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Magnetic Weyl semimetals Weyl semimetals (WSMs)—materials that host exotic quasiparticles called Weyl fermions—must break either spatial inversion or time-reversal symmetry. A number of WSMs that break inversion symmetry have been identified, but showing unambiguously that a material is a time-reversal-breaking WSM is tricky. Three groups now provide spectroscopic evidence for this latter state in magnetic materials (see the Perspective by da Silva Neto). Belopolski et al. probed the material Co 2 MnGa using angle-resolved photoemission spectroscopy, revealing exotic drumhead surface states. Using the same technique, Liu et al. studied the material Co 3 Sn 2 S 2 , which was complemented by the scanning tunneling spectroscopy measurements of Morali et al. These magnetic WSM states provide an ideal setting for exotic transport effects. Science , this issue p. 1278 , p. 1282 , p. 1286 ; see also p. 1248

Much of the dramatic growth in research on topological materials has focused on topologically protected surface states. While the domain walls of topological materials such as Weyl semimetals with broken inversion or time-reversal symmetry can provide a hunting ground for exploring topological interfacial states, such investigations have received little attention to date. Here, utilizing in-situ cryogenic transmission electron microscopy combined with first-principles calculations, we discover intriguing domain-wall structures in MoTe2, both between polar variants of the low-temperature(T) Weyl phase, and between this and the high-T high-order topological phase. We demonstrate how polar domain walls can be manipulated with electron beams and show that phase domain walls tend to form superlattice-like structures along the c axis. Scanning tunneling microscopy indicates a possible signature of a conducting hinge state at phase domain walls. Our results open avenues for investigating topological interfacial states and unveiling multifunctional aspects of domain walls in topological materials., 6 figures

All-electric magnetization manipulation at low power is a prerequisite for a wide adoption of spintronic devices. Materials such as heavy metals1–3 or topological insulators4,5 provide good charge-to-spin conversion efficiencies. They enable magnetization switching in heterostructures with either metallic ferromagnets or with magnetic insulators. Recent work suggests a pronounced Edelstein effect in Weyl semimetals due to their non-trivial band structure6,7; the Edelstein effect can be one order of magnitude stronger than it is in topological insulators or Rashba systems. Furthermore, the strong intrinsic spin Hall effect from the bulk states in Weyl semimetals can contribute to the spin current generation8. The Td phase of the Weyl semimetal WTe2 (WTe2 hereafter) possesses strong spin–orbit coupling6,9 and non-trivial band structures10 with a large spin polarization protected by time-reversal symmetry in both the surface and bulk states9–11. Atomically flat surfaces, which can be produced with high quality12, facilitate spintronic device applications. Here, we use WTe2 as a spin current source in WTe2/Ni81Fe19 (Py) heterostructures. We report field-free current-induced magnetization switching at room temperature. A charge current density of ~2.96 × 105 A cm−2 suffices to switch the magnetization of the Py layer. With the charge current along the b axis of the WTe2 layer, the thickness-dependent charge-to-spin conversion efficiency reaches 0.51 at 6–7 GHz. At the WTe2/Py interface, a Dzyaloshinskii–Moriya interaction (DMI) with a DMI constant of −1.78 ± 0.06 mJ m−2 induces chiral domain wall tilting. Our study demonstrates the capability of WTe2 to efficiently manipulate magnetization and sheds light on the role of the interface in Weyl semimetal/magnet heterostructures. The Weyl semimetal WTe2 possesses strong spin–orbit coupling and time-reversal-protected spin polarization in surface and bulk states. In a WTe2/permalloy heterostructure, WTe2 can act as a spin current source that enables magnetization switching at low current densities.

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.

Two-dimensional (2D) materials exhibit unique electronic properties compared with their bulks. A systematical study of new type 2D tetragonal materials of MPn (M = Sc and Y; Pn = P, As and Sb) nanosheets and the corresponding nanoribbons are proposed by density functional theory calculations. Several thermodynamically stable 2D tetragonal structures were firstly determined, and such novel tetragonal structures bilayer MPn(100) exhibit extraordinary Weyl semimetal electronic structures, while monolayer MPn(110) are semiconductors. Moreover, bilayer MPn(100) nanoribbons with zigzag edges show metallic behavior, whereas those with linear edges show semiconducting properties. The band gaps for bilayer MPn(100) nanoribbons with linear edges can be significantly tuned by their widths. The zero-gap semiconducting behaviors of 2D tetragonal MPn nanosheets and the tunable band gaps of 1D MPn nanoribbons provide these MPn nanosheets and nanoribbons with promising applications in nanoscale electronic devices.

