Following the realization of Weyl semimetals in quantum electronic materials, classical wave analogues of Weyl materials have also been theorized and experimentally demonstrated in photonics and acoustics. Weyl points in elastic systems, however, have been a much more recent discovery. In this study, we report on the design of an elastic fully-continuum three-dimensional material that, while offering structural and load-bearing functionalities, is also capable of Weyl degeneracies and surface topologically-protected modes in a way completely analogous to the quantum mechanical counterpart. The topological characteristics of the lattice are obtained by \textit{ab initio} numerical calculations without employing any further simplifications. The results clearly characterize the topological structure of the Weyl points and are in full agreement with the expectations of surface topological modes. Finally, full field numerical simulations are used to confirm the existence of surface states and to illustrate their extreme robustness towards lattice disorder and defects.
We show that Multiple Weyl and double Weyl points arise in a chiral elastic system through stacking many two-dimensional honeycomb mechanical structures. On the distinct kz plane, the band structures calculated from tight-binding model exhibit the presence of Weyl points at Brillouin vertices and double Weyl Points at Brillouin centre. Based on the tight-binding model, we design a practical chiral mechanical structure which can be fabricated by current 3D printing technology. The numerical calculation illustrates several Weyl and double-Weyl points as expected in our analysis of tight-binding …
We show that, as it happens in graphene, elastic deformations couple to the electronic degrees of freedom as pseudo gauge fields in Weyl semimetals. We derive the form of the elastic gauge fields in a tight-binding model hosting Weyl nodes and see that this vector electron-phonon coupling is chiral, providing an example of axial gauge fields in three dimensions. As an example of the new response functions that arise associated to these elastic gauge fields, we derive a non-zero phonon Hall viscosity for the neutral system at zero temperature. The axial nature of the fields provides a test of t…
We generalize the concept of three-dimensional topological Weyl semimetal to a class of five dimensional (5D) gapless solids, where Weyl points are generalized to Weyl surfaces which are two-dimensional closed manifolds in the momentum space. Each Weyl surface is characterized by a U(1) second Chern number $C_2$ defined on a four-dimensional manifold enclosing the Weyl surface, which is equal to its topological linking number with other Weyl surfaces in 5D. In analogy to the Weyl semimetals, the surface states of the 5D metal take the form of topologically protected Weyl fermion arcs, which co…
We study two Weyl semimetal generalizations in five dimensions (5d) which have Yang monopoles and linked Weyl surfaces in the Brillouin zone, respectively, and carry the second Chern number as a topological number. In particular, we show a Yang monopole naturally reduces to a Hopf link of two Weyl surfaces when the $\mathbf{TP}$ (time-reversal combined with space-inversion) symmetry is broken. We then examine the phase transition between insulators with different topological numbers in 5d. In analogy to the 3d case, 5d Weyl semimetals emerge as intermediate phases during the topological phase …
The electronic bands are classified according to their topology. We compute the connection and curvature for the electronic bands and show that the physical properties are determined by topological invariants which are equivalent to the existence of the zero modes. We apply this method to the Topological Insulators and Topogical Superconductors.
