In 1929, Hermann Weyl derived the massless solutions from the Dirac equation - the relativistic wave equation for electrons. Neutrinos were thought, for decades, to be Weyl fermions until the discovery of the neutrino mass. Moreover, it has been suggested that low energy excitations in condensed matter can be the solutions to the Weyl Hamiltonian. Recently, photons have also been proposed to emerge as Weyl particles inside photonic crystals. In all cases, two linear dispersion bands in the three-dimensional (3D) momentum space intersect at a single degenerate point - the Weyl point. Remarkably, these Weyl points are monopoles of Berry flux with topological charges defined by the Chern numbers. These topological invariants enable materials containing Weyl points to exhibit a wide variety of novel phenomena including surface Fermi arcs, chiral anomaly, negative magnetoresistance, nonlocal transport, quantum anomalous Hall effect, unconventional superconductivity[15] and others [16, 17]. Nevertheless, Weyl points are yet to be experimentally observed in nature. In this work, we report on precisely such an observation in an inversion-breaking 3D double-gyroid photonic crystal without breaking time-reversal symmetry.
We report the existence of Weyl points in a class of non-central symmetric metamaterials, which has time reversal symmetry, but does not have inversion symmetry due to chiral coupling between electric and magnetic fields. This class of metamaterial exhibits either type-I or type-II Weyl points depending on its non-local response. We also provide a physical realization of such metamaterial consisting of an array of metal wires in the shape of elliptical helixes which exhibits type-II Weyl points.
In this letter, we report the presence of novel type of plasmon Weyl points in a naturally existing material - magnetized plasma. In such a medium, conventional, purely longitudinal bulk plasma oscillations exists only along the direction of applied magnetic field (z direction). With strong enough magnetic field, there exist helical propagating modes along z direction with circular polarizations. The orthogonality between the longitudinal bulk plasmon mode and the transverse helical propagating modes guarantees their crossing at the bulk plasmon frequency. These crossing points, embedded in th…
Weyl points in three-dimensional photonic crystals behave as monopoles of Berry flux in momentum space. Here, based on general symmetry analysis, we show that a minimal number of four symmetry-related (consequently equifrequency) Weyl points can be realized in time-reversal invariant photonic crystals. We further propose an experimentally-feasible way to modify double-gyroid photonic crystals to realize four equifrequency Weyl points, which is explicitly confirmed by our first-principle photonic band-structure calculations. Remarkably, photonic crystals with equifrequency Weyl points are quali…
The discovery of Weyl semimetals opens the door for searching topological semimetals in physical science. The Weyl points are generally recognized as conventional, quadratic, spin-1, and those of high topological charges. Here we report the observation of the quadruple Weyl point of charge 4, the highest topological charge a twofold degenerate node can carry. Besides the quadruple Weyl point, the phononic semimetal also hosts conventional, quadratic, and spin-1 Weyl points, which stands as a system with yet the richest types of Weyl points. The quadruple-helicoid surface states, specific to th…
As one of Weyl semimetals discovered recently, NbP exhibits two groups of Weyl points with one group lying inside the $k_z=0$ plane and the other group staying away from this plane. All Weyl points have been assumed to be type-I, for which the Fermi surface shrinks into a point as the Fermi energy crosses the Weyl point. In this work, we have revealed that the second group of Weyl points are actually type-II, which are found to be touching points between the electron and hole pockets in the Fermi surface. Corresponding Weyl cones are strongly tilted along a line approximately $17^\circ$ off th…
Weyl points, serving as monopoles in the momentum space and laying the foundation of topological gapless phases, have recently been experimentally demonstrated in various physical systems. However, none of the observed Weyl degeneracies are ideal: they either offset in energy or coexist with trivial dispersions at other momenta. The lack of an ideal Weyl system sets a serious limit to the further development of Weyl physics and potential applications. Here, by constructing a photonic metamaterial, we experimentally observe an ideal Weyl system, whose nodal frequencies are pinned by symmetries …
