation of 1.5 eV and wide space distribution without and with the spin orbit coupling effect. Besides, the surface states are well separated from the bulk state. These ideal features together make TiS₂ a promising nodal line semimetal for experimental investigation. In combination with the other two isostructural compounds TiSe₂ and TiTe₂ with similar properties, their further experimental synthesis and characterization can be highly expected and the corresponding study for the topological nodal line state can thus be greatly facilitated.

Topological phase transition associated with structural phase transition in ternary half Heusler compound LiAuBi

In this article, we report detailed theoretical investigations of topological phases in non-centrosymmetric half Heusler compound LiAuBi up to a pressure of 30 GPa. It is found that the compound forms into a dynamically stable face-centered cubic (FCC) lattice structure of space groupF4¯3m(216) at ambient pressure. The compound is topologically non-trivial at ambient pressure, but undergoes a quantum phase transition to trivial topological phase at 23.4 GPa. However, the detailed investigations show a structural phase transition from FCC lattice (space group 216) to a honeycomb lattice (space group 194) at 13 GPa, which is also associated with a non-trivial to trivial topological phase transition. Further investigations show that the compound also carries appreciable thermoelectric properties at ambient pressure. The figure of merit (ZT) increases from 0.21 at room temperature to a maximum value of 0.22 at 500 K. The theoretical findings show its potential for practical applications in spintronics as well as thermoelectricity, therefore LiAuBi needs to be synthesized and investigated experimentally for its applications.

Dimensionality of the Superconductivity in the Transition Metal Pnictide WP

We report theoretical and experimental results on the transition metal pnictide WP. The theoretical outcomes based on tight-binding calculations and density functional theory indicate that WP is a three-dimensional superconductor with an anisotropic electronic structure and nonsymmorphic symmetries. On the other hand, magnetoresistance experimental data and the analysis of superconducting fluctuations of the conductivity in external magnetic field indicate a weakly anisotropic three-dimensional superconducting phase.

Photocurrent-driven transient symmetry breaking in the Weyl semimetal TaAs

Symmetry plays a central role in conventional and topological phases of matter, making the ability to optically drive symmetry changes a critical step in developing future technologies that rely on such control. Topological materials, like topological semimetals, are particularly sensitive to a breaking or restoring of time-reversal and crystalline symmetries, which affect both bulk and surface electronic states. While previous studies have focused on controlling symmetry via coupling to the crystal lattice, we demonstrate here an all-electronic mechanism based on photocurrent generation. Using second harmonic generation spectroscopy as a sensitive probe of symmetry changes, we observe an ultrafast breaking of time-reversal and spatial symmetries following femtosecond optical excitation in the prototypical type-I Weyl semimetal TaAs. Our results show that optically driven photocurrents can be tailored to explicitly break electronic symmetry in a generic fashion, opening up the possibility of driving phase transitions between symmetry-protected states on ultrafast timescales.

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.

Two-dimensional Weyl points and nodal lines in pentagonal materials and their optical response

Two-dimensional pentagonal structures based on the Cairo tiling are the basis of a family of layered materials with appealing physical properties. In this work we present a theoretical study of the symmetry-based electronic and optical properties of these pentagonal materials. We provide a complete classification of the space groups that support pentagonal structures for binary and ternary systems. By means of first-principles calculations, the electronic band structures and the local spin textures in momentum space are analyzed for four examples of these materials, namely, PdSeTe, PdSeS, InP₅ and GeBi₂, all of which are dynamically stable. Our results show that pentagonal structures can be realized in chiral and achiral lattices with Weyl nodes pinned at high-symmetry points and nodal lines along the Brillouin zone boundary; these degeneracies are protected by the combined action of crystalline and time-reversal symmetries. Additionally, we computed the linear and nonlinear optical features of the proposed pentagonal materials and discuss some particular features such as the shift current, which shows an enhancement due to the presence of nodal lines and points, and their possible applications.