We discuss the tight-binding models of solid state physics with the $Z_2$ sublattice symmetry in the presence of elastic deformations, and their important particular case -the tight binding model of graphene. In order to describe the dynamics of electronic quasiparticles we explore Wigner-Weyl formalism. It allows to calculate the two-point Green's function in the presence of both slowly varying external electromagnetic fields and the inhomogeneous modification of the hopping parameters resulted from the elastic deformations. The developed formalism allows us to consider the influence of elast…
We propose a different route to time-reversal invariant Weyl semimetals employing multilayer heterostructures comprising ordinary "trivial" insulators and nontrivial insulators with \textit{pairs} of protected Dirac cones on the surface. We consider both the case of weak topological insualtors, where surface Dirac cones are pinned to time-reversal invariant momenta, and of topological crystalline insulators with unpinned surface Dirac cones. For both realizations we explain phenomenologically how the proposed construction leads to the emergence of a Weyl semimetal phase. We further formulate e…
We demonstrate that topological transport phenomena, characteristic of Weyl semimetals, namely the semi-quantized anomalous Hall effect and the chiral magnetic effect (equilibrium magnetic-field-driven current), may be thought of as two distinct manifestations of the same underlying phenomenon, the chiral anomaly. We show that the topological response in Weyl semimetals is fully described by a $θ$-term in the action for the electromagnetic field, where $θ$ is not a constant parameter, like e.g. in topological insulators, but is a field, which has a linear dependence on the space-time coordinat…
We consider the properties of the type II Weyl semimetals at low temperatures basing on the particular tight - binding model. In the presence of electric field directed along the line connecting the Weyl points of opposite chirality the occupied states flow along this axis giving rise to the creation of electron - hole pairs. The electrons belong to a vicinity of one of the two type II Weyl points while the holes belong to the vicinity of the other. This process may be considered as the manifestation of the chiral anomaly that exists without any external magnetic field. It may be observed expe…
The coupling of lattice deformations to the low energy electronic excitations of Dirac matter involve novel types of electron--phonon couplings as the celebrated elastic gauge fields first analyzed in graphene. In the continuum low energy approach, lattice deformations coupling to the electronic degrees of freedom are characterized by the (symmetric) strain tensor defined in elasticity theory. We review these couplings in Weyl semimetals and examine the coupling of electronic excitations to the antisymmetric part of the deformation gradient tensor associated to rotational strain. The new coupl…
In this work we introduce a thermal magnetotorsional effect (TME) as a novel topological response in magnetic Weyl semimetals. We predict that magnetization gradients perpendicular to the Weyl node separation give rise to temperature gradients depending only on the local positions of the Weyl nodes. The TME is a consequence of magnetization-induced effective torsional spacetime geometry and the finite temperature Nieh-Yan anomaly. Similarly to anomalous Hall effect and chiral anomaly, the TME has a universal material-independent form. We predict that the TME can be observed in magnetic Weyl se…
We consider the tight-binding model with cubic symmetry that may be relevant for the description of a certain class of Weyl semimetals. We take into account elastic deformations of the semimetal through the modification of hopping parameters. This modification results in the appearance of emergent gauge field and the coordinate dependent anisotropic Fermi velocity. The latter may be interpreted as emergent gravitational field.
Ideal Weyl points, which are related by symmetry and thus reside at the same frequency, could promote the deep development and utilization of the Weyl physics. Although the ideal type-I Weyl points have been achieved in photonic crystals, the ideal type-II Weyl points with tilted cone-like band dispersions, are still beyond discovery. Here we realize ideal type-II Weyl points of minimal number in three-dimensional layer-stacked phononic crystals, and demonstrate topological phase transition from Weyl semimetal to valley insulators of two distinct types. The Fermi-arc surface states exist on th…
Weyl points emerge as topological monopoles of Berry flux in the three-dimensional (3D) momentum space and have been extensively studied in topological semimetals. As the underlying topological principles apply to any type of waves under periodic boundary conditions, Weyl points can also be realized in classical wave systems, which are easier to engineer compared to condensed matter materials. Here, we made an acoustic Weyl phononic crystal by breaking space inversion (P) symmetry using a combination of slanted acoustic waveguides. We conducted angle-resolved transmission measurements to chara…