Demonstration of van der Waals (vdW) semiconductor/metal heterostructures (SMHs) based on transition metal dichalcogenides has been a central approach in high-speed electronics by introducing ultrafast carrier dynamics. In this regard, a Weyl semimetal WTe2 is of great interest due to its vdW layered nature, low work function, and superior electrical properties. However, little is still known about its heterostructures, and a few picoseconds photocarrier lifetimes hinder its applications in high-speed electronics. Here, we propose a SMH: semimetallic Td phase WTe2 with its sister compound of semiconducting 2H phase MoTe2. Time-resolved terahertz (THz) spectroscopy demonstrated that WTe2 exhibited the significantly shorter carrier lifetimes of sub-picosecond when forming a junction with MoTe2. We provided explicit characteristic signatures, revealing charge transfer across the interface and the subsequent interlayer exciton decay. This work not only offers the extension of the THz detection scope of ultrafast phenomena from atomically thin materials but also provides a building block of vertical SMHs for high-speed electronic devices with sub-picosecond photocarrier lifetimes.

We investigate theoretically the effect of periodic magnetic barriers on the transport for a Weyl semimetal. We find that there are momentum and spin filtering tunneling behaviors, which is controlled by the numbers of the magnetic barriers. For the tunneling through periodic square-shaped magnetic barriers, the transmission is angular φ asymmetry, and the asymmetrical transmission probability becomes more pronounced with increasing the superlattice number n. However, the transmission is symmetric with respect to angle γ, and the window of the transmission become more and more narrower with increasing the number of barriers, i.e., the collimator behavior. This feature comes from the electron Fabry-Pérot modes among the barriers. We find that the constructive interference of the backscattering amplitudes suppress transmissions, and consequently form the minigaps of the transmission. The transmission can be switched on/off by tuning the incident energies and angles, the heights and numbers of the magnetic barriers, and result in the interesting collimator behavior.

The discovery of topological insulators with unique metallic surface states has added a new dimension in the field of electronics and spintronics. Following the initial breakthrough, the topologically non-trivial materials have been extended to various categories namely weak topological insulator, topological crystalline insulator, Dirac semimetal and Weyl semimetal. Interestingly, most of the topological materials are also good candidates for thermoelectric energy conversion because both demand similar material features such as heavy constituent elements, narrow band gap, and high spin-orbit coupling. Heavy metal chalcogenides satisfy these criteria and present a nice platform for exploring both thermoelectrics and topological insulation. Here, we present a brief overview of both topological materials and thermoelectrics with examples based on heavy metal chalcogenides from the perception of a solid-state chemist. Last part of this review deals with the major challenges at the intersection of these two fields and possible solutions to establish the strong correlation between topological and thermoelectric materials.

We provide a discussion of our previously collected data (Chinotti et al., Phys. Rev. B 94, 245101 (2016)) on the electrodynamic response in YbMnBi2, a representative Weyl semimetal, and in its gapped semimetal counterpart EuMnBi2, which can be fairly well reproduced within a recent devoted theoretical treatment (S.P. Mukherjee and J.P. Carbotte, J. Phys.: Condens. Matter 29 (2017) 425301). This allows identifying and catching all the essential features of their peculiar electronic structure as imaged by the excitation spectrum.

In unconventional high temperature superconductors, supercurrent vortices are known to spoil the Landau levels. In this thesis the emergence of Landau levels is studied in different types of superconductors: Weyl superconductors, and the Fu-Kane heterostructure. It is shown that in those materials the zeroth Landau level can withstand the scattering off vortices.

The topological effect in thermoelectric transport is an important research aspect in semimetals, but whether an anomalous Nernst effect exists in nonmagnetic topological semimetals in a finite external field is still under debate. To demonstrate how to discern the topological effect in nonmagnetic topological semimetals, we present a comprehensive study on the magnetothermoelectric properties for four Weyl semimetals: TaAs, TaP, NbAs, and NbP. We observe large magneto-Seebeck and Nernst signals at intermediate temperatures, which are attributed to a multiband ordinary contribution and an inelastic, phonon-drag effect, while the latter is ignored in previous studies. This phonon-drag effect also induces an unusual, prominent temperature and field dependence of quantum oscillations in thermoelectric transport signals. On the other hand, only signatures of a relatively small anomalous thermoelectric effect are found in TaAs compared with the ordinary effect.

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 momentun-space spectroscopy and real-space visualization. Our findings may offer new opportunities to manipulate classical waves such as sound and light., Accepted by PRL

As condensed-matter manifestations of the chiral anomaly, the coexistence of positive longitudinal magnetoconductivity (LMC) and the planar Hall effect (PHE) is regarded as a characteristic transport signal for the Weyl semimetal (WSM) phase. By including a finite Newtonian mass into the general linearized WSM model, we derive an analytical expression for the chiral chemical potential, which includes a topological term of the chiral anomaly and a nontopological term. The nontopological term stems from the Zeeman-field-induced tilt of the Weyl cones, which breaks the symmetry of the fermion filling between the Weyl valleys of opposite chiralities and further leads to a chiral chemical potential $\ensuremath{\propto}\mathbit{E}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{B}$, much as the effect of the chiral anomaly. We demonstrate that the resulting LMC is positive and can coexist with the PHE without invoking the mechanism of the chiral anomaly. Hence, the chiral chemical potential might not be exclusively respected to the chiral anomaly. Experimentally, one can distinguish the chiral anomaly from the proposed tilt mechanism by inspecting the dependence of magnetoconductivity on the Fermi energy.