Topological Quantum Materials from the Viewpoint of Chemistry

Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space, namely atoms, valence electrons, bonds, and orbitals, and reciprocal space, namely bands and Fermi surfaces, via symmetry and topology, classifying topological materials within a single-particle picture is possible. Currently, most materials are classified as trivial insulators, semimetals, and metals or as topological insulators, Dirac and Weyl nodal-line semimetals, and topological metals. The key ingredients for topology are certain symmetries, the inert pair effect of the outer electrons leading to inversion of the conduction and valence bands, and spin-orbit coupling. This review presents the topological concepts related to solids from the viewpoint of a solid-state chemist, summarizes techniques for growing single crystals, and describes basic physical property measurement techniques to characterize topological materials beyond their structure and provide examples of such materials. Finally, a brief outlook on the impact of topology in other areas of chemistry is provided at the end of the article.

Studying local Berry curvature in 2H-WSe2 by circular dichroism photoemission utilizing crystal mirror plane

It was recently reported that circular dichroism in angle-resolved photoemission spectroscopy (CD-ARPES) can be used to observe the Berry curvature in 2H-WSe₂ (Cho et al. in Phys Rev Lett 121:186401, 2018). In that study, the mirror plane of the experiment was intentionally set to be perpendicular to the crystal mirror plane, such that the Berry curvature becomes a symmetric function about the experimental mirror plane. In the present study, we performed CD-ARPES on 2H-WSe₂ with the crystal mirror plane taken as the experimental mirror plane. Within such an experimental constraint, two experimental geometries are possible for CD-ARPES. The Berry curvature distributions for the two geometries are expected to be antisymmetric about the experimental mirror plane and exactly opposite to each other. Our experimental CD intensities taken with the two geometries were found to be almost opposite near the corners of the 2D projected hexagonal Brillouin zone (BZ) and were almost identical near the center of the BZ. This observation is well explained by taking the Berry curvature or the atomic orbital angular momentum (OAM) into account. The Berry curvature (or OAM) contribution to the CD intensities can be successfully extracted through a comparison of the CD-ARPES data for the two experimental geometries. Thus, the CD-ARPES experimental procedure described provides a method for mapping Berry curvature in the momentum space of topological materials, such as Weyl semimetals.

Tuning the crystalline electric field and magnetic anisotropy along the CeCuBi2-xSbx series

We have performed X-ray powder diffraction, magnetization, electrical resistivity, heat capacity and inelastic neutron scattering (INS) to investigate the physical properties of the intermetallic series of compounds CeCuBi 2 - x Sb x . These compounds crystallize in a tetragonal structure with space group P 4 ∕ n m m and present antiferromagnetic transition temperatures ranging from 3.6 K to 16 K. Remarkably, the magnetization easy axis changed along the series, which is closely related to the variations of the tetragonal crystalline electric field (CEF) parameters. This evolution was analyzed using a mean field model, which included an anisotropic nearest-neighbor interactions and the tetragonal CEF Hamiltonian. We obtained the CEF parameters by fitting the magnetic susceptibility data with the constraints given by the INS measurements. More broadly, we discuss how this CEF evolution can affect the Kondo physics and the search for a superconducting state in this family.

Electronic correlations and flattened band in magnetic Weyl semimetal candidate Co3Sn2S2

The interplay between electronic correlations and topological protection may offer a rich avenue for discovering emergent quantum phenomena in condensed matter. However, electronic correlations have so far been little investigated in Weyl semimetals (WSMs) by experiments. Here, we report a combined optical spectroscopy and theoretical calculation study on the strength and effect of electronic correlations in a magnet Co₃Sn₂S₂. The electronic kinetic energy estimated from our optical data is about half of that obtained from single-particle ab initio calculations in the ferromagnetic ground state, which indicates intermediate-strength electronic correlations in this system. Furthermore, comparing the energy and side-slope ratios between the interband-transition peaks at high energies in the experimental and single-particle-calculation-derived optical conductivity spectra with the bandwidth-renormalization factors obtained by many-body calculations enables us to estimate the Coulomb-interaction strength (U ∼ 4 eV) in Co₃Sn₂S₂. Besides, a sharp experimental optical conductivity peak at low energy, which is absent in the single-particle-calculation-derived spectrum but is consistent with the optical conductivity peaks obtained by many-body calculations with U ∼ 4 eV, indicates that an electronic band connecting the two Weyl cones is flattened by electronic correlations and emerges near the Fermi energy in Co₃Sn₂S₂. Our work paves the way for exploring flat-band-generated quantum phenomena in WSMs.

