Experimental discovery of a topological Weyl semimetal state in TaP

Diameter-dependent phase selectivity in 1D-confined tungsten phosphides

Topological materials confined in 1D can transform computing technologies, such as 1D topological semimetals for nanoscale interconnects and 1D topological superconductors for fault-tolerant quantum computing. As such, understanding crystallization of 1D-confined topological materials is critical. Here, we demonstrate 1D template-assisted nanowire synthesis where we observe diameter-dependent phase selectivity for tungsten phosphides. A phase bifurcation occurs to produce tungsten monophosphide and tungsten diphosphide at the cross-over nanowire diameter regime of 35-70 nm. Four-dimensional scanning transmission electron microscopy is used to identify the two phases and to map crystallographic orientations of grains at a few nm resolution. The 1D-confined phase selectivity is attributed to the minimization of the total surface energy, which depends on the nanowire diameter and chemical potentials of precursors. Theoretical calculations are carried out to construct the diameter-dependent phase diagram, which agrees with experimental observations. Our findings suggest a crystallization route to stabilize topological materials confined in 1D.

Topological behavior of spectral singularities in topological Weyl semimetals

In this study, we examine the topological character of spectral singularities by using transverse magnetic (TM) mode configuration in a Topological Weyl Semimetal (TWSM). TM mode configuration restrains the effect of Kerr/Faraday rotations and therefore does not allow an extra degree of freedom to occur. We find out that surface currents arise due to topological terms on the surface of TWSM slab where no Fermi arcs are localized. We also investigate the contribution of the Θ-term, which is the origin of axions in topological materials, and especially theb-term, to the topological properties. As a result of our study, we clearly reveal the topological character ofb-term for the first time and we demonstrate the Weyl degeneracy situation in an obvious manner. Our system produces circular currents in the plane of propagation, maintaining a cyclotron shape motion. The presence ofb-term causes the induced current to be topologically protected. Our findings verify that topological properties of TWSM containing two opposite chirality Weyl fermions are robust against external influences. With the findings of our study, the appropriate conditions for the construction of a topological laser and the values that the system parameters can take have been demonstrated.

Tunable optical spatial differential operation via photonic spin Hall effect in a Weyl semimetal

Optical differential operation is the basic principle of optical image edge detection, which has the advantages of high efficiency, simple structure and markerless compared with the traditional digital image processing methods. In this paper, we propose an optical differential operation with high contrast based on the photonic spin Hall effect in a Weyl semimetal, which enables to switch between one- and two-dimensional edge detection. Due to the unique optical and electrical properties of the Weyl semimetal, a transport model for the differential operation is established, which is closely related to the beam shifts. By tuning the incidence conditions, we effectively manipulate the in-plane and transverse shifts to switch differential operations between one and two dimensions. The contrast of the differential operation is further regulated by changing the physical parameters of the Weyl semimetal, and can be improved by two orders of magnitude compared to the conventional differentiator. This study provides new possibilities in edge detection and image processing owing to the advantages of switchable dimension and high contrast.

Noncentrosymmetric two-dimensional Weyl semimetals in porous Si/Ge structures

In this work we predict a family of noncentrosymmetric two-dimensional (2D) Weyl semimetals (WSMs) composed by porous Ge and SiGe structures. These systems are energetically stable graphenylene-like structures with a buckling, spontaneously breaking the inversion symmetry. The nontrivial topological phase for these 2D systems occurs just below the Fermi level, resulting in nonvanishing Berry curvature around the Weyl nodes. The emerged WSMs are protected byC3symmetry, presenting one-dimensional edge Fermi-arcs connecting Weyl points with opposite chiralities. Our findings complete the family of Weyl in condensed-matter physics, by predicting the first noncentrosymmetric class of 2D WSMs.

Topological Metamaterials

The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.

Superconductor Vortex Spectrum Including Fermi Arc States in Time-Reversal Symmetric Weyl Semimetals

Using semiclassics to surmount the hurdle of bulk-surface inseparability, we derive the superconductor vortex spectrum in nonmagnetic Weyl semimetals and show that it stems from the Berry phase of orbits made of Fermi arcs on opposite surfaces and bulk chiral modes. Tilting the vortex transmutes it between bosonic, fermionic, and supersymmetric, produces periodic peaks in the density of states that signify novel nonlocal Majorana modes, and yields a thickness-independent spectrum at magic "magic angles." We propose (Nb,Ta)P as candidate materials and tunneling spectroscopy as the ideal experiment.