We investigate interacting spin susceptibilities in lattice models for $\mathcal{T}$-reversal symmetry-broken Weyl semimetals. We employ a random phase approximation (RPA) method for the spin-SU(2)-symmetry-broken case that includes mixtures of ladder and bubble diagrams, beyond a SU(2)-symmetric case. Within this approach, the relations between the tendency towards magnetic order and the band structure tilt parameter $\gamma$ under different temperatures are explored. The critical interaction strength $U_c$ for magnetic ordering decreases as the tilt term changes from type-I Weyl semimetals to type-II. The lower temperature, the sharper is the drop in $U_c$ at the critical point between them. The variation of $U_c$ with a slight doping near half-filling is also studied. It is generally found that these Weyl systems show a strongly anisotropic spin response with an enhanced doubly degenerate transverse susceptibility perpendicular to tilt direction, inherited from $\mathcal{C}_{4z}$ rational symmetry of bare Hamiltonian, but with the longitudinal response suppressed with respect to that. For small tilts $\gamma$ and strong enough interaction, we find two degenerate ordering patterns with spin order orthogonal to the tilt direction but much shorter spin correlation length parallel to the spin direction. With increasing the tilt, the system develops instabilities with respect to in-plane magnetic orders with wavevector $(0,\pi, q_z)$ and $(\pi,0, q_z)$, with $q_z$ increasing from 0 to $\pi$ before the transition to a type-II Weyl semimetal is reached. These results indicate a greater richness of magnetic phases in correlated Weyl semimetals that also pose challenges for precise theoretical descriptions., Comment: 10 pages, 8 figures

Topological fermions have mainly been addressed in the limit of weakly correlated systems, while the realization of Kondo-like physics arising from Dirac-Weyl fermions and implying strong correlations is rare. The noncentrosymmetric Weyl fermion $R\mathrm{AlGe}$ compounds (with $R=\mathrm{La} \mathrm{and} \mathrm{Ce}$) provide a promising playground for revealing the impact of electronic correlations driven by $f$-electron states on Weyl fermions. Here, we tackle their charge dynamics as a function of temperature. Besides spotting typical optical signatures of a type-II Weyl semimetal in both materials, we discover that electronic correlations at low temperatures renormalize the nontrivial bands hosting the Weyl nodes and lead to a reduction of the Fermi velocity as well as an enhancement of the charge carriers effective mass in CeAlGe with respect to LaAlGe, both being a fingerprint of a so-called Weyl-Kondo system.

A nodal ring semimetal (NRSM) can be driven to a spin-polarized NRSM or a spin-polarized Weyl semimetal (WSM) by a high-frequency electromagnetic field. We investigate the conditions in realizing these phases and propose a switchable spin-polarized currents generator based on periodically driven NRSMs. Both bulk and surface polarized currents are investigated. The polarization of bulk current is sensitive to the amplitude of the driving field and robust against the direction and polarization of the driving, the opaqueness of the lead–device interface and the misalignment between the nodal ring and the interface, which provides sufficient flexibility in manipulating the devices. Similar switchable polarized surface currents are also expected, which is contributed by the Fermi arc surface state associated with the WSM phases. The generation of polarized currents and the polarization switching effect offer opportunities to design periodic driving controlled topological spintronics devices based on NRSMs.

We report a unique type of gap in a magnetic Weyl semimetal ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ where the electrons are spin polarized and preserve the spin-momentum locking feature of Weyl fermions. Such spin-polarized gaps are associated with the Weyl node annihilation, where a pair of Weyl nodes with opposite chirality touch each other at \ensuremath{\sim}210 meV above the Fermi energy. These are revealed by both time- and spin-resolved ultrafast spectroscopy experiments, combined with first-principles calculations. The spin-polarized gap opening is accompanied by a topological phase transition, and the gap magnitude exhibits an unconventional temperature dependence originated from the Weyl physics. Furthermore, we propose possible circularly polarized terahertz-midinfrared radiation from such a spin-polarized gap. Our results shed light on exploring the topological properties of excited states and endow application potentials for gapped materials based on chirality.