Interlayer quantum transport in Dirac semimetal BaGa2

The quantum limit is quite easy to achieve once the band crossing exists exactly at the Fermi level (EF) in topological semimetals. In multilayered Dirac fermion systems, the density of Dirac fermions on the zeroth Landau levels (LLs) increases in proportion to the magnetic field, resulting in intriguing angle- and field-dependent interlayer tunneling conductivity near the quantum limit. BaGa2 is an example of a multilayered Dirac semimetal with its quasi-2D Dirac cone located at EF, providing a good platform to study its interlayer transport properties. In this paper, we report the negative interlayer magnetoresistance induced by the tunneling of Dirac fermions between the zeroth LLs of neighboring Ga layers in BaGa2. When the field deviates from the c-axis, the interlayer resistivity ρzz(θ) increases and finally results in a peak with the applied field perpendicular to the c-axis. These unusual interlayer transport properties are observed together in the Dirac semimetal under ambient pressure and are well explained by the model of tunneling between Dirac fermions in the quantum limit.

Magneto-Optics of a Weyl Semimetal beyond the Conical Band Approximation: Case Study of TaP

Landau-level spectroscopy, the optical analysis of electrons in materials subject to a strong magnetic field, is a versatile probe of the electronic band structure and has been successfully used in the identification of novel states of matter such as Dirac electrons, topological materials or Weyl semimetals. The latter arise from a complex interplay between crystal symmetry, spin-orbit interaction, and inverse ordering of electronic bands. Here, we report on unusual Landau-level transitions in the monopnictide TaP that decrease in energy with increasing magnetic field. We show that these transitions arise naturally at intermediate energies in time-reversal-invariant Weyl semimetals where the Weyl nodes are formed by a partially gapped nodal-loop in the band structure. We propose a simple theoretical model for electronic bands in these Weyl materials that captures the collected magneto-optical data to great extent.

Topological Semimetal Nanostructures: From Properties to Topotronics

Characterized by bulk Dirac or Weyl cones and surface Fermi-arc states, topological semimetals have sparked enormous research interest in recent years. The nanostructures, with large surface-to-volume ratio and easy field-effect gating, provide ideal platforms to detect and manipulate the topological quantum states. Exotic physical properties originating from these topological states endow topological semimetals attractive for future topological electronics (topotronics). For example, the linear energy dispersion relation is promising for broadband infrared photodetectors, the spin-momentum locking nature of topological surface states is valuable for spintronics, and the topological superconductivity is highly desirable for fault-tolerant qubits. For real-life applications, topological semimetals in the form of nanostructures are necessary in terms of convenient fabrication and integration. Here, we review the recent progresses in topological semimetal nanostructures and start with the quantum transport properties. Then topological semimetal-based electronic devices are introduced. Finally, we discuss several important aspects that should receive great effort in the future, including controllable synthesis, manipulation of quantum states, topological field effect transistors, spintronic applications, and topological quantum computation.

Realization of Epitaxial NbP and TaP Weyl Semimetal Thin Films

Weyl semimetals (WSMs) exhibit an electronic structure governed by linear band dispersions and degenerate (Weyl) points that lead to exotic physical phenomena. While WSMs were established in bulk monopnictide compounds several years ago, the growth of thin films remains a challenge. Here, we report the bottom-up synthesis of single-crystalline NbP and TaP thin films, 9 to 70 nm thick, by means of molecular beam epitaxy. The as-grown epitaxial films feature a phosphorus-rich stoichiometry, a tensile-strained unit cell, and a homogeneous surface termination, unlike their bulk crystal counterparts. These properties result in an electronic structure governed by topological surface states as directly observed using in situ momentum photoemission microscopy, along with a Fermi-level shift of -0.2 eV with respect to the intrinsic chemical potential. Although the Fermi energy of the as-grown samples is still far from the Weyl points, carrier mobilities close to 103 cm2/(V s) have been measured at room temperature in patterned Hall-bar devices. The ability to grow thin films of Weyl semimetals that can be tailored by doping or strain, is an important step toward the fabrication of functional WSM-based devices and heterostructures.