Atomically Sharp Internal Interface in a Chiral Weyl Semimetal Nanowire

Internal interfaces in Weyl semimetals (WSMs) are predicted to host distinct topological features that are different from the commonly studied external interfaces (crystal-to-vacuum boundaries). However, the lack of atomically sharp and crystallographically oriented internal interfaces in WSMs makes it difficult to experimentally investigate topological states buried inside the material. Here, we study a unique internal interface known as merohedral twin boundary in chemically synthesized single-crystal nanowires (NWs) of CoSi, a chiral WSM of space group P2₁3 (No. 198). Scanning transmission electron microscopy reveals that this internal interface is a (001) twin plane which connects two enantiomeric counterparts at an atomically sharp interface with inversion twinning. Ab initio calculations show localized internal Fermi arcs at the (001) twin plane that can be clearly distinguished from both external Fermi arcs and bulk states. These merohedrally twinned CoSi NWs provide an ideal platform to explore topological properties associated with internal interfaces in WSMs.

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.

Real-space imaging and control of chiral anomaly induced current at room temperature in topological Dirac semimetal

Chiral fermions (CFs) in condensed matters, distinguished by right (+) or left (-) handedness, hold a promise for emergent quantum devices. Although a chiral anomaly induced current, J_chiral = J(+) - J(-), occurs in Weyl semimetals due to the charge imbalance of the CFs, monitoring spatial flow and temporal dynamics of J_chiral has not been demonstrated yet. Here, we report real-space imaging and control of J_chiral on the topological Dirac semimetal KZnBi at room temperature (RT) by near-field terahertz (THz) spectroscopy, establishing a relation for an electromagnetic control of J_chiral. In THz electric and external magnetic fields, we visualize a spatial flow of coherent J_chiral in macroscopic length scale and monitor its temporal dynamics in picosecond time scale, revealing its ultralong transport length around 100 micrometers. Such coherent J_chiral is further found to be controlled according to field directions, suggesting the feasibility of information science with topological Dirac semimetals at RT.

Anomalous Hall effect in topological Weyl and nodal-line semimetal Heusler compound Co2VAl

Magnetic topological semimetals (TSMs) with broken time-reversal symmetry are very rare and have drawn significant attention in condensed matter physics due to their numerous intriguing topological properties. Among these various magnetic TSMs, Co₂-based full Heusler compounds are of current interest, since a few of these materials exhibit Weyl and nodal fermions in their topological band structure. In this work, we report a comprehensive study of anomalous Hall effect (AHE) in the ferromagnetic full Heusler compound Co₂VAl. Recent studies indicate that the intrinsic AHE is closely related to the Berry curvature of the occupied electronic Bloch states. The present study of Co₂VAl attempts to understand and explore the possibility of topology-induced AHE. The anomalous Hall resistivityρxyAis observed to scale quadratically with the longitudinal resistivityρ_xx. Our experimental results also reveal that the anomalous Hall conductivity (AHC) is ∼85 cm^-1at 2 K with an intrinsic contribution of ∼75.6 S cm^-1, and is nearly insensitive to temperature. The first principle calculations note that the Berry curvature originated from a gapped nodal line and symmetry-protected Weyl nodes near the Fermi level (EF) is the main source of AHE in this compound. Thus, this investigation on Co₂VAl discloses that it is a ferromagnetic Weyl and nodal-line TSM. The theoretically calculated AHC is in well agreement with the experimentally obtained AHC.

Chiral anomaly induced magnetoconductances in an irradiated type-I Weyl semimetal

Magneto conductivities in Weyl semimetals (WSMs) in presence of small fields are studied using quasi-classical Boltzmann transport equations. Following such formalism here we consider irradiation via circularly polarized light on a two-node time reversal breaking WSM already under a dc/static electric field and study the magneto-transport properties due to the presence of chiral anomaly. Chiral anomaly affects both longitudinal magnetoconductivity as well as planar Hall conductivity. As our field set-up causes continuous time variation in the relative orientation between the fields, one naturally expects interesting magneto-transport behavior for different field strengths and tilting. The type-I tilting that we study here displays both positive and negative magnetoconductances depending on the field strengths and time. Furthermore, we find that a direct temporal tuning of the irradiated field strengths can lead to fluctuating magneto-transport behavior which can be easily improvised and checked in the laboratories.

Evidence for topological features in the electronic and phononic bands of ZGeSb (Z = Hf, Zr, Ti) class of compounds

Nontrivial topological properties in materials have been found in either the electronic or the phononic bands, but they have seldom been shown in both for a compound. With the aid of first-principle calculations, our paper attempts to find topological features in the electron and phonon band structures of ZGeSb (Z = Hf, Zr, Ti) class of compounds. The electron band structure exhibits two nodal rings in each of these compounds. Furthermore, drumhead surface states (DSS) have also been shown. The phonon band structure depicts one nodal ring in each of these compounds. DSS is also seen in the phonon surface states. Layering possibility has also been explored in HfGeSb, which admits a nodal ring each in its electronic and phononic band structure. Finally, these compounds (bulk and mono-layer) possess Dirac points robust to spin-orbit coupling effects, with at least one such Dirac point with its linear dispersion extending to the Fermi energy. Therefore, these compounds fall under the topological nodal line metals class, which is rarely seen in materials. These compounds' theoretical nontrivial topological nature in their electronic and phononic band structure provides a profound grasp of electronic and phononic nodal-line physics and is a good candidate for experimental verification. The existence of Dirac points close to the Fermi level could also motivate one to look for extreme magnetoresistance in these compounds. Moreover, given their largely metallic nature, these compounds become an excellent arena for novel device applications.