We use ultrahigh resolution, tunable, vacuum ultraviolet laser angle-resolved photoemission spectroscopy (ARPES) to study the electronic properties of WTe$_2$, a material that was predicted to be a type-II Weyl semimetal. The Weyl fermion states in WTe2 were proposed to emerge at the crossing points of electron and hole pockets; and Fermi arcs connecting electron and hole pockets would be visible in the spectral function on (001) surface. Here we report the observation of such Fermi arcs in WTe2 confirming the theoretical predictions. This provides strong evidence for type-II Weyl semimetallic…
Weyl semimetal (WSM) is a newly discovered quantum phase of matter that exhibits topologically protected states characterized by two separated Weyl points with linear dispersion in all directions. Here, via combining theoretical analysis and magneto-infrared spectroscopy of an archetypal Weyl semimetal, niobium phosphide, we demonstrate that the coupling between Weyl points can significantly modify the electronic structure of a WSM and provide a new twist to the protected states. These findings suggest that the coupled Weyl points should be considered as the basis for analysis of realistic WSM…
Weyl semimetals are extraordinary systems where exotic phenomena such as Fermi arcs, pseudo-gauge fields and quantum anomalies arise from topological band degeneracy in crystalline solids for electrons and metamaterials for photons and phonons. On the other hand, higher-order topological insulators unveil intriguing multidimensional topological physics beyond the conventional bulk-edge correspondences. However, it is unclear whether higher-order topology can emerge in Weyl semimetals. Here, we report the experimental discovery of higher-order Weyl semimetals in its phononic analog which exhibi…
Weyl fermions have not been found in nature as elementary particles, but they emerge as nodal points in the band structure of electronic and classical wave crystals. Novel phenomena such as Fermi arcs and chiral anomaly have fueled the interest in these topological points which are frequently perceived as monopoles in momentum space. Here we report the experimental observation of generalized optical Weyl points inside the parameter space of a photonic crystal with a specially designed four-layer unit cell. The reflection at the surface of a truncated photonic crystal exhibits phase vortexes du…
Weyl photons appear when two three-dimensional photonic bands with linear dispersion are degenerate at a single momentum point, labeled as Weyl point. These points have remarkable properties such as being robust topological monopoles of Berry curvature as well as an associated vanishing density of states. In this work, we report on a systematic theoretical study of the quantum optical consequences of such Weyl photons. First, we analyze the dynamics of a single quantum emitter coupled to a Weyl photonic bath as a function of its detuning with respect to the Weyl point and study the corrrespond…
Based on $ab$ $initio$ calculations and low-energy effective $k{\cdot}p$ model, we propose a type of Weyl nodal point-line fermion, composed of 0D Weyl points and 1D Weyl nodal line, in ferromagnetic material Eu$_5$Bi$_3$. In the absence of spin-orbital coupling (SOC), the spin-up bands host a pair of triply degenerate points together with a unique bird-cage like node structure. In the presence of SOC with (001) magnetization, each triplet point splits into a double Weyl point and a single Weyl point accompanied by two nodal rings, forming two sets of Weyl nodal point-line fermions near the Fe…
The "Hydrogen atom" of magnetic Weyl semimetals, with the minimum number of Weyl points, have received growing attention recently due to the possible presence of Weyl-related phenomena. Here, we report a nontrivial electronic structure of the ferromagnetic alluaudite-type compound K$_{2}$Mn$_3$(AsO$_{4}$)$_3$. It exhibits only a pair of Weyl points constrained in the $z$-direction by the two-fold rotation symmetry, leading to extremely long Fermi arc surface states. In addition, the study of its low-energy effective model results in the discovery of various topological superconducting states, …
We employ {\it ab-initio} fully-relativistic electronic structure calculations to study the stability of the Weyl points in the momentum space within the class of the half-metallic ferromagnetic full Heusler materials, by focusing on Co$_2$TiAl as a well-established prototype compound. Here we show that both the number of the Weyl points together with their $k$-space coordinates can be controlled by the orientation of the magnetization. This alternative degree of freedom, which is absent in other topological materials (e.g. in Weyl semimetals), introduces novel functionalities, specific for th…