Understanding magnetism and its possible correlations to topological properties has emerged to the forefront as a difficult topic in studying magnetic Weyl semimetals. ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ is a newly discovered magnetic Weyl semimetal with a kagome lattice of cobalt ions and has triggered intense interest for rich fantastic phenomena. Here, we report the magnetic exchange couplings of ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ using inelastic neutron scattering and two density functional theory (DFT) based methods: constrained magnetism and multiple-scattering Green's function methods. ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ exhibits highly anisotropic magnon dispersions and linewidths below ${T}_{C}$, and paramagnetic excitations above ${T}_{C}$. The spin-wave spectra in the ferromagnetic ground state is well described by the dominant third-neighbor ``across-hexagon'' ${J}_{d}$ model. Our density functional theory calculations reveal that both the symmetry-allowed 120\ifmmode^\circ\else\textdegree\fi{} antiferromagnetic orders support Weyl points in the intermediate temperature region, with distinct numbers and the locations of Weyl points. Our study highlights the important role ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ can play in advancing our understanding of kagome physics and exploring the interplay between magnetism and band topology.

The Weyl semimetal $\mathrm{Mo}{\mathrm{Te}}_{2}$ offers a rare opportunity to study the interplay between Weyl physics and superconductivity. Recent studies have found that Se substitution can boost the superconductivity up to 1.5 K, but suppresses the ${T}_{d}$ structure phase that is essential for the emergence of the Weyl state. A microscopic understanding of the possible coexistence of enhanced superconductivity and the ${T}_{d}$ phase has not been established so far. Here, we use scanning tunneling microscopy to study an optimally doped superconductor $\mathrm{Mo}{\mathrm{Te}}_{1.85}{\mathrm{Se}}_{0.15}$ with bulk ${T}_{c}\ensuremath{\sim}1.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. By means of quasiparticle interference imaging, we identify the existence of a low-temperature ${T}_{d}$ phase with broken inversion symmetry where superconductivity globally coexists. Furthermore, we find that the superconducting coherence length, extracted from both the upper critical field and the decay of density of states near a vortex, is much larger than the characteristic length scale of the existing chemical disorder. Our findings of robust superconductivity arising from a Weyl semimetal normal phase in $\mathrm{Mo}{\mathrm{Te}}_{1.85}{\mathrm{Se}}_{0.15}$ make it a promising candidate for realizing topological superconductivity.

By using optical pump THz probe spectroscopy, the transient photoconductivity (Δσ) of semimetallic MoTe2 thin film was investigated in the temperature range from 5K to 290 K. For 1T’-MoTe2, at room temperature, photoexcitation induces positive THz Δσ that decays within a few picoseconds. In contrast, the negative THz Δσ of MoTe2 appears at low temperature following the initial positive Δσ. The negative Δσ relaxes to the equilibrium within time scale of nanoseconds. The negative Δσ in MoTe2 at low temperature is ascribed to the formation of small polaron in Weyl semimetal phase.

Weyl nodes and Fermi arcs in type-II Weyl semimetals (WSMs) have led to lots of exotic transport phenomena. Recently, ${\mathrm{Mo}}_{0.25}{\mathrm{W}}_{0.75}{\mathrm{Te}}_{2}$ has been established as a type-II WSM with Weyl points located near Fermi level, which offers an opportunity to study its intriguing band structure by electrical transport measurements. Here, by selecting a special sample with the thickness gradient across two- (2D) and three-dimensional (3D) regimes, we show strong evidence that ${\mathrm{Mo}}_{0.25}{\mathrm{W}}_{0.75}{\mathrm{Te}}_{2}$ is a type-II Weyl semimetal by observing the following two dimensionality-dependent transport features: (1) a chiral-anomaly-induced anisotropic magnetoconductivity enhancement, proportional to the square of in-plane magnetic field (${B}_{\mathrm{in}}^{2}$); and (2) an additional quantum oscillation with thickness-dependent phase shift. Our theoretical calculations show that the observed quantum oscillation originates from a Weyl-orbit-like scenario due to the unique band structure of ${\mathrm{Mo}}_{0.25}{\mathrm{W}}_{0.75}{\mathrm{Te}}_{2}$. The in situ dimensionality-tuned transport experiment offers an alternative strategy to search for type-II WSMs.

In this work, we propose a ferromagnetic Bi2Se3 as a candidate to hold the coexistence of Weyl- and nodal-line semimetal phases, which breaks the time reversal symmetry. We demonstrate that the type-I Weyl semimetal phase, type-I-, type-II- and their hybrid nodal-line semimetal phases can arise by tuning the Zeeman exchange field strength and the Fermi velocity. Their topological responses under U(1) gauge field are also discussed. Our results raise a new way for realizing Weyl and nodal-line semimetals and will be helpful in understanding the topological transport phenomena in three-dimensional material systems.