Experimental Realization of Weyl Exceptional Rings in a Synthetic Three-Dimensional Non-Hermitian Phononic Crystal

Weyl points-topological monopoles of quantized Berry flux-are predicted to spread to Weyl exceptional rings in the presence of non-Hermiticity. Here, we use a one-dimensional Aubry-Andre-Harper model to construct a Weyl semimetal in a three-dimensional parameter space comprising one reciprocal dimension and two synthetic dimensions. The inclusion of non-Hermiticity in the form of gain and loss produces a synthetic Weyl exceptional ring (SWER). The topology of the SWER is characterized by both its topological charge and non-Hermitian winding numbers. We experimentally observe the SWER and synthetic Fermi arc in a one-dimensional phononic crystal with the non-Hermiticity introduced by active acoustic components. Our findings pave the way for studying the high-dimensional non-Hermitian topological physics in acoustics.

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.

Benchmarking Noise and Dephasing in Emerging Electrical Materials for Quantum Technologies

As quantum technologies develop, a specific class of electrically conducting materials is rapidly gaining interest because they not only form the core quantum-enabled elements in superconducting qubits, semiconductor nanostructures, or sensing devices, but also the peripheral circuitry. The phase coherence of the electronic wave function in these emerging materials will be crucial when incorporated in the quantum architecture. The loss of phase memory, or dephasing, occurs when a quantum system interacts with the fluctuations in the local electromagnetic environment, which manifests in "noise" in the electrical conductivity. Hence, characterizing these materials and devices therefrom, for quantum applications, requires evaluation of both dephasing and noise, although there are very few materials where these properties are investigated simultaneously. Here, the available data on magnetotransport and low-frequency fluctuations in electrical conductivity are reviewed to benchmark the dephasing and noise. The focus is on new materials that are of direct interest to quantum technologies. The physical processes causing dephasing and noise in these systems are elaborated, the impact of both intrinsic and extrinsic parameters from materials synthesis and devices realization are evaluated, and it is hoped that a clearer pathway to design and characterize both material and devices for quantum applications is thus provided.

Synthesis of Weyl Semi-Metal Co3Sn2S2 by Hydrothermal Method and Its Physical Properties

In the field of condensed matter physics, as new quantum materials, topological semimetals have a special topological energy band structure and nontrivial band crossings in the energy band, which will have many excellent topological properties, such as internal insulation of topological insulators and the presence of conduction electrons on the surface; this makes topological semimetals exhibit wider application prospects in electronic devices. So far, the experimental synthesis of topological semimetals was performed using physical methods to synthesize bulk single crystals, which is not conducive to the commercial application of micro and small devices. Weyl semimetal Co3Sn2S2 with shandite structure was successfully synthesized experimentally by a green and environmentally friendly hydrothermal method. Adjusting its reaction temperature, molar atomic ratio of elements and annealing temperature, and other experimental conditions, we analyze the crystal structure and physical properties of Co3Sn2S2, with the nanocrystal size being about 200 nm. We found that the Co3Sn2S2 synthesized by the hydrothermal method has a Curie temperature at 100 K to undergo ferromagnetic transition.

Tunable topological electronic states in the honeycomb-kagome lattices of nitrogen/oxygen-doped graphene nanomeshes

The rich and exotic electronic properties of graphene nanomeshes (GNMs) have been attracting interest due to their superiority to pristine graphene. Using first-principles calculations, we considered three graphene meshes doped with nitrogen and oxygen atoms (C₁₀N₃, C₉N₄ and C₁₀O₃). The electronic band structures of these GNMs in terms of the proximity of the Fermi level featured a two-dimensional (2D) honeycomb-kagome lattice with concurrent kagome and Dirac bands. The position of the Fermi level can be regulated by the doping ratio, resulting in different topological quantum states, namely topological Dirac semimetals and Dirac nodal line (DNL) semimetals. More interestingly, the adsorption of rhenium (Re) atoms in the voids of the C₁₀N₃ (Re@ C₁₀N₃) GNMs induced quantum anomalous Hall (QAH) states, as verified by the nonzero Chern numbers and chiral edge states. These GNMs offer a promising platform superior to pristine graphene for regulating multiple topological states.