Searching for the signature of the violation of chiral charge conservation in solids has inspired a growing passion on the magneto-transport in topological semimetals. One of the open questions is how the conductivity depends on magnetic fields in a semimetal phase when the Fermi energy crosses the Weyl nodes. Here, we study both the longitudinal and transverse magnetoconductivity of a topological Weyl semimetal near the Weyl nodes with the help of a two-node model that includes all the topological semimetal properties. In the semimetal phase, the Fermi energy crosses only the 0th Landau bands…
Topological states of matter have been a subject of intensive studies in recent years because of their exotic properties such as the topologically protected edge and surface states. The initial studies were exclusively for electron systems. It is now known that topological states can also exist for other particles. Indeed, topologically protected edge states have already been found for phonons and photons. In spite of active searching for topological states in many fields, the studies in magnetism are relatively rare although topological states are apparently important and useful in magnonics.…
We demonstrate that in Weyl semimetals, the momentum-space helical spin texture can couple to the chirality of the Weyl node to generate a frequency-independent magnetization in response to circularly polarized light through the inverse Faraday effect. This frequency-independence is rooted in the topology of the Weyl node. Since the helicity and the chirality are always locked for Weyl nodes, this effect is not subject to any symmetry constraint. Finally, we show that the photoinduced frequency-independent magnetization is robust against lattice effect and has a magnitude large enough to reali…
Floquet engineering, the concept of tailoring a system by a periodic drive, is increasingly exploited to design and manipulate topological phases of matter. In this work, we study periodically driven higher-order topological Dirac semimetals associated with a $k$-dependent quantized quadrupole moment by applying circularly polarized light. The undriven Dirac semimetals feature gapless higher-order hinge Fermi arc states which are the consequence of the higher-order topology of the Dirac nodes. Floquet Weyl semimetal phases with hybrid-order topology, characterized by both a $k$-dependent quant…
College of Physics, Hebei Normal University（河北师范大学物理学院）；International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Hefei National Laboratory（合肥国家实验室）
Weyl semimetals are crystals in which electron bands cross at isolated points in momentum space. Associated with each crossing point (or Weyl node) is an integer topological invariant known as the Berry monopole charge. The discovery of new classes of Weyl materials is driving the search for novel properties that derive directly from the Berry charge. The circular photogalvanic effect (CPGE), whereby circular polarized light generates a current whose direction depends on the helicity of the absorbed photons, is a striking example of a macroscopic property that emerges from Weyl topology. Recen…
We systematically investigate the properties of bulk, surface and edge plasmons in Weyl semimetals in presence of a magnetic field. It is found that unidirectional plasmons with different properties exist on different surfaces, which is in consistent with the nontrivial topology of the three-dimensional (3D) bulk plasmons. These novel plasmons possess momentum-location lock and may travel between surfaces. The anomalous Hall conductivity brings about abundant anisotropic plasmon dispersions, from linear to parabolic or even hyperbolic bands. With the help of a semiclassical picture for the for…
We propose a simple realization of the three-dimensional (3D) Weyl semimetal phase, utilizing a multilayer structure, composed of identical thin films of a magnetically-doped 3D topological insulator (TI), separated by ordinary-insulator spacer layers. We show that the phase diagram of this system contains a Weyl semimetal phase of the simplest possible kind, with only two Dirac nodes of opposite chirality, separated in momentum space, in its bandstructure. This particular type of Weyl semimetal has a finite anomalous Hall conductivity, chiral edge states, and occurs as an intermediate phase b…
We theoretically show that IV-VI semiconducting compounds with low-temperature rhombohedral crystal structure represent a new potential platform for topological semimetals. By means of minimal $\mathbf{k}\cdot\mathbf{p}$ models we find that the two-step structural symmetry reduction of the high-temperature rocksalt crystal structure, comprising a rhombohedral distortion along the [111] direction followed by a relative shift of the cation and anion sublattices, gives rise to topologically protected Weyl semimetal and nodal line semimetal phases. We derive general expressions for the nodal featu…
We consider a natural generalization of the lattice model for a periodic array of two layers, A and B, of spinless electrons proposed by Fu [Phys. Rev. Lett. 106, 106802 (2011)] as a prototype for a crystalline insulator. This model has time-reversal symmetry and broken inversion symmetry. We show that when the intralayer next-nearest-neighbor hoppings ta2, a = A, B vanish, this model supports a Weyl semimetal phase for a wide range of the remaining model parameters. When the effect of ta2 is considered, topological crystalline insulating phases take place within the Weyl semimetal one. By map…