We show that type-II Weyl point formation in MnBi2-xSbxTe4 is more likely than in MnBi2Te4 when x reaches 0.5, as the alloy case does not suffer from the same degree of lattice parameter sensitivity as in MnBi2Te4. To further substantiate the stability of type-II Weyl points in MnBi2-xSbxTe4, we demonstrate that among the three conditions of establishing a type-II Weyl point, two are robustly satisfied by the zone-folded dispersion of Bi and Te pz orbitals and spin-orbit coupling already available in MnBi2Te4, and that the control over MnBi2-xSbxTe4 alloy composition provides a rational means …
Weyl points with monopole charge $\pm 1$ have been extensively studied, however, real materials of multi-Weyl points, whose monopole charges are higher than $1$, have yet to be found. In this Rapid Communication, we show that nodal-line semimetals with nontrivial line connectivity provide natural platforms for realizing Floquet multi-Weyl points. In particular, we show that driving crossing nodal lines by circularly polarized light generates double-Weyl points. Furthermore, we show that monopole combination and annihilation can be observed in crossing-nodal-line semimetals and nodal-chain semi…
Condensed matter systems have now become a fertile ground to discover emerging topological quasi-particles with symmetry protected modes. While many studies have focused on Fermionic excitations, the same conceptual framework can also be applied to bosons yielding new types of topological states. Motivated by the recent theoretical prediction of double-Weyl phonons in transition metal monosilicides [Phys. Rev. Lett. 120, 016401 (2018)], we directly measured the phonon dispersion in parity-breaking FeSi using inelastic x-ray scattering. By comparing the experimental data with theoretical calcul…
Weyl semimetals and nodal line semimetals are characterized by linear band touching at zero-dimensional points and one-dimensional lines, respectively. We predict that a circularly polarized light drives nodal line semimetals into Weyl semimetals. The Floquet Weyl points thus obtained are tunable by the incident light, which enables investigations of them in a highly controllable manner. The transition from nodal line semimetals to Weyl semimetals is accompanied by the emergence of a large and tunable anomalous Hall conductivity. Our predictions are experimentally testable by transport measure…
In three-dimensional noncentrosymmetric materials two-fold screw rotation symmetry forces electron's energy bands to have Weyl points at which two bands touch. This is illustrated for space groups No. 19 ($P2_12_12_1$) and No. 198 ($P2_13$), which have three orthogonal screw rotation axes. In the case of space groups No. 61 ($Pbca$) and No. 205 ($P$a-3) that have extra inversion symmetry, Weyl points are promoted to four-fold degenerate line nodes in glide-invariant planes. The three-fold rotation symmetry present in the space groups No. 198 and No. 205 allows Weyl and Dirac points, respective…
Topological semimetal states having the minimal number, i.e., only a single pair, of Weyl points are desirable for the study of effects associated with chiral topological charges. So far, the search for such states is focused on magnetic spinful systems. Here, we find that nonmagnetic spinless systems can host a class of single-pair-Weyl-point (SP-WP) states, where the two Weyl points are located at two high-symmetry time-reversal-invariant momenta. We identify 32 candidate space groups that host such states, and we show that the chiral charge of each Weyl point in the SP-WP state must be an e…
The interplay between light and matter attracts tremendous interest for exploring novel topological quantum states and their phase transitions. Here we show by first-principles calculations and the Floquet theorem that a carbon allotrope bct-C$_{16}$, a typical nodal-line semimetal, exhibits exotic photoinduced Floquet mixed-Weyl semimetallic features. Under the irradiation of a linearly polarized light, bct-C$_{16}$ undergos a topological phase transition from a Driac nodal-line semimetal to a Weyl semimetal with two pairs of tunable Weyl points. With increasing the light intensity, left-hand…
We report the surface electronic structure of niobium phosphide NbP single crystal on (001) surface by vacuum ultraviolet angle-resolved photoemission spectroscopy. Combining with our first principle calculations, we identify the existence of the Fermi arcs originated from topological surface states. Furthermore, the surface states exhibit circular dichroism pattern, which may correlate with its non-trivial spin texture. Our results provide critical evidence for the existence of the Weyl Fermions in NbP, which lays the foundation for further investigations.