Materials and possible mechanisms of extremely large magnetoresistance: a review

Magnetoresistance (MR) is a characteristic that the resistance of a substance changes with the external magnetic field, reflecting various physical origins and microstructures of the substance. A large MR, namely a huge response to a low external field, has always been a useful functional feature in industrial technology and a core goal pursued by physicists and materials scientists. Conventional large MR materials are mainly manganites, whose colossal MR (CMR) can be as high as -90%. The dominant mechanism is attributed to spin configuration aligned by the external field, which reduces magnetic scattering and thus resistance. In recent years, some new systems have shown an extremely large unsaturated MR (XMR). Unlike ordinary metals, the positive MR of these systems can reach 10³%-10⁸% and is persistent under super high magnetic fields. The XMR materials are mainly metals or semimetals, distributed in high-mobility topological or non-topological systems, and some are magnetic, which suggests a wide range of application scenarios. Various mechanisms have been proposed for the potential physical origin of XMR, including electron-hole compensation, steep band, ultrahigh mobility, high residual resistance ratio, topological fermions, etc. It turns out that some mechanisms play a leading role in certain systems, while more are far from clearly defined. In addition, the researches on XMR are largely overlapped or closely correlated with other recently rising physics and materials researches, such as topological matters and two-dimensional (2D) materials, which makes elucidating the mechanism of XMR even more important. Moreover, the disclosed novel properties will lay a broad and solid foundation for the design and development of functional devices. In this review, we will discuss several aspects in the following order: (I) introduction, (II) XMR materials and classification, (III) proposed mechanisms for XMR, (IV) correlation with other systems (featured), and (V) conclusions and outlook.

Tip-induced superconductivity

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

2D weak anti-localization in thin films of the topological semimetal Pd[Formula: see text]Bi[Formula: see text]S[Formula: see text]

Pd[Formula: see text]Bi[Formula: see text]S[Formula: see text] (PBS) is a recently proposed topological semimetal candidate. However, evidence for topological surface states have not yet been revealed in transport measurements due to the large mobility of bulk carriers. We report the growth and magneto-transport studies of PBS thin films where the mobility of the bulk carriers is reduced by two orders of magnitude, revealing for the first time, contributions from the 2-dimensional (2D) topological surface states in the observation of the 2D weak anti-localization (WAL) effect in magnetic field and angle dependent conductivity measurements. The magnetotransport data is analysed within the 2D Hikami-Larkin-Nagaoka (HLN) theory. The analysis suggests that multiple conduction channels contribute to the transport. It is also found that the temperature dependence of the dephasing length can't be explained only by electron-electron scattering and that electron-phonon scattering also contributes to the phase relaxation mechanism in PBS films.

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.

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.

An ab-initio study on structural, elastic, electronic, bonding, thermal, and optical properties of topological Weyl semimetal TaX (X = P, As)

In recent days, study of topological Weyl semimetals have become an active branch of physics and materials science because they led to realization of the Weyl fermions and exhibited protected Fermi arc surface states. Therefore, topological Weyl semimetals TaX (X = P, As) are important electronic systems to investigate both from the point of view of fundamental physics and potential applications. In this work, we have studied the structural, elastic, mechanical, electronic, bonding, acoustic, thermal and optical properties of TaX (X = P, As) in detail via first-principles method using the density functional theory. A comprehensive study of elastic constants and moduli shows that both TaP and TaAs possesses low to medium level of elastic anisotropy (depending on the measure), reasonably good machinability, mixed bonding characteristics with ionic and covalent contributions, brittle nature and relatively high Vickers hardness with a low Debye temperature and melting temperature. The minimum thermal conductivities and anisotropies of TaX (X = P, As) are calculated. Bond population analysis supports the bonding nature as predicted by the elastic parameters. The bulk electronic band structure calculations reveal clear semi-metallic features with quasi-linear energy dispersions in certain sections of the Brillouin zone near the Fermi level. A pseudogap in the electronic energy density of states at the Fermi level separating the bonding and the antibonding states indicates significant electronic stability of tetragonal TaX (X = P, As).The reflectivity spectra show almost non-selective behavior over a wide range of photon energy encompassing visible to mid-ultraviolet regions. High reflectivity over wide spectral range makes TaX suitable as reflecting coating. TaX (X = P, As) are very efficient absorber of ultraviolet radiation. Both the compounds are moderately optically anisotropic owing to the anisotropic nature of the electronic band structure. The refractive indices are very high in the infrared to visible range. All the energy dependent optical parameters show metallic features and are in complete accord with the underlying bulk electronic density of states calculations.

Field-Modulated Anomalous Hall Conductivity and Planar Hall Effect in Co3Sn2S2 Nanoflakes

Time-reversal-symmetry-breaking Weyl semimetals (WSMs) have attracted great attention recently because of the interplay between intrinsic magnetism and topologically nontrivial electrons. Here, we present anomalous Hall and planar Hall effect studies on Co₃Sn₂S₂ nanoflakes, a magnetic WSM hosting stacked Kagome lattice. The reduced thickness modifies the magnetic properties of the nanoflake, resulting in a 15-time larger coercive field compared with the bulk, and correspondingly modifies the transport properties. A 22% enhancement of the intrinsic anomalous Hall conductivity (AHC), as compared to bulk material, was observed. A magnetic field-modulated AHC, which may be related to the changing Weyl point separation with magnetic field, was also found. Furthermore, we showed that the PHE in a hard magnetic WSM is a complex interplay between ferromagnetism, orbital magnetoresistance, and chiral anomaly. Our findings pave the way for a further understanding of exotic transport features in the burgeoning field of magnetic topological phases.