Magnetic Weyl semimetal phase in a Kagomé crystal

Weyl semimetals are crystalline solids that host emergent relativistic Weyl fermions and have characteristic surface Fermi-arcs in their electronic structure. Weyl semimetals with broken time reversal symmetry are difficult to identify unambiguously. In this work, using angle-resolved photoemission spectroscopy, we visualized the electronic structure of the ferromagnetic crystal Co₃Sn₂S₂ and discovered its characteristic surface Fermi-arcs and linear bulk band dispersions across the Weyl points. These results establish Co₃Sn₂S₂ as a magnetic Weyl semimetal that may serve as a platform for realizing phenomena such as chiral magnetic effects, unusually large anomalous Hall effect and quantum anomalous Hall effect.

Signatures of Sixfold Degenerate Exotic Fermions in a Superconducting Metal PdSb2

Multifold degenerate points in the electronic structure of metals lead to exotic behaviors. These range from twofold and fourfold degenerate Weyl and Dirac points, respectively, to sixfold and eightfold degenerate points that are predicted to give rise, under modest magnetic fields or strain, to topological semimetallic behaviors. The present study shows that the nonsymmorphic compound PdSb₂ hosts six-component fermions or sextuplets. Using angle-resolved photoemission spectroscopy, crossing points formed by three twofold degenerate parabolic bands are directly observed at the corner of the Brillouin zone. The group theory analysis proves that under weak spin-orbit interaction, a band inversion occurs.

Intrinsic Anomalous Hall Effect in Ni-Substituted Magnetic Weyl Semimetal Co3Sn2S2

Topological Weyl semimetals have recently attracted considerable attention among materials scientists as their properties are predicted to be protected against perturbations such as lattice distortion and chemical substitution. However, any experimental proof of such robustness is still lacking. In this study, we experimentally demonstrate that the topological properties of the ferromagnetic kagomé compound Co₃Sn₂S₂ are preserved upon Ni substitution. We systematically vary the Ni content in Co₃Sn₂S₂ single crystals and study their magnetic and anomalous transport properties. For the intermediate Ni substitution, we observe a remarkable increase in the coercive field while still maintaining significant anomalous Hall conductivity. The large anomalous Hall conductivity of these compounds is intrinsic, consistent with first-principles calculations, which proves its topological origin. Our results can guide further studies on the chemical tuning of topological materials for better understanding.

Quasiparticle interference evidence of the topological Fermi arc states in chiral fermionic semimetal CoSi

Chiral fermions in solid state feature "Fermi arc" states, connecting the surface projections of the bulk chiral nodes. The surface Fermi arc is a signature of nontrivial bulk topology. Unconventional chiral fermions with an extensive Fermi arc traversing the whole Brillouin zone have been theoretically proposed in CoSi. Here, we use scanning tunneling microscopy/spectroscopy to investigate quasiparticle interference at various terminations of a CoSi single crystal. The observed surface states exhibit chiral fermion-originated characteristics. These reside on (001) and (011) but not (111) surfaces with p-rotation symmetry, spiral with energy, and disperse in a wide energy range from ~-200 to ~+400 mV. Owing to the high-energy and high-space resolution, a spin-orbit coupling-induced splitting of up to ~80 mV is identified. Our observations are corroborated by density functional theory and provide strong evidence that CoSi hosts the unconventional chiral fermions and the extensive Fermi arc states.