Weyl semi-metal is the three dimensional analog of graphene. According to the quantum field theory, the appearance of Weyl points near the Fermi level will cause novel transport phenomena related to chiral anomaly. In the present paper, we report the first experimental evidence for the long-anticipated negative magneto-resistance generated by the chiral anomaly in a newly predicted time-reversal invariant Weyl semi-metal material TaAs. Clear Shubnikov de Haas oscillations (SdH) have been detected starting from very weak magnetic field. Analysis of the SdH peaks gives the Berry phase accumulate…
A Weyl semimetal possesses spin-polarized band-crossings, called Weyl nodes, connected by topological surface arcs. The low-energy excitations near the crossing points behave the same as massless Weyl fermions, leading to exotic properties like chiral anomaly. To have the transport properties dominated by Weyl fermions, Weyl nodes need to locate nearly at the chemical potential and enclosed by pairs of individual Fermi surfaces with nonzero Fermi Chern numbers. Combining angle-resolved photoemission spectroscopy and first-principles calculation, here we show that TaP is a Weyl semimetal with o…
Following the discovery of topological insulators (TIs), topological Dirac/Weyl semimetal has attracted much recent interest. A prevailing mechanism for the formation of Weyl points is by breaking time-reversal symmetry (TRS) or spatial inversion symmetry of a Dirac point. Here we demonstrate a generic formation mechanism for Weyl points by breaking TRS of a three-dimensional (3D) TI featured with highly degenerate 3D flat bands (FBs). It is in direct contrast to the conventional view that breaking TRS of a 2D/3D TI leads to a Chern insulator exhibiting quantum anomalous Hall effect. Based on …
Weyl points are often believed to appear in pairs with opposite chirality. In this work, we show by first-principles calculations and symmetry analysis that single Weyl phonons with linear dispersion and double Weyl phonons with quadratic dispersion are simultaneously present between two specific phonon branches in realistic materials with trigonal or hexagonal lattices. These phonon Weyl points are guaranteed to locate at high-symmetry points due to the screw rotational symmetry, forming a unique triangular Weyl complex. In sharp contrast to conventional Weyl systems with surface arcs termina…
We report a combined theoretical and experimental study on TaIrTe4, a potential candidate of the minimal model of type-II Weyl semimetals. Unexpectedly, an intriguing node structure with twelve Weyl points and a pair of nodal lines protected by mirror symmetry was found by first-principle calculations, with its complex signatures such as the topologically non-trivial band crossings and topologically trivial Fermi arcs cross-validated by angle-resolved photoemission spectroscopy. Through external strain, the number of Weyl points can be reduced to the theoretical minimum of four, and the appear…
We study the occurrence of symmetry-enforced topological band crossings in tetragonal crystals with strong spin-orbit coupling. By computing the momentum dependence of the symmetry eigenvalues and the global band topology in the entire Brillouin zone, we determine all symmetry-enforced band crossings in tetragonal space groups. In particular, we classify all Dirac and Weyl degeneracies on points, lines, and planes, and find a rich variety of topological degeneracies. This includes, among others, double Weyl points, fourfold-double Weyl points, fourfold-quadruple Weyl points, Weyl and Dirac nod…
Topological band theory has revolutionized our understanding of electronic structure of materials, in particular, a novel state - Weyl semimetal - has been predicted for systems with strong spin-orbit coupling (SOC). Here, a new class of Weyl semimetals, solely made of light elements with negligible SOC, is proposed. Our first-principles calculations show that conjugated p orbital interactions in a three-dimensional pure carbon network, termed interpenetrated graphene network, is sufficient to produce the same Weyl physics. This carbon allotrope has an exceptionally good structural stability. …
Unconventional Weyl point with nonlinear dispersion features higher topological charge $|{\cal{C}}|>1$ and multiple topologically protected Fermi arc states at its boundary. As a novel topological state, it has been attracting widespread attention. However, the unconventional Weyl point with $|{\cal{C}}|=3$ has not yet been reported in realistic materials, even though it has been theoretically proposed for more than a decade. In this work, based on first-principles calculations and theoretical analysis, we predict the existing material, $\rmα$-LiIO$_3$ as the first realistic example with this …