Weyl semimetals are expected to open up new horizons in physics and materials science because they provide the first realization of Weyl fermions and exhibit protected Fermi arc surface states. However, they had been found to be extremely rare in nature. Recently, a family of compounds, consisting of TaAs, TaP, NbAs and NbP was predicted as Weyl semimetal candidates. Here, we experimentally realize a Weyl semimetal state in TaP. Using photoemission spectroscopy, we directly observe the Weyl fermion cones and nodes in the bulk and the Fermi arcs on the surface. Moreover, we find that the surfac…
We study a general phase transition between spinless topological nodal-line semimetal and Weyl semimetal phases. We classify topological nodal lines into two types based on their positions and shapes, and their phase transitions depends on their types. We show that the topological nodal-line semimetal becomes the Weyl semimetal by breaking time-reversal symmetry when the nodal lines enclose time-reversal invariant momenta (type-A nodal lines). We also discuss an effect of crystallographic symmetries determining the band structure of the topological nodal-line semimetals. Thanks to protection b…
We investigate the effects of periodic fields and disorder on topological properties of a Weyl-semimetal thin film. The two periodic fields, i.e., a periodic magnetic field and elliptically polarized light, are discussed respectively. By use of the Floquet theory, we find that both the two periodic drives can resonantly induce the topological transitions from normal insulator (NI) phases to Floquet topological insulator (FTI) phases. The Floquet topological transitions are characterized by variation of Chern number. Moreover, we show that the Floquet topological transitions can be explained by…
We propose characterization of the three-dimensional topological insulator by using the Chern number for the entanglement Hamiltonian (entanglement Chern number). Here we take the extensive spin partition of the system, that pulls out the quantum entanglement between up spin and down spin of the many-body ground state. In three dimensions, the topological insulator phase is described by the section entanglement Chern number, which is the entanglement Chern number for a periodic plane in the Brillouin zone. The section entanglement Chern number serves as an interpolation of the $Z_2$ invariants…
Multi-Weyl semimetals are a kind of topological phase of matter with discrete Weyl nodes characterized by multiple monopole charges, in which the chiral anomaly, the anomalous nonconservation of an axial current, occurs in the presence of electric and magnetic fields. Electronic transport properties related to the chiral anomaly in the presence of both electromagnetic fields and axial electromagnetic fields in multi-Weyl semimetals are systematically studied. It has been found that the anomalous Hall conductivity has a modification linear in the axial vector potential from inhomogeneous strain…
Recent years have brought an explosion of activities in the research of topological aspects of condensed-matter systems. Topologically non-trivial phases of matter are typically accompanied by protected surface states or exotic degenerate excitations such as Majorana end states or Haldane's localized spinons. Topologically protected degeneracies can, however, also appear in the bulk. An intriguing example is provided by Weyl semimetals, where topologically protected electronic band degeneracies and exotic surface states emerge even in the absence of interactions. Here we demonstrate experiment…
Weyl points (WPs), as nodal degenerate points in three-dimensional (3D) momentum space, are ideal if they are symmetry-related, well-separated, residing at the same energy and far from the nontopological bands. Although type-II WPs show some unique features compared with type-I counterparts, ideal type-II WPs have not yet been reported due to the lack of an ideal Weyl system with enough flexibility to tilt the dispersion bands. By stacking two-dimensional (2D) layers of inductor-capacitor (LC) resonator dimers with the breaking of parity inversion symmetry, here we experimentally realize the t…
We perform a complete classification of two-band $\bk\cdot\mathbf{p}$ theories at band crossing points in 3D semimetals with $n$-fold rotation symmetry and broken time-reversal symmetry. Using this classification, we show the existence of new 3D topological semimetals characterized by $C_{4,6}$-protected double-Weyl nodes with quadratic in-plane (along $k_{x,y}$) dispersion or $C_6$-protected triple-Weyl nodes with cubic in-plane dispersion. We apply this theory to the 3D ferromagnet HgCr$_2$Se$_4$ and confirm it is a double-Weyl metal protected by $C_4$ symmetry. Furthermore, if the direction…
We formulate a bulk spectroscopic method for direct measurement of the topological invariant of nondegenerate band crossings in Weyl semimetals. We demonstrate how polarization-resolved resonant x-ray scattering captures the winding of the Berry flux around Weyl nodes. The spectra obtained by the proposed strategy feature an integer number of zero-crossings that is directly related to the topological charge of the measured nodes. We benchmark the proposed protocol on TaAs, using realistic low-energy models derived from density-functional theory to accurately represent the states close to the F…