Strong and Tunable Electrical Anisotropy in Type-II Weyl Semimetal Candidate WP2 with Broken Inversion Symmetry

A transition metal diphosphide, WP₂ , is a candidate for type-II Weyl semimetals (WSMs) in which spatial inversion symmetry is broken and Lorentz invariance is violated. As one of the prerequisites for the presence of the WSM state in WP₂ , spatial inversion symmetry breaking in this compound has rarely been investigated. Furthermore, the anisotropy of the WP₂ electrical properties and whether its electrical anisotropy can be tuned remain elusive. Angle-resolved polarized Raman spectroscopy, electrical transport, optical spectroscopy, and first-principle studies of WP₂ are reported. The energies of the observed Raman-active phonons and the angle dependences of the detected phonon intensities are consistent with results obtained by first-principle calculations and analysis of the proposed crystal symmetry without spatial inversion, showing that spatial inversion symmetry is broken in WP₂ . Moreover, the measured ratio (R_c /R_a ) between the crystalline c-axis and a-axis electrical resistivities exhibits a weak dependence on temperature (T) in the temperature range from 100 to 250 K, but increases abruptly at T ≤ 100 K, and then reaches the value of ≈8.0 at T = 10 K, which is by far the strongest in-plane electrical resistivity anisotropy among the reported type-II WSM candidates with comparable carrier concentrations. Optical spectroscopy study, together with the first-principle calculations on the electronic band structure, reveals that the abrupt enhancement of the electrical resistivity anisotropy at T ≤ 100 K mainly arises from a sharp increase in the scattering rate anisotropy at low temperatures. More interestingly, the R_c /R_a of WP₂ at T = 10 K can be tuned from 8.0 to 10.6 as the magnetic field increases from 0 to 9 T. The so-far-strongest and magnetic-field-tunable electrical resistivity anisotropy found in WP₂ can serve as a degree of freedom for tuning the electrical properties of type-II WSMs, which paves the way for the development of novel electronic applications based on type-II WSMs.

Growth and Strain Engineering of Trigonal Te for Topological Quantum Phases in Non-Symmorphic Chiral Crystals

Strained trigonal Te has been predicted to host Weyl nodes supported by a non-symmorphic chiral symmetry. Using low-pressure physical vapor deposition, we systematically explored the growth of trigonal Te nanowires with naturally occurring strain caused by curvature of the wires. Raman spectra and high mobility electronic transport attest to the highly crystalline nature of the wires. Comparison of Raman spectra for both straight and curved nanowires indicates a breathing mode that is significantly broader and shifted in frequency for the curved wires. Strain induced by curvature during growth therefore may provide a simple pathway to investigate topological phases in trigonal Te.

Large Contribution of Fermi Arcs to the Conductivity of Topological Metals

Surface-state contributions to the dc conductivity of most homogeneous metals exposed to uniform electric fields are usually as small as the system size is large compared to the lattice constant. In this Letter, we show that surface states of topological metals can contribute with the same order of magnitude as the bulk, even in large systems. This effect is intimately related to the intrinsic anomalous Hall effect, in which an applied voltage induces chiral surface-state currents proportional to the system size. Unlike the anomalous Hall effect, the large contribution of surface states to the dc conductivity is also present in time-reversal invariant Weyl semimetals, where the surface states come in counterpropagating time-reversed pairs. While the Hall voltage vanishes in the presence of time-reversal symmetry, the twinned chiral surface currents develop similarly as in the time-reversal-broken case. For this effect to occur, the relaxation length associated with scattering between time-reversed partner states needs to be larger than the separation of contributing surfaces, which results in a characteristic size dependence of the resistivity and a highly inhomogeneous current-density profile across the sample.

Topological Lifshitz transitions and Fermi arc manipulation in Weyl semimetal NbAs

Surface Fermi arcs (SFAs), the unique open Fermi-surfaces (FSs) discovered recently in topological Weyl semimetals (TWSs), are unlike closed FSs in conventional materials and can give rise to many exotic phenomena, such as anomalous SFA-mediated quantum oscillations, chiral magnetic effects, three-dimensional quantum Hall effect, non-local voltage generation and anomalous electromagnetic wave transmission. Here, by using in-situ surface decoration, we demonstrate successful manipulation of the shape, size and even the connections of SFAs in a model TWS, NbAs, and observe their evolution that leads to an unusual topological Lifshitz transition not caused by the change of the carrier concentration. The phase transition teleports the SFAs between different parts of the surface Brillouin zone. Despite the dramatic surface evolution, the existence of SFAs is robust and each SFA remains tied to a pair of Weyl points of opposite chirality, as dictated by the bulk topology.