A Weyl semimetal with strong electron-phonon interaction can show axionic coupling in its insulator state at low temperatures, owing to the formation of a charge density wave (CDW). Such a CDW emerges in the linear-chain-compound Weyl semimetal ${\mathrm{Ta}}_{2}{\mathrm{Se}}_{8}\mathrm{I}$ below 263 K, resulting in the appearance of the dynamical condensed-matter axion quasiparticle. In this paper, we demonstrate that the interchain coupling in ${\mathrm{Ta}}_{2}{\mathrm{Se}}_{8}\mathrm{I}$ can be varied to suppress the CDW formation with pressure, while retaining the Weyl semimetal phase at high temperatures. Above 17 GPa, the Weyl semimetal phase does not survive, and we induce superconductivity, due to the amorphization of the iodine sublattice. Structurally, the quasi-one-dimensional Ta-Se chains remain intact and provide a channel for superconductivity. We highlight that our results show a near-complete suppression of the gap induced by the axionic charge density wave at pressures inaccessible to previous studies. Including this CDW phase, our experiments and theoretical predictions and analysis reveal the complete phase diagram of ${\mathrm{Ta}}_{2}{\mathrm{Se}}_{8}\mathrm{I}$ and its relationship to the nearby superconducting state. The results demonstrate ${\mathrm{Ta}}_{2}{\mathrm{Se}}_{8}\mathrm{I}$ to be a distinctively versatile platform for exploring correlated topological states.

The unique bulk crossing points in the band structure of topological Weyl semimetals have been shown to enhance nonlinear optical and optoelectronic properties, even for light at optical wavelengths. Such pronounced nonlinear optical effects have been studied in type-I Weyl semimetals, yet few studies have quantified these effects in type-II Weyl semimetals. We here present an optical experimental study with polarization resolution of two nonlinear optical effects in the type-II Weyl semimetal ${T}_{\mathrm{d}}\text{\ensuremath{-}}\mathrm{W}{\mathrm{Te}}_{2}$. We begin by investigating the bulk optical second-harmonic response of this material using the rotational anisotropy of the second-harmonic generation. This technique allows us to simultaneously investigate the dependence of the second-harmonic response on the symmetry of the crystal and to quantify the size of that response, which we compare to other nonlinear crystals. We then use polarized time-resolved optical reflectivity spectroscopy to identify the nonlinear optical effect of impulsive stimulated Raman scattering as the origin of the coherent oscillations of the 0.25-THz shear mode. We find that the strength of this response in ${T}_{\mathrm{d}}\text{\ensuremath{-}}\mathrm{W}{\mathrm{Te}}_{2}$ is enhanced compared with the observation of other modes excited through the displacive excitation of coherent phonons. Notably, both the second-harmonic response and the coherent excitations of the phonons demonstrate strong anisotropy, displaying a clear dependence on the polarization of the light used in the experiments. We use point-symmetry analyses of the material to guide our understanding of these observations and perform fluence-dependent measurements to investigate the electron-phonon coupling.

Recent works have provided evidence that an axial anomaly can arise in Weyl semimetals. If this is the case, then the electromagnetic response of Weyl semimetals should be governed by the equations of axion electrodynamics. These equations capture both the chiral magnetic and anomalous Hall effects in the limit of linear response, while at higher orders their solutions can provide detectable electromagnetic signatures of the anomaly. In this work, we consider three versions of axion electrodynamics that have been proposed in the Weyl semimetal literature. These versions differ in the form of the chiral magnetic term and in whether or not the axion is treated as a dynamical field. In each case, we look for solutions to these equations for simple sample geometries subject to applied external fields. We find that in the case of a linear chiral magnetic term generated by a non-dynamical axion, self-consistent solutions can generally be obtained. In this case, the magnetic field inside of the Weyl semimetal can be magnified significantly, providing a testable signature for experiments. Self-consistent solutions can also be obtained for dynamical axions, but only in cases where the chiral magnetic term vanishes identically. Finally, for a nonlinear form of the chiral magnetic term frequently considered in the literature, we find that there are no self-consistent solutions aside from a few special cases.

In the topological semimetals, electrons in the vicinity of the Weyl or Dirac nodes behave like massless relativistic fermions that are of interest both for basic research and future electronic applications. Thus far, a detection of these Dirac or Weyl quasiparticles in topological semimetals is often elusive since in these materials, conventional charge carriers exist as well. Here, considering a prototype topological Weyl semimetal TaAs as an example, we show that when the massless quasiparticles reach the ultra-quantum limit, the magnetostriction of the semimetal is appreciably produced by the relativistic fermions. This field-induced expansion of TaAs measured along the [001] direction exhibits a weak dependence on the magnetic-field orientation and is in striking contrast to the magnetostriction measured along the [100] axis. The latter quantity experiences immense changes from large positive to large negative values with minute deviations of the applied field from the [001] direction. Employing a rigid-band approximation, we work out a theory of the magnetostriction for the Weyl semimetals and point out the features of this thermodynamic probe that can serve as hallmarks of the Weyl quasiparticles. Using the theory, we quantitatively describe a part of the obtained experimental data and find a number of the parameters characterizing TaAs. The derived dependence of the Fermi level on the magnetic field should be also relevant to understanding some other field-dependent properties of this topological semimetal, in particular, the negative longitudinal magnetoresistance. Our results illustrate how a magnetostriction may be used to unveil Weyl fermions in topological semimetals with a noncetrosymmetric crystal structure.