Distinct to type-I Weyl semimetals (WSMs) that host quasiparticles described by the Weyl equation, the energy dispersion of quasiparticles in type-II WSMs violates Lorentz invariance and the Weyl cones in the momentum space are tilted. Since it was proposed that type-II Weyl fermions could emerge from (W,Mo)Te2 and (W,Mo)P2 families of materials, a large numbers of experiments have been dedicated to unveil the possible manifestation of type-II WSM, e.g. the surface-state Fermi arcs. However, the interpretations of the experimental results are very controversial. Here, using angle-resolved phot…
Three-dimensional Dirac and Weyl semimetals have attracted widespread interest in condensed matter physics and material science. Here, based on first-principles calculations and symmetry analysis, we report that Ag$_2$S with P2$_1$2$_1$2$_1$ symmetry is a topological Dirac semimetal in the absence of spin-orbit coupling (SOC). Every Dirac points are composed of two Weyl points with the same chirality overlapping in the momentum space. After taking the SOC into consideration, each Dirac point is split into two Weyl points. The Weyl points with the opposite chirality are far from each other in t…
In 1929, H. Weyl proposed that the massless solution of Dirac equation represents a pair of new type particles, the so-called Weyl fermions [1]. However the existence of them in particle physics remains elusive for more than eight decades. Recently, significant advances in both topological insulators and topological semimetals have provided an alternative way to realize Weyl fermions in condensed matter as an emergent phenomenon: when two non-degenerate bands in the three-dimensional momentum space cross in the vicinity of Fermi energy (called as Weyl nodes), the low energy excitation behaves …
The asymmetric electron dispersion in type-II Weyl semimetal theoretically hosts anisotropic transport properties. Here we observe the significant anisotropic Adler-Bell-Jackiw (ABJ) anomaly in the Fermi-level delicately adjusted WTe$_{1.98}$ crystals. Quantitatively, $C_w$ , a coefficient representing intensity of ABJ anomaly, along a- and b-axis of WTe$_{1.98}$ are 0.030 and 0.051 T$^{-2}$ at 2 K, respectively. We found that temperature-sensitive ABJ anomaly is attributed to topological phase transition from type-II Weyl semimetal to trivial semimetal, which is verified by first-principles c…
Controllability of ultracold atomic gases has reached an unprecedented level, allowing for experimental realization of the long-sought-after Thouless pump, which can be interpreted as a dynamical quantum Hall effect. On the other hand, Weyl semimetals and Weyl nodal line semimetals with touching points and rings in band structures have sparked tremendous interest in various fields in the past few years. Here, we show that dynamical Weyl points and dynamical 4D Weyl nodal rings, which are protected by the first Chern number on a parameter surface formed by quasi-momentum and time, emerge in a t…
Topological Weyl semimetal WTe2 with large-scale film form has a promising prospect for new-generation spintronic devices. However, it remains a hard task to suppress the defect states in large-scale WTe2 films due to the chemical nature. Here, we significantly improve the crystalline quality and remove the Te vacancies in WTe2 films by post annealing. We observe the distinct Shubnikov-de Haas quantum oscillations in WTe2 films. The nontrivial Berry phase can be revealed by Landau fan diagram analysis. The Hall mobility of WTe2 films can reach 1245 cm2V-1s-1 and 1423 cm2V-1s-1 for holes and el…
We study the inelastic neutron scattering cross section in the vicinity of touching points in magnon bands. Among the possible touching points are magnon Weyl points in three dimensional ordered magnets with significant spin-orbit coupling that are characterized by a linear dispersion in their vicinity. A Weyl point is topologically protected by its net chirality and here we show that this leads to a characteristic form for the dynamical structure factor. To address this question, we show that scattering intensities in the vicinity of arbitrary magnon two-band touching points are identical to …
In the time-reversal-breaking centrosymmetric systems, the appearance of Weyl points can be guaranteed by an odd number of all the even/odd parity occupied bands at eight inversion-symmetry-invariant momenta. Here, based on symmetry analysis and first-principles calculations, we demonstrate that for the time-reversal-invariant systems with $S_4$ symmetry, the Weyl semimetal phase can be characterized by the inequality between a well-defined invariant $η$ and an $S_4$ indicator $z_2$. By applying this criterion, we find that some candidates, previously predicted to be topological insulators, ar…