Surface Fermi arcs (SFAs) are characteristic features of a topological Weyl semimetal but there is no easy way to manipulate them so far. Here, the authors report manipulation of the shape, size and connections of SFAs in a Weyl semimetal NbAs, leading to an unusual topological Lifshitz transition.

The coupling effects of surface plasmons and Fermi arc plasmons in Weyl semimetals

We study the effects of coupling between surface plasmon and Fermi arc plasmon modes on a planar surface of the Weyl semimetal. A model Hamiltonian is proposed in the second quantization representation for the system of coupled surface plasmon and Fermi arc plasmon modes. We obtain the dispersion relations of coupled modes using the Bogoliubov transformation technique. We identify the upper coupled mode as the renormalized surface plasmon and the lower coupled mode as the renormalized Fermi arc plasmon. It is shown how the magnitude of the coupling depends on both the bare mode dispersions and their dampings. We also demonstrate that coupling increases the surface plasmon mode lifetime. Obtained results for the surface plasmon mode are qualitatively consistent with the recent experimental data of Weyl semimetals.

Extremely high conductivity observed in the triple point topological metal MoP

Weyl and Dirac fermions have created much attention in condensed matter physics and materials science. Recently, several additional distinct types of fermions have been predicted. Here, we report ultra-high electrical conductivity in MoP at low temperature, which has recently been established as a triple point fermion material. We show that the electrical resistivity is 6 nΩ cm at 2 K with a large mean free path of 11 microns. de Haas-van Alphen oscillations reveal spin splitting of the Fermi surfaces. In contrast to noble metals with similar conductivity and number of carriers, the magnetoresistance in MoP does not saturate up to 9 T at 2 K. Interestingly, the momentum relaxing time of the electrons is found to be more than 15 times larger than the quantum coherence time. This difference between the scattering scales shows that momentum conserving scattering dominates in MoP at low temperatures.

Tracking Ultrafast Photocurrents in the Weyl Semimetal TaAs Using THz Emission Spectroscopy

We investigate polarization-dependent ultrafast photocurrents in the Weyl semimetal TaAs using terahertz (THz) emission spectroscopy. Our results reveal that highly directional, transient photocurrents are generated along the noncentrosymmetric c axis regardless of incident light polarization, while helicity-dependent photocurrents are excited within the ab plane. This is consistent with earlier static photocurrent experiments, and demonstrates on the basis of both the physical constraints imposed by symmetry and the temporal dynamics intrinsic to current generation and decay that optically induced photocurrents in TaAs are inherent to the underlying crystal symmetry of the transition metal monopnictide family of Weyl semimetals.

Orbital Fingerprint of Topological Fermi Arcs in the Weyl Semimetal TaP

The monopnictides TaAs and TaP are well-established Weyl semimetals. Yet, a precise assignment of Fermi arcs, accommodating the predicted chiral charge of the bulk Weyl points, has been difficult in these systems, and the topological character of different surface features in the Fermi surface is not fully understood. Here, employing a joint analysis from linear dichroism in angle-resolved photoemission and first-principles calculations, we unveil the orbital texture on the full Fermi surface of TaP(001). We observe pronounced switches in the orbital texture at the projected Weyl nodes, and show how they facilitate a topological classification of the surface band structure. Our findings establish a critical role of the orbital degrees of freedom in mediating the surface-bulk connectivity in Weyl semimetals.

Quantum transport properties of single-crystalline Ag2Se0.5Te0.5 nanowires as a new topological material

We report a ternary silver chalcogenide, Ag2Se0.5Te0.5, as a new topological material with improved quantum transport properties. Single-crystalline nanostructures of ternary silver chalcogenides Ag2SexTe1-x are synthesized with a tunable chemical composition via the chemical vapor transport method. Quantum transport studies reveal that Ag2Se0.5Te0.5 nanowires present topological surface states with higher electron mobility and longer mean free path compared to binary Ag-chalcogenides. First-principles calculations also indicate that Ag2Se0.5Te0.5 is a topological insulator, and the observed enhancement in transport properties could imply reduced bulk carrier contribution in the new ternary silver chalcogenide.