A Weyl semimetal carries topological charges at the Weyl nodes; a light beam can also carry a topological charge, when it has an orbital angular momentum (OAM). Recently there has been a lot of interest in understanding how the spin angular momentum (SAM) of light interacts with materials to induce photocurrents (circular photogalvanic effect, CPGE), but not many studies have focused on photocurrents generated by the OAM of light. Here we report a unique orbital photogalvanic effect (OPGE) in a type-II Weyl semimetal WTe2, featured by a photocurrent winding around the axis of OAM-carrying beams, whose intensity is directly proportional to the topological winding number of the light field, and can be attributed to a discretized dynamical Hall effect. In addition to obtaining evidence of OAM induced electron excitations, our measurements show promise for on-chip detection of the phase of light.

We investigate the surface plasmon polariton dispersion and optical spectra of a thin film of tilted Weyl semimetal. Tilted Weyl semimetals possess tilted Weyl cones at the Weyl nodes and are categorized to type-I with closed Fermi surfaces and type-II with overtilted Weyl cones and open Fermi surfaces. We find that the surface plasmon polariton dispersion of this system is nonreciprocal even in the absence of the external magnetic field. Moreover, we demonstrate that the tilt parameter has a profound effect in controlling this nonreciprocity. We reveal that the thin film of type-II Weyl semimetal hosts the surface plasmon polariton modes with the negative group velocity. Furthermore, we show that the angular optical spectra of this structure are highly asymmetric and this angular asymmetry in the absorptivity and reflectivity depends profoundly on the tilt parameter of the tilted Weyl semimetal. These exciting features propose employing the tilted Weyl semimetals in optical sensing devices, optical data storage, and devices for quantum information processing.

Magnetic topological semimetals have brought new insights into topological aspects because they nicely combine the band topology with intrinsic magnetic order. Comparing with ferromagnetic topological semimetals, antiferromagnetic (AFM) ones are even more special since they can break the time-reversal symmetry but show no net magnetic moment, and are highly expected for applications of topological AFM spintronics. Here, we report ${\mathrm{LiTi}}_{2}{\mathrm{O}}_{4}$ compound is an ideal AFM Weyl nodal line semimetal. It shows time-reversal breaking Weyl nodal lines in both the spin-up and spin-down channels. Each nodal line arises from the band in one single spin channel, thus is spin-polarized. The nodal lines locate quite near the Fermi level and do not coexist with other extraneous bands. The drumhead surface state of the nodal line can be clearly identified. The nodal lines are protected by the glide mirror symmetry and are robust against spin-orbit coupling. We also show that ${\mathrm{LiTi}}_{2}{\mathrm{O}}_{4}$ can transform into an AFM Weyl semimetal under an in-plane external magnetic field. Our results suggest ${\mathrm{LiTi}}_{2}{\mathrm{O}}_{4}$ can serve as an excellent platform to investigate AFM topological semimetals with attractive features.

The physical realization of Chern insulators is of fundamental and practical interest, as they are predicted to host the quantum anomalous Hall (QAH) effect and topologically protected chiral edge states which can carry dissipationless current. Current realizations of the QAH state often require complex heterostructures and sub-Kelvin temperatures, making the discovery of intrinsic, high temperature QAH systems of significant interest. In this work we show that time-reversal symmetry breaking Weyl semimetals, being essentially stacks of Chern insulators with inter-layer coupling, may provide a new platform for the higher temperature realization of robust chiral edge states. We present combined scanning tunneling spectroscopy and theoretical investigations of the magnetic Weyl semimetal, Co3Sn2S2. Using modeling and numerical simulations we find that depending on the strength of the interlayer coupling, chiral edge states can be localized on partially exposed kagome planes on the surfaces of a Weyl semimetal. Correspondingly, our dI/dV maps on the kagome Co3Sn terraces show topological states confined to the edges which display linear dispersion. This work provides a new paradigm for realizing chiral edge modes and provides a pathway for the realization of higher temperature QAH effect in magnetic Weyl systems in the two-dimensional limit., Magnetic Weyl semimetals in the 2D limit may behave like 2D Chern insulators and host the quantum anomalous Hall effect at high temperatures. Here, the authors report the observation of linearly dispersing topological states confined to the edges of the kagome Co3Sn terraces in the magnetic Weyl system Co3Sn2S2.