Anomalous Hall transport in tilted multi-Weyl semimetals

We study the effect of a perpendicular magnetic fieldBon a multinode Weyl semimetal (mWSM) of arbitrary integer monopole chargen, with the two Weyl multinodes separated ink-space. Besides type-I mWSMs, there exist type-II mWSMs which are characterized by the tilted minimal dispersion for low-energy excitations; the Weyl points in type-II mWSMs are still protected crossings but appear at the contact of the electron and hole pockets, after the Lifshitz transition. We find that the presence of a perpendicular magnetic field quantizes the occupation pockets due to the presence of Fermi tubes. In this theory, the Hilbert space is spanned by a set ofnchiral degenerate ground states, and a countably infinite number of particle-hole symmetric Landau levels (LLs). We calculate the Hall conductivity for the tilt-symmetric case of type-I mWSM using the Kubo formula, in the zero-frequency (DC) limit, and recover the well-known vacuum contribution. We compute the Fermi surface corrections and show that the expression generalizes from the formula for elementary (n= 1) type-I WSMs. We derive an expression for the type-II mWSM Hall conductivity, which is bounded by a LL cutoff introduced on physical grounds. Interestingly, we find that the anomalous vacuum Hall conductivity is vanishing in the type-II phase at all temperatures. The corresponding thermal Hall and Nernst conductivities are evaluated and characterized for both phases. The qualitative and quantitative observations presented here may serve in the characterization of generic mWSMs of both types.

Broken symmetries and the related interface-induced effects at Weyl-system TaAs in proximity of noble metals

Weyl semimetal TaAs, congenially accommodating the massless Weyl fermions, furnishes a platform to observe a spontaneous breaking of either the time-reversal or the inversion symmetry and the concurrent genesis of pairs of Weyl nodes with significant topological durability. Former experimental analysis, which reveals that the near-zero spin-polarization of bulk TaAs, experiences a boost in proximity of point-contacts of non-magnetic metals along with the associated tip-induced superconductivity, provides the impetus to study the large-area stacked interfaces of TaAs with noble metals like Au and Ag. The primary outcomes of the present work can be listed as follows: (1) First-principles calculations on the interfacial systems have manifested an increment of the interface-induced spin-polarization and contact-induced transport spin-polarization of TaAs in proximity of noble metals; (2) In contrast to the single interface, for vertically stacked cases, the broken inversion symmetry of the system introduces a z-directional band-dispersion, resulting in an energetically separated series of non-degenerate band crossings. The simultaneous presence of such band-crossings and spin-polarization indicated the coexistence of both broken time reversal and inversion symmetries for metal-semimetal stacked interfaces; (3) quantum transport calculations on different device geometries reveal the importance of contact geometry for spin-transport in TaAs devices. Lateral contacts are found to be more effective in obtaining a uniform spin transport and larger transport spin polarization; (4) the phonon dispersion behaviour of TaAs displays a closure of band-gap with the associated increase of phonon-density of states for the acoustic modes in proximity of lateral contacts of noble metals.

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.

Chiral-Anomaly-Driven Casimir-Lifshitz Torque between Weyl Semimetals

We propose a new mechanism to generate the Casimir-Lifshitz torque between Weyl semimetals arising from the chiral anomaly. For short distances ranging from a nanometer to a few tens of nanometers, chiral anomaly is manifested via a Casimir-Lifshitz torque ∼sin(θ) with θ being the twisting angle. As the distance between Weyl semimetals increases from a submicrometer to a few micrometers, chiral-anomaly-driven Casimir-Lifshitz torque between Weyl semimetals is remarkably large, which is comparable with that of conventional birefringent materials.

Scanning tunneling spectroscopy studies of topological materials

Topological materials have become promising materials for next-generation devices by utilizing their exotic electronic states. Their exotic states caused by spin-orbital coupling usually locate on the surfaces or at the edges. Scanning tunneling spectroscopy (STS) is a powerful tool to reveal the local electronic structures of condensed matters. Therefore, STS provides us with an almost perfect method to access the exotic states of topological materials. In this topical review, we report the current investigations by several methods based on the STS technique for layered topological material from transition metal dichalcogenide Weyl semimetals (WTe₂ and MoTe₂) to two dimensional topological insulators (layered bismuth and silicene). The electronic characteristics of these layered topological materials are experimentally identified.