Nontrivial topology of bulk HgSe from the study of cyclotron effective mass, electron mobility and phase shift of Shubnikov-de Haas oscillations

In this paper, the authors report the results of an experimental study of effective mass, electron mobility and phase shift of Shubnikov-de Haas oscillations of transverse magnetoresistance in an extended electron concentration region from 8.8  ×  10¹⁵ cm^-3 to 4.3  ×  10¹⁸ cm^-3 in single crystals of mercury selenide. The revealed features indicate that Weyl semimetal phase may exist in HgSe at low electron density. The most significant result is the discovery of an abrupt change of Berry phase [Formula: see text] at electron concentration [Formula: see text] 2  ×  10¹⁸ cm^-3, which we explain in terms of a manifestation of topological Lifshitz transition in HgSe that occurs by tuning Fermi energy via doping.

Nonlinear magnetotransport shaped by Fermi surface topology and convexity

The nature of Fermi surface defines the physical properties of conductors and many physical phenomena can be traced to its shape. Although the recent discovery of a current-dependent nonlinear magnetoresistance in spin-polarized non-magnetic materials has attracted considerable attention in spintronics, correlations between this phenomenon and the underlying fermiology remain unexplored. Here, we report the observation of nonlinear magnetoresistance at room temperature in a semimetal WTe₂, with an interesting temperature-driven inversion. Theoretical calculations reproduce the nonlinear transport measurements and allow us to attribute the inversion to temperature-induced changes in Fermi surface convexity. We also report a large anisotropy of nonlinear magnetoresistance in WTe₂, due to its low symmetry of Fermi surfaces. The good agreement between experiments and theoretical modeling reveals the critical role of Fermi surface topology and convexity on the nonlinear magneto-response. These results lay a new path to explore ramifications of distinct fermiology for nonlinear transport in condensed-matter.

Two-dimensional honeycomb borophene oxide: strong anisotropy and nodal loop transformation

The search for topological semimetals is mainly focused on heavy-element compounds by following the footsteps of previous research on topological insulators, with less attention on light-element materials. However, the negligible spin orbit coupling with light elements may turn out to be beneficial for realizing topological band features. Here, using first-principles calculations, we propose a new two-dimensional light-element material-the honeycomb borophene oxide (h-B2O), which has nontrivial topological properties. The proposed structure is based on the recently synthesized honeycomb borophene on an Al (111) substrate [W. Li, L. Kong, C. Chen, J. Gou, S. Sheng, W. Zhang, H. Li, L. Chen, P. Cheng and K. Wu, Sci. Bull., 2018, 63, 282-286]. The h-B2O monolayer is completely flat, unlike the oxides of graphene or silicene. We systematically investigate the structural properties of h-B2O, and find that it has very good stability and exhibits significant mechanical anisotropy. Interestingly, the electronic band structure of h-B2O hosts a nodal loop centered around the Y point in the Brillouin zone, protected by the mirror symmetry. Furthermore, under moderate lattice strain, the single nodal loop can be transformed into two loops, each penetrating through the Brillouin zone. The loops before and after the transition are characterized by different [Doublestruck Z] × [Doublestruck Z] topological indices. Our work not only predicts a new two-dimensional material with interesting physical properties, but also offers an alternative approach to search for new topological phases in 2D light-element systems.

Realization of interlayer ferromagnetic interaction in MnSb2Te4 toward the magnetic Weyl semimetal state

Magnetic properties of MnSb2Te4 were examined through magnetic susceptibility, specific-heat, and neutron-diffraction measurements. As opposed to isostructural MnBi2Te4 with the antiferromagnetic ground state, MnSb2Te4 develops a spontaneous magnetization below 25 K. From our first-principles calculations on the material in a ferromagnetic state, the state could be interpreted as a type-II Weyl semimetal state with broken time-reversal symmetry. Detailed structural refinements using x-ray-diffraction and neutron-diffraction data reveal the presence of site mixing between Mn and Sb sites, leading to the ferrimagnetic ground state. With theoretical calculations, we found that the presence of site mixing plays an important role for the interlayer Mn-Mn ferromagnetic interactions.