We study the disorder-induced phase transition of higher-order Weyl semimetals (HOWSMs) and the fate of the topological features of disordered HOWSMs. We obtain a global phase diagram of HOWSMs according to the scaling theory of Anderson localization. Specifically, a phase transition from the Weyl semimetal (WSM) to the HOWSM is uncovered, distinguishing the disordered HOWSMs from the traditional WSMs. Further, we confirm the robustness of Weyl-nodes for HOWSMs. Interestingly, the unique topological properties of HOWSMs show different behaviors: (i) the quantized quadrupole moment and the corresponding quantized charge of hinge states are fragile to weak disorder; (ii) the hinge states show moderate stability which enables the feasibility in experimental observation. Our study deepens the understanding of the topological nature of HOWSMs and paves a possible way to the characterization of such a phase in experiments., Comment: 9 pages, 8 figures

The study of charge-density wave (CDW) distortions in Weyl semimetals has recently returned to the forefront, inspired by experimental interest in materials such as (TaSe4)2I. However, the interplay between collective phonon excitations and charge transport in Weyl-CDW systems has not been systematically studied. In this paper, we examine the longitudinal electromagnetic response due to collective modes in a Weyl semimetal gapped by a quasi one-dimensional charge-density wave order, using both continuum and lattice regularized models. We systematically compute the contributions of the collective modes to the linear and nonlinear optical conductivity of our models, both with and without tilting of the Weyl cones. We discover that, unlike in a single-band CDW, the gapless CDW collective mode does not contribute to the conductivity unless the Weyl cones are tilted. Going further, we show that the lowest nontrivial collective mode contribution to charge transport with untilted Weyl cones comes in the third-order conductivity, and is mediated by the gapped amplitude mode. We show that this leads to a sharply peaked third harmonic response at frequencies below the single-particle energy gap. We discuss the implications of our findings for transport experiments in Weyl-CDW systems., v2: fixed typos, improved convention for Feynman rules. v1: 33 pages, 19 figures

The magnetic van der Waals crystals MnBi_{2}Te_{4}/(Bi_{2}Te_{3})_{n} have drawn significant attention due to their rich topological properties and the tunability by external magnetic field. Although the MnBi_{2}Te_{4}/(Bi_{2}Te_{3})_{n} family have been intensively studied in the past few years, their close relatives, the MnSb_{2}Te_{4}/(Sb_{2}Te_{3})_{n} family, remain much less explored. In this work, combining magnetotransport measurements, angle-resolved photoemission spectroscopy, and first principles calculations, we find that MnSb_{4}Te_{7}, the n=1 member of the MnSb_{2}Te_{4}/(Sb_{2}Te_{3})_{n} family, is a magnetic topological system with versatile topological phases that can be manipulated by both carrier doping and magnetic field. Our calculations unveil that its A-type antiferromagnetic (AFM) ground state stays in a Z_{2} AFM topological insulator phase, which can be converted to an inversion-symmetry-protected axion insulator phase when in the ferromagnetic (FM) state. Moreover, when this system in the FM phase is slightly carrier doped on either the electron or hole side, it becomes a Weyl semimetal with multiple Weyl nodes in the highest valence bands and lowest conduction bands, which are manifested by the measured notable anomalous Hall effect. Our work thus introduces a new magnetic topological material with different topological phases that are highly tunable by carrier doping or magnetic field.

$\mathrm{Mn}{\mathrm{Sb}}_{2}{\mathrm{Te}}_{4}$ has been proposed to have magnetic topological states as a potential Weyl semimetal. We synthesized single crystals of $\mathrm{Mn}{\mathrm{Sb}}_{2}{\mathrm{Te}}_{4}$ and systematically investigated their structural and physical properties. $\mathrm{Mn}{\mathrm{Sb}}_{2}{\mathrm{Te}}_{4}$ has an isostructural septuple-layered structure that is similar to the magnetic topological insulator $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ but possesses transpositional Mn and Sb atoms between the sublayers. Magnetic and specific-heat measurements revealed a ferrimagnetic phase transition with a Curie temperature ${T}_{\mathrm{C}}$ of \ensuremath{\sim}31 K in $\mathrm{Mn}{\mathrm{Sb}}_{2}{\mathrm{Te}}_{4}$, which originates from the interaction of the interexchanged ${\mathrm{Mn}}^{2+}$ ions. As the temperature decreases below ${T}_{\mathrm{C}}$, negative longitudinal magnetoresistance and anomalous Hall effect are observed, implying a non-negligible connection between the magnetism and expected transport carriers that may be driven by topological bands. Our results indicate that ferrimagnetic $\mathrm{Mn}{\mathrm{Sb}}_{2}{\mathrm{Te}}_{4}$ provides insights for further studies on magnetic topological materials.

Weyl semimetals host a variety of exotic effects that have no counterpart in conventional materials, such as the chiral anomaly and magnetic monopole in momentum space. These effects give rise to unusual transport properties, including a negative magnetoresistance and a planar Hall effect, etc. Here, we report a new type of Hall and magnetoresistance effect in a magnetic Weyl semimetal. Unlike antisymmetric (with respect to either magnetic field or magnetization) Hall and symmetric magnetoresistance in conventional materials, the discovered magnetoresistance and Hall effect are antisymmetric in both magnetic field and magnetization. We show that the Berry curvature, the tilt of the Weyl node, and the chiral anomaly synergically produce these phenomena. Our results reveal a unique property of Weyl semimetals with broken time reversal symmetry.