Magneto-conductivity of Weyl semimetals: the roles of inter-valley scattering and high-order Feynman diagrams

Within the theoretical framework of Kubo formula and self-consistent Born approximation, we theoretically study the transversal and longitudinal magneto-conductivity of a type-I Weyl semimetal. We focus mainly on the peculiar role of inter-valley scattering on linear transversal magnetoresistance (LTMR) and negative longitudinal magnetoresistance (NLMR). At first, we find that the contributions of high-order Feynman diagrams to the transversal magneto-conductivity play the distinct roles between the cases of intra- and inter-valley scatterings. The former suppresses the transversal conductivity whereas the latter enhances it. Then, with the increase of scattering strength, the LTMR is destroyed, accompanying a sizable increase of transversal conductivity, in particular, in the case of the tilted cone. For longitudinal magneto-transport, inter-valley scattering contributes only trivial magnetoresistance. In contrast, intra-valley scattering is invalid for longitudinal magneto-transport which means a very large NLMR. In addition, the high-order Feynman diagrams always play the nontrivial role on the longitudinal conductivity even in the weak scattering limit. Finally, when altering the Fermi energy among low-lying Landau level, the peaks of transversal conductivity just correspond to the valleys of the longitudinal conductivity.

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.

Nodal line topological superfluid and multiply protected Majorana Fermi arc in a three-dimensional time-reversal-invariant superfluid model

We theoretically study a time-reversal-invariant three-dimensional superfluid model by stacking in z direction identical bilayer models with intralayer spin-orbit coupling and contrary Zeeman energy splitting for different layers, which has been suggested recently to realize two-dimensional time-reversal-invariant topological superfluid. We find that this model shows two kinds of topologically nontrivial phases: gapless phases with nodal lines in pairs protected by chiral symmetry and a gapped phase, both of which support a time-reversal-invariant Majorana Fermi arc (MFA) on the yz and xz side surface. These MFA abide by time-reversal and particle-hole symmetries and are topologically protected by the winding numbers in mirror subspaces and the Z ₂ numbers of two-dimensional DIII class topological superfluid, which are different from MFA in the time-reversal broken Weyl superfluid protected by nonzero Chern numbers. This important observation means that MFA in our model represents a new type of topological state not explored previously. The Zeeman field configuration in our model is relevant to the antiferromagnetic topological insulator MnBi₂Te₄, thus our work stimulates the further studies on superconducting effects in the realistic antiferromagnetic topological insulator.

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.

Andreev reflection in nodal-line Weyl semimetal

Based on the Bogoliubov-de Gennes equation, the quantum scattering problem through a nodal-line Weyl semimetal based normal metal/superconductor heterojunction has been theoretically studied. Since the crystallographic anisotropy in the material, two different orientations between the crystalline axis and the superconducting interface have been revealed. Considering a heterojunction with the interface paralleling to the basal plane, it is found that Andreev reflection with [Formula: see text] due to Klein-like scattering gives rise to a perfect scattering. Deviation from the critical value, Andreev reflection falls down and normal reflection goes up. While the interface is perpendicular to the basal plane, the pure intra-mode retro-Andreev reflection (RAR) and inter-mode specular Andreev reflection (SAR) are manifested at the normal incident. Moreover, the reflection coefficient exhibits the reentrant behavior with the Fermi energy. Fundamentally, such features are a consequence of the torus-like iso-energy surfaces of the nodal-line Weyl semimetals, which is in sharp contrast to the case of conventional materials, graphene, and Weyl-point semimetals. Those novel scattering processes also result in a distinctive tunneling conductance, such as the sub-gap nonmonotonic features, the interface directional dependent zero bias conductances and the reentrant behavior, which can be served as a smoking gun to distinguish the mode-resolved Andreev reflections in experiments.

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.

Thickness dependent transition from the 1T' to Weyl semimetal phase in ultrathin MoTe2: electrical transport, noise and Raman studies

Bulk 1T'-MoTe₂ shows a structural phase transition from the 1T' to Weyl semimetallic (WSM) T_d phase at ∼240 K. This phase transition and transport properties in the two phases have not been investigated on ultra-thin crystals. Here we report electrical transport, 1/f noise and Raman studies on ultra-thin 1T'-MoTe₂ (∼5 to 16 nm thick) field-effect transistor (FETs) devices as a function of temperature. The electrical resistivities for a thickness of 16 nm and 11 nm show maxima at temperatures of 208 K and 178 K, respectively, making a transition from the semiconducting to semi-metallic phase, hitherto not observed in bulk samples. Raman frequencies and linewidths for an 11 nm thick crystal show a change around 178 K, attributed to the additional contribution to the phonon self-energy due to the enhanced electron-phonon interaction in the WSM phase. Furthermore, the resistivity at low temperature shows an upturn below 20 K along with the maximum in the power spectral density of the low frequency 1/f noise. The latter rules out the metal-insulator transition (MIT) being responsible for the upturn of resistivity below 20 K. The low temperature resistivity follows ρ∝ 1/T, changing to ρ∝T with increasing temperature supports electron-electron interaction physics at electron-hole symmetric Weyl nodes below 20 K. These observations will pave the way to unravel the properties of the WSM state in layered ultra-thin van der Waals materials.