Weyl semimetals possess low energy excitations which act as monopoles of Berry curvature in momentum space. These emergent monopoles are at the heart of the extensive novel transport properties that Weyl semimetals exhibit. The singular nature of the Berry curvature around the nodal points in Weyl semimetals allows for the possibility of large anomalous transport coefficients in zero applied magnetic field. Recently a new class, termed type-II Weyl semimetals, has been demonstrated in a variety of materials, where the Weyl nodes are tilted. We present here a study of anomalous transport in thi…
Recently discovered Dirac semimetals (DSMs) with two Dirac nodes, such as Na$_{3}$Bi and Cd$_{2}$As$_{3}$, are regarded to carry the $\mathbb{Z}_{2}$ topological charge in addition to the chiral charge. Here, we study the Floquet phase transition of $\mathbb{Z}_{2}$ topological DSMs subjected to a beam of circularly polarized light. Due to the resulting interplay of the chiral and $\mathbb{Z}_{2}$ charges, the Weyl nodes are not only chirality-dependent but also spin-dependent, which constrains the behaviors in creation and annihilation of the Weyl nodes in pair. Interestingly, we find a novel…
We investigate multilayer systems of a normal insulator and a Weyl semimetal. We calculate the bulk band structure and determine phase diagrams by changing the thickness of the normal insulator and that of the Weyl semimetal layer using two models; one is from the effective model for a Weyl semimetal, and the other is the lattice model. We compare the results between the two models, and found that they agree well. As a result, we find that the multilayer system shows a qualitatively different behavior depending on the stacking direction relative to the displacement vector connecting between tw…
We study the single-particle spectrum of three-dimensional Weyl semimetals taking into account electron-phonon interactions that are the result of straining the material. We find that a well-defined fermionic excitation appears in addition to the standard peak corresponding to quasiparticle states as suggested by Landau-Fermi liquid theory. Contrary to the case of Dirac systems interacting via the Coulomb interaction, these satellite peaks appear even at lowest order in perturbation theory. The new excitations are anisotropic, as opposed to the single-particle spectrum, and their behavior is d…
A Drude-Sommerfeld topological model (DSTM) is proposed to describe Weyl fermions under residual collisions. They are nearly free and dressed by their own weak magnetic field that breaks the reflection and time symmetries around a layer. This weak magnetic field brings topological stability to the states through a non-trivial Chern-Simons number which is here calculated in the limit of a Dirac linear spectrum. The Weyl fermions display an energy gap and much above this gap the spectrum becomes Dirac linear. They are obtained from a Schroedinger like hamiltonian for particles with spin and magn…
We discuss the possibility of realizing Weyl semimetal phase in the magnetically doped topological band insulators. When the magnetic moments are ferromagnetically polarized, we show that there are three phases in the system upon the competition between topological mass and magnetic mass: topological band insulator phase, Weyl semimetal phase, and trivial phase. We explicitly derive the low energy theory of Weyl points from the general continuum Hamiltonian of topological insulators near the Dirac point, e.g. ${\bf k} \cdot {\bf p}$ theory near $Γ$ point for Bi_{2}Se_{3}. Furthermore, we intro…
The Fermi arcs of topological surface states in the three-dimensional multi-Weyl semimetals on surfaces by a continuum model are investigated systematically. We calculated analytically the energy spectra and wave function for bulk quadratic- and cubic-Weyl semimetal with a single Weyl point. The Fermi arcs of topological surface states in Weyl semimetals with single- and double-pair Weyl points are investigated systematically. The evolution of the Fermi arcs of surface states variating with the boundary parameter is investigated and the topological Lifshitz phase transition of the Fermi arc co…
We show that isolated Weyl nodes can arise in a system of parallel topological insulator nano-wires arranged in a honeycomb fashion. This introduces another theoretical example of a topological semi-metal phase with more than one pair of Weyl nodes and due to the simple form of its Hamiltonian it can be used to study various interesting phenomena associated with this phase. Our result emphasizes that depending on the separation of the Weyl nodes a topological electromagnetic response might or might not emerge and two pairs might have overall cancelling contributions to the net anomalous Hall c…
We calculate the extremal cross sectional areas and cyclotron masses for the Fermi-surface pockets in Dirac and Weyl topological semimetals. The calculation is carried out for the most general form of the electron energy bands in the vicinity of the Weyl and Dirac points. Using the obtained formulas, one can find parameters characterizing the Dirac and Weyl electrons in the topological semimetals from appropriate experimental data. As an example, we consider the W1 electrons in TaAs.