The quantum Hall effect (QHE) is usually observed in two-dimensional systems. Recently, the QHE has been proposed to exist in three-dimensional (3D) Weyl semimetals when the Fermi energy is precisely at the Weyl nodes at zero temperature, which is hardly achievable experimentally. However, the QHE has been experimentally realized in the 3D topological semimetal ${\text{Cd}}_{3}{\text{As}}_{2}$ at finite temperatures. It has been found that a Weyl semimetal may translate to a chiral excitonic insulator due to the interplay between the interaction and band topology. In a Weyl semimetal slab, we show that the Fermi arc surface states can exist not only in the Weyl semimetal but also in the chiral excitonic insulator. As long as the Fermi energy crosses the Fermi arc states, the QHE can be generated under the combined action of bulk states and Fermi arc surface states. Therefore, the integer quantization of Hall conductivity can be observed for a finite energy range, or equivalently at finite temperatures.

The Weyl semimetal in a constant magnetic field is investigated with the ground state for the lowest ($n=0$) Landau levels corresponding to spin-down (${\ensuremath{\sigma}}_{3}=\ensuremath{-}1$). In the presence of an electron-phonon coupling in the ground state, an attractive interaction for the polarized spin and opposite chirality is generated. A two-body attractive interaction projected to the two lowest ($n=0$) chiral Landau levels with the same spin polarization is obtained. The higher Landau level states ($n\ensuremath{\ne}0$) are treated at the one-loop approximation with the two chiralities containing spins polarized as ${\ensuremath{\sigma}}_{3}=\ifmmode\pm\else\textpm\fi{}1$. Using the chiral anomaly in one dimension we show that the sliding phase is controlled by the electric field. This theory, for a Weyl semimetal with two nodes in the direction of the applied magnetic field, gives rise to a sliding charge density wave observed by Gooth et al. [Nature (London) 575, 315 (2019)].

Since the discovery of the Harper-Hofstadter model, it has been known that condensed matter systems with periodic modulations can be promoted to non-trivial topological states with emergent gauge fields in higher dimensions. In this work, we develop a general procedure to compute the gauge fields in higher dimensions associated to low-dimensional systems with periodic (charge- and spin-) density wave modulations. We construct two-dimensional (2D) models with modulations that can be promoted to higher-order topological phases with $U(1)$ and $SU(2)$ gauge fields in 3D. Corner modes in our 2D models can be pumped by adiabatic sliding of the phase of the modulation, yielding hinge modes in the promoted models. We also examine a 3D Weyl semimetal (WSM) gapped by charge-density wave (CDW) order, possessing quantum anomalous Hall (QAH) surface states. We show that this 3D system is equivalent to a 4D nodal line system gapped by a $U(1)$ gauge field with a nonzero second Chern number. We explain the recently identified interpolation between inversion-symmetry protected phases of the 3D WSM gapped by CDWs using the corresponding 4D theory. Our results can extend the search for (higher-order) topological states in higher dimensions to density wave systems., Comment: v2: approximately published version, fixed typos and references, and added extensions to arbitrary orbital positions. 21+37 pages, 5+10 figures. v1: 20+33 pages, 5+10 figures

Noncentrosymmetric PrAlGe is considered to be a magnetic Weyl semimetal that breaks both time-reversal and inversion symmetry, in which the Weyl nodes can be moved by magnetization. However, the magnetic interaction of this system remains poorly understood. In this work we perform a systematical investigation on magnetic properties and critical behaviors in single-crystal PrAlGe. The temperature, field, and angle dependence of magnetization reveal a strong magnetic anisotropy along the $c$ axis and absolute isotropic characteristic in the $ab$ plane. By fitting to the magnetic entropy change $[\mathrm{\ensuremath{\Delta}}{S}_{M}(T,H)]$ around the critical temperature ${T}_{C}=16$ K, critical exponents $\ensuremath{\beta}=0.136(6), \ensuremath{\gamma}=1.801(7)$, and $\ensuremath{\delta}=14.2(6)$ are obtained. Based on the obtained critical exponents, $\mathrm{\ensuremath{\Delta}}{S}_{M}(T,H)$ and $M(T,H)$ curves are scaled into universality curves under the framework of universality principle. The critical behaviors and exponents suggest that the magnetic interaction in PrAlGe is of a two-dimensional Ising type, revealing a uniaxial magnetic interaction along the $c$ axis. However, the ordering moments are tilted from the $c$ axis, which causes antiferromagnetism in the $ab$ plane. The clarification of the magnetic interaction and magnetic structure is of significance for unveiling its interplay with topological properties in this system.