The recently discovered type-II Weyl points appear at the boundary between electron and hole pockets. Type-II Weyl semimetals that host such points are predicted to exhibit a new type of chiral anomaly and possess thermodynamic properties very different from their type-I counterparts. In this Letter, we describe the prediction of a type-II Weyl semimetal phase in the transition metal diphosphides MoP$_2$ and WP$_2$. These materials are characterized by relatively simple band structures with four pairs of type-II Weyl points. Neighboring Weyl points have the same chirality, which makes the pred…
We report detailed magneto-transport measurements on single crystals of the magnetic Weyl semi-metal Co$_{3}$Sn$_{2}$S$_{2}$. Recently a large anomalous Hall effect and chiral anomaly have been observed in this material which have been suggested to be related to the large Berry curvature between the Weyl points (Liu et al., Nature Physics (2018).). Another effect expected to result from the topological band structure of magnetic Weyl materials is the planar Hall effect (PHE). In this work we report observation of this intrinsic effect in single crystals of Co$_{3}$Sn$_{2}$S$_{2}$. Crucially, t…
Double-Weyl fermions, as novel topological states of matter, have been mostly discussed in nonmagnetic materials. Here, based on density-functional theory and symmetry analysis, we propose the realization of fully spin-polarized double-Weyl fermions in a family ferromagnetic materials X2RhF6 (X= K, Rb, Cs). These materials have the half-metal ground states, where only the bands from the spin-down channel present near the Fermi energy. The spin-down bands form a pair of triply degenerate nodal points (TDNPs) if spin-orbit coupling (SOC) is not included. Under SOC, one TDNP splits into two doubl…
To investigate the electronic structure of Weyl semimetals Ta$Pn$ ($Pn=$P, As), optical conductivity [$σ(ω)$] spectra are measured over a wide range of photon energies and temperatures, and these measured values are compared with band calculations. Two significant structures can be observed: a bending structure at $\hbarω\sim$85 meV in TaAs, and peaks at $\hbarω\sim$ 50 meV (TaP) and $\sim$30 meV (TaAs). The bending structure can be explained by the interband transition between saddle points connecting a set of $W_2$ Weyl points. The temperature dependence of the peak intensity can be fitted b…
Topological semimetal, hosting spin-1 Weyl point beyond Dirac and Weyl points, has attracted a great deal of attention. However, the spin-1 Weyl semimetal, which possesses exclusively the spin-1 Weyl points in a clean frequency window, without shadowed by any other nodal points, is yet to be discovered. Here, we report for the first time a spin-1 Weyl semimetal in a phononic crystal. Its spin-1 Weyl points, touched by two linear dispersions and an additional flat band, carry monopole charges (-2,0,2) or (2,0,-2) for the three bands from bottom to top, and result in double Fermi arcs existing b…
We investigate the surface electronic structures of polar 1T'-MoTe2, the Weyl semimetal candidate realized through the nonpolar-polar structural phase transition, by utilizing the laser angle-resolved photoemission spectroscopy (ARPES) combined with first-principles calculations. Two kinds of domains with different surface band dispersions are observed from a single-crystalline sample. The spin-resolved measurements further reveal that the spin polarizations of the surface and the bulk-derived states show the different domain-dependences, indicating the opposite bulk polarity. For both domains…
The Weyl semimetal exhibits various interesting physical phenomena because of the Weyl points, i.e., linear band-crossings. We show by Floquet theory that a linearly polarized light applied to a band insulator can induce controllable Weyl points. In a tight-binding model, we classify different types of photoinduced Weyl points that lead to a rich phase diagram characterized by the Chern number defined on each momentum slices of the bulk states. Taking account of the nonequilibrium electron distribution, we calculate and explain the nonmonotonous anomalous Hall conductivity in terms of the ligh…
A two-dimensional (2D) Weyl semimetal featuring a spin-polarized linear band dispersion and a nodal Fermi surface is a new topological phase of matter. It is a solid-state realization of Weyl fermions in an intrinsic 2D system. The nontrivial topology of 2D Weyl cones guarantees the existence of a new form of topologically protected boundary states, Fermi string edge states. In this work, we report the realization of a 2D Weyl semimetal in monolayer-thick epitaxial bismuthene grown on SnS(Se) substrate. The intrinsic band gap of bismuthene is eliminated by the space-inversion-symmetry-breaking…