Landau Quantization in Coupled Weyl Points: A Case Study of Semimetal NbP

Weyl semimetal (WSM) is a newly discovered quantum phase of matter that exhibits topologically protected states characterized by two separated Weyl points with linear dispersion in all directions. Here, via combining theoretical analysis and magneto-infrared spectroscopy of an archetypal Weyl semimetal, niobium phosphide, we demonstrate that the coupling between Weyl points can significantly modify the electronic structure of a WSM and provide a new twist to the protected states. These findings suggest that the coupled Weyl points should be considered as the basis for analysis of realistic WSMs.

Anomalous Hall effect in Weyl semimetal half-Heusler compounds RPtBi (R = Gd and Nd)

Topological materials ranging from topological insulators to Weyl and Dirac semimetals form one of the most exciting current fields in condensed-matter research. Many half-Heusler compounds, RPtBi (R = rare earth), have been theoretically predicted to be topological semimetals. Among various topological attributes envisaged in RPtBi, topological surface states, chiral anomaly, and planar Hall effect have been observed experimentally. Here, we report an unusual intrinsic anomalous Hall effect (AHE) in the antiferromagnetic Heusler Weyl semimetal compounds GdPtBi and NdPtBi that is observed over a wide temperature range. In particular, GdPtBi exhibits an anomalous Hall conductivity of up to 60 Ω-1⋅cm-1 and an anomalous Hall angle as large as 23%. Muon spin-resonance (μSR) studies of GdPtBi indicate a sharp antiferromagnetic transition (TN) at 9 K without any noticeable magnetic correlations above TN Our studies indicate that Weyl points in these half-Heuslers are induced by a magnetic field via exchange splitting of the electronic bands at or near the Fermi energy, which is the source of the chiral anomaly and the AHE.

Comparative study of the compensated semi-metals LaBi and LuBi: a first-principles approach

We have investigated the electronic structures of LaBi and LuBi, employing the full-potential all electron method as implemented in Wien2k. Using this, we have studied in detail both the bulk and the surface states of these materials. From our band structure calculations we find that LuBi, like LaBi, is a compensated semi-metal with almost equal and sizable electron and hole pockets. In analogy with experimental evidence in LaBi, we thus predict that LuBi will also be a candidate for extremely large magneto-resistance (XMR), which should be of immense technological interest. Our calculations reveal that LaBi, despite being gapless in the bulk spectrum, displays the characteristic features of a [Formula: see text] topological semi-metal, resulting in gapless Dirac cones on the surface, whereas LuBi only shows avoided band inversion in the bulk and is thus a conventional compensated semi-metal with extremely large magneto-resistance.

Electronic properties of topological insulator candidate CaAgAs

The topological phases of matter provide the opportunity to observe many exotic properties, such as the existence of 2D topological surface states in the form of Dirac cones in topological insulators and chiral transport through the open Fermi arc in Weyl semimetals. However, these properties affect the transport characteristics and, therefore, may be useful for applications only if the topological phenomena occur near the Fermi level. CaAgAs is a promising candidate for which the ab initio calculations predict line-nodes at the Fermi energy. However, the compound transforms into a topological insulator on considering spin-orbit interaction. In this study, we investigated the electronic structure of CaAgAs with angle-resolved photoemission spectroscopy (ARPES), ab initio calculations, and transport measurements. The results from ARPES show that the bulk valence band crosses the Fermi energy at the Γ-point. The measured band dispersion matches the ab initio calculations closely when shifting the Fermi energy in the calculations by  -0.5 eV. The ARPES results are in good agreement with transport measurements, which show abundant p-type carriers.

Size effect in the electronic transport of thin films of Bi2Se3

Thin films of a topological insulator (TI) Bi2Se3 of various thicknesses from 20 nm to 75 nm were obtained. The resistivity measurements were carried out according to the conventional 4-contact DC technique. This allows to “separate” the bulk and surface conductivities at different temperatures and magnetic fields. It was suggested that similar effects should be observed in other TIs and systems with inhomogeneous distribution of dc-current on sample cross section.