Lattice-dependent spin Hall effect of light in a Weyl semimetal

We systematically study the lattice-dependent spin Hall effect of light (SHEL) in a Weyl semimetal (WSM) by considering left-handed polarization of the incident beam, and propose a new simple method to sense the lattice spacing precisely. It is revealed that the lattice spacing plays as essential a role as the Weyl points separation in the influences on the SHEL, and the variations of SHEL shifts are closely related to the real part of Hall conductivity. Specifically, the SHEL shifts increase to the peak values first and then decrease gradually with the increase of lattice spacing, and a quantitative relationship between the SHEL and the lattice spacing is established. By simulating weak measurement experiments, the lattice-dependent SHEL shifts are amplified and measured in desirable accuracies. Subsequently, we propose a method of precisely sensing the lattice spacing based on the amplified SHEL shifts. These researches provide theoretical basis for manipulating the SHEL in WSMs, and may open the possibility of fabricating the WSM parameter sensors.

Anomalous spin Nernst effect in Weyl semimetals

The spin Nernst effect describes a transverse spin current induced by the longitudinal thermal gradient in a system with the spin-orbit coupling. Here we study the spin Nernst effect in a mesoscopic four-terminal cross-bar Weyl semimetal device under a perpendicular magnetic field. Because the spin current is a tensor, it has three elements with the spin direction pointing to the x, y  and z directions when the spin current flows along the transverse lead. By using the tight-binding Hamiltonian combined with the nonequilibrium Green's function method, the three elements of the spin current in the transverse leads and the spin Nernst coefficients are obtained. The results show that the spin Nernst effect in the Weyl semimetal has an essential difference to the traditional Nernst effect: we found that the z direction spin current is zero without the magnetic field while it appears under the magnetic field, and the x and y  direction spin currents in the two transverse leads flow out or in together, in contrast to the traditional spin Nernst effect, in which the spin current is induced by the spin-orbit coupling and flows out from one lead and flows in on the other. We call it the anomalous spin Nernst effect. In addition, we show that the Weyl semimetals have inversion-type symmetry, mirror-reversal-type symmetry and electron-hole-type symmetry, which lead to the spin Nernst coefficients being either odd or even functions of the Fermi energy, the magnetic field and the transverse terminals. Moreover, the spin Nernst effect in the Weyl semimetals are strongly anisotropic and its coefficients are strongly dependent on both the direction of thermal gradient and the direction of the transverse lead connection. Three non-equivalent connection modes (x-z, z-x and x-y  modes) are studied in detail, and the spin Nernst coefficients for three different modes exhibit very different behaviors. These strongly anisotropic behaviors of the spin Nernst effect can be used as the characterization of magnetic Weyl semimetals.

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.

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.

Anisotropic thermoelectric properties of Weyl semimetal NbX (X = P and As): a potential thermoelectric material

Weyl semimetal, a newly developed thermoelectric material, has aroused much interest due to its extraordinary transport properties. In this work, the thermoelectric transport properties of NbX (X = P and As), a prototypical Weyl semimetal, are investigated using the first-principles calculations together with Boltzmann transport theory. The calculated room-temperature lattice thermal conductivities along the a and c directions are 2.0 W mK-1 and 0.6 W mK-1 for NbP and 1.4 W mK-1 and 0.4 W mK-1 for NbAs, respectively. The low thermal conductivities may be useful in the thermoelectric applications. It is found that the acoustic branches have obvious contribution to the total lattice thermal conductivity, and the size dependence of the thermal conductivities can provide guidance for designing thermoelectric nanostructures. Our results show that the anisotropic structures of these compounds bring about the anisotropy of transport coefficients along the a and c directions, and the preferred direction is the c direction in thermoelectric applications. Moreover, NbP and NbAs show high ZT values of 0.82 and 0.50 along the c direction for p-type at an optimal carrier concentration, indicating that they are potential thermoelectric materials.

Proximity-induced surface superconductivity in Dirac semimetal Cd3As2

Cd₃As₂ is a three-dimensional Dirac semimetal with separated Dirac points in momentum space. In spite of extensive transport and spectroscopic studies on its exotic properties, the evidence of superconductivity in its surface states remains elusive. Here, we report the observation of proximity-induced surface superconductivity in Nb/Cd₃As₂ hybrid structures. Our four-terminal transport measurement identifies a pronounced proximity-induced pairing gap (gap size comparable to Nb) on the surfaces, which exhibits a flat conductance plateau in differential conductance spectra, consistent with our theoretical simulations. The surface supercurrent from Nb/Cd₃As₂/Nb junctions is also achieved with a Fraunhofer/SQUID-like pattern under out-of-plane/in-plane magnetic fields, respectively. The resultant mapping shows a predominant distribution on the top and bottom surfaces as the bulk carriers are depleted, which can be regarded as a higher dimensional analog of edge supercurrent in two-dimensional quantum spin Hall insulators. Our study provides the evidence of surface superconductivity in Dirac semimetals.