Two-dimensional topological edge states, immunizing against defects and disorders, have greatly revolutionized our scientific cognition on propagation and scattering of acoustic waves. Recently, the similar states have been predicted in three-dimensional acoustic systems consisting of chiral coupling resonance cavities. However, the direct observation of topological surface propagation, especially in a 3D acoustic system with simple scatterers but not complicatedly coupling resonances, has still not been exploited. Here, we design and fabricate a 3D acoustic semimetal composed of rotationally …
Despite of a rapidly expanding inventory of possible crystalline Weyl semimetals, all of them are constrained by the Nielsen-Ninomiya no-go theorem, namely, that left- and right-handed Weyl points appear in pairs. With time-reversal (T) symmetry, an even stronger version holds for the semimetals, i.e., all eight time-reversal-invariant points in the Brillouin zone (BZ) simultaneously host Weyl points or not. However, all the well-known conclusions from the no-go theorem are implicitly within the current framework of topological semimetals, and in this work, we shall go beyond it by exploring c…
Using topological band theory analysis we show that the nonsymmorphic symmetry operations in hexagonal lattices enforce Weyl points at the screw-invariant high-symmetry lines of the band structure. The corepresentation theory and connectivity group theory show that Weyl points are generated by band crossings in accordion-like and hourglass-like dispersion relations. These Weyl points are stable against weak perturbations and are protected by the screw rotation symmetry. Based on first-principles calculations we found a complete agreement between the topological predicted energy dispersion rela…
Based on $k\cdot p$ analysis and realistic tight-binding calculations, we find that time-reversal-breaking Weyl semimetals can be realized in magnetically-doped (Mn, Eu, Cr etc.) Sn$_{1-x}$Pb$_x$(Te,Se) class of topological crystalline insulators. All the Weyl points are well separated in momentum space and possess nearly the same energy due to high crystalline symmetry. Moreover, both the Weyl points and Fermi arcs are highly tunable by varying Pb/Sn composition, pressure, magnetization, temperature, surface potential etc., opening up the possibility of manipulating Weyl points and rewiring t…
We investigate the orthorhombic phase (Td) of layered transition-metal-dichalcogenide MoTe$_2$ as a Weyl semimetal candidate, which was discovered to be a superconductor in our recent experiment. MoTe$_2$ exhibits four pairs of Weyl points lying slightly ($\sim$ 6 meV) above the Fermi energy in the bulk band structure. Unlike its cousin WTe$_2$, which was predicted to be a type-II Weyl semimetal recently, the spacing between each pair of Weyl points is found to be as large as 4 percent of the reciprocal lattice in MoTe$_2$ (six times larger than that of WTe$_2$). When projected to the surface,…
As the development of topological band theory, comprehensive databases about time reversal and crystalline symmetries protected nonmagnetic topological materials were developed via first-principles calculations recently. However, owing to the low symmetry requirement of Weyl points, the symmetry-based topological indicator cannot be applied to Weyl semimetals (WSMs). Hitherto, the WSMs with Weyl points in arbitrary positions are still absent in the well-known databases. In this work, we develop an efficient algorithm to search for Weyl points automatically and establish a database of nonmagnet…
Although topological invariants have been introduced to classify the appearance of protected electronic states at surfaces of insulators, there are no corresponding indexes for Weyl semimetals whose nodal points may appear randomly in the bulk Brillouin Zone (BZ). Here we use a well-known result that every Weyl point acts as a Dirac monopole and generates integer Berry flux to search for the monopoles on rectangular BZ grids that are commonly employed in self-consistent electronic structure calculations. The method resembles data mining technology of computer science and is demonstrated on loc…
We report angle-resolved photoemission experiments resolving the distinct electronic structure of the inequivalent top and bottom (001) surfaces of WTe2. On both surfaces, we identify a surface state that forms a large Fermi-arc emerging out of the bulk electron pocket. Using surface electronic structure calculations, we show that these Fermi arcs are topologically trivial and that their existence is independent of the presence of type-II Weyl points in the bulk band structure. This implies that the observation of surface Fermi arcs alone does not allow the identification of WTe2 as a topologi…