Surface superconductivity in a Dirac semimetal remains rarely studied. Here, Huang and Zhou et al. report the evidence of proximity-induced surface superconductivity in a superconductor/Dirac semimetal hybrid system Nb/Cd₃As₂.

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.

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.

Nonsaturating large magnetoresistance in semimetals

The rapidly expanding class of quantum materials known as topological semimetals (TSMs) displays unique transport properties, including a striking dependence of resistivity on applied magnetic field, that are of great interest for both scientific and technological reasons. So far, many possible sources of extraordinarily large nonsaturating magnetoresistance have been proposed. However, experimental signatures that can identify or discern the dominant mechanism and connect to available theories are scarce. Here we present the magnetic susceptibility (χ), the tangent of the Hall angle ([Formula: see text]), along with magnetoresistance in four different nonmagnetic semimetals with high mobilities, NbP, TaP, NbSb₂, and TaSb₂, all of which exhibit nonsaturating large magnetoresistance (MR). We find that the distinctly different temperature dependences, [Formula: see text], and the values of [Formula: see text] in phosphides and antimonates serve as empirical criteria to sort the MR from different origins: NbP and TaP are uncompensated semimetals with linear dispersion, in which the nonsaturating magnetoresistance arises due to guiding center motion, while NbSb₂ and TaSb₂ are compensated semimetals, with a magnetoresistance emerging from nearly perfect charge compensation of two quadratic bands. Our results illustrate how a combination of magnetotransport and susceptibility measurements may be used to categorize the increasingly ubiquitous nonsaturating large magnetoresistance in TSMs.

Surface plasmons in Weyl semimetals

The surface plasmon excitation spectrum is calculated for the Weyl semimetal within the random phase approximation. Recently, a surface plasmon mode has been predicted to exist at the three-dimensional Dirac semimetal surface due to the Dirac plasmon mode in the bulk. In addition, Weyl semimetals possess Fermi arc electron states on their surfaces resulting in an anisotropic Fermi arc plasmon mode. In the present work we consider the modification of the surface plasmon mode due to the Fermi arc plasmon mode. We introduce an effective surface dielectric function of Fermi arc electrons which comprises the Fermi arc plasmon mode and the surface dielectric function that determines the bare surface plasmon mode present due to the plasmon mode in the bulk from Weyl electrons. As a result, we obtain the dispersion of the renormalized surface plasmon mode from the effective surface dielectric function. We find that a renormalization of the bare surface plasmon mode increases with increases in the Fermi arc plasmon frequency. The obtained spectrum will be useful for experimentally exploring the surface spectral properties of Weyl semimetals.

Tunable double-Weyl Fermion semimetal state in the SrSi2 materials class

We discuss first-principles topological electronic structure of noncentrosymmetric SrSi2 materials class based on the hybrid exchange-correlation functional. Topological phase diagram of SrSi2 is mapped out as a function of the lattice constant with focus on the semimetal order. A tunable double-Weyl Fermion state in Sr1-xCaxSi2 and Sr1-xBaxSi2 alloys is identified. Ca doping in SrSi2 is shown to yield a double-Weyl semimetal with a large Fermi arc length, while Ba doping leads to a transition from the topological semimetal to a gapped insulator state. Our study indicates that SrSi2 materials family could provide an interesting platform for accessing the unique topological properties of Weyl semimetals.

Bulk Fermi Surfaces of the Dirac Type-II Semimetallic Candidates MAl_{3} (Where M=V, Nb, and Ta)

We report a de Haas-van Alphen (dHvA) effect study on the Dirac type-II semimetallic candidates MAl_{3} (where, M=V, Nb and Ta). The angular dependence of their Fermi surface (FS) cross-sectional areas reveals a remarkably good agreement with our first-principles calculations. Therefore, dHvA supports the existence of tilted Dirac cones with Dirac type-II nodes located at 100, 230 and 250 meV above the Fermi level ϵ_{F} for VAl_{3}, NbAl_{3} and TaAl_{3} respectively, in agreement with the prediction of broken Lorentz invariance in these compounds. However, for all three compounds we find that the cyclotron orbits on their FSs, including an orbit nearly enclosing the Dirac type-II node, yield trivial Berry phases. We explain this via an analysis of the Berry phase where the position of this orbit, relative to the Dirac node, is adjusted within the error implied by the small disagreement between our calculations and the experiments. We suggest that a very small amount of doping could displace ϵ_{F} to produce topologically nontrivial orbits encircling their Dirac node(s).