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…
Topological Weyl semimetals (TWS) can be classified as type-I TWS, in which the density of states vanishes at the Weyl nodes, and type-II TWS where an electron and a hole pocket meet with finite density of states at the nodal energy. The dispersions of type-II Weyl nodes are tilted and break Lorentz invariance, allowing for physical properties distinct from those in a type-I TWS. We present minimal lattice models for both time-reversal-breaking and inversion-breaking type-II Weyl semimetals, and investigate their bulk properties and topological surface states. These lattice models capture the …
We present a feasible protocol to mimic topological Weyl semimetal phase in a small one-dimensional circuit-QED lattice. By modulating the photon hopping rates and on-site photon frequencies in parametric spaces, we demonstrate that the momentum space of this one-dimensional lattice model can be artificially mapped to three dimensions accompanied by the emergence of topological Weyl semimetal phase. Furthermore, via a lattice-based cavity input-output process, we show that all the essential topological features of Weyl semimetal phase, including the topological charge associated with each Weyl…
We develop a topological theory for disordered Weyl semimetals in the framework of gauge invariance of replica formalism and boundary-bulk correspondence of Chern insulators. An anisotropic topological $θ$-term is analytically derived for the effective non-linear sigma model. It is this nontrivial topological term that ensures the bulk transverse transport of Weyl semimetals to be robust against disorders. Moreover, we establish a general diagram that reveals the intrinsic relations among topological terms in the non-linear sigma models and gauge response theories respectively for $(2n + 2)$-d…
We define and study a three dimensional lattice model which displays a Weyl semi-metallic phase. This model consists of coupled layers of quantum (anomalous) Hall insulators. The Weyl semi-metallic phase appears between a resulting quantum Hall insulating phase and a normal insulating phase. Weyl fermions in this Weyl semi-metal, similar to Dirac fermions in graphene, have their lattice pseudo-spin locked to their momenta. We investigate surface states and Fermi arcs, and their evolution for different phases, by exactly diagonalizing the lattice model as well as by analyzing their topological …
We study theoretically the ultrafast electron dynamics of three-dimensional Weyl semimetals in the field of a laser pulse. For a circularly-polarized pulse, such dynamics is governed by topological resonance, which manifests itself as a specific conduction band population distribution in the vicinity of the Weyl points. The topological resonance is determined by the competition between the topological phase and the dynamic phase and depends on the handedness of a circularly polarized pulse. Also, we show that the conduction band population induced by a circularly-polarized pulse that consists …
We construct a generic two-band model which can describe topological Weyl semimetals with multiple closed Weyl loops. All the existing multi-Weyl-loop semimetals including the nodal-net, or nodal-chain and Hopf-link states can be examined within one same framework. Based on a two-loop model, the corresponding drum-head surface states for these topologically different bulk states are studied and compared with each other. The connection of our model with Hopf insulators is also discussed. Furthermore, to identify experimentally these topologically different Weyl semimetal states, especially dist…
Topological mechanical structures exhibit robust properties protected by topological invariants. In this letter, we study a family of deformed square lattices that display topologically protected zero-energy bulk modes analogous to the massless fermion modes of Weyl semimetals. Our findings apply to sufficiently complex lattices satisfying the Maxwell criterion of equal numbers of constraints and degrees of freedom. We demonstrate that such systems exhibit pairs of oppositely charged Weyl points, corresponding to zero-frequency bulk modes, that can appear at the origin of the Brillouin zone an…
This chapter describes topological (Dirac and Weyl) semimetals from the viewpoint of their observable electromagnetic response. We argue that this response may be represented by topological terms with unquantized (non-integer) coefficients and make a connection with the Luttinger's theorem, which relates the size of the Fermi surface of an ordinary metal to the number of electrons per unit cell. We discuss observable transport phenomena, associated with this topological response.
We show that in three-dimensional (3D) topological metals, a subset of the van Hove singularities of the density of states sits exactly at the transitions between topological and trivial gapless phases. We may refer to these as topological van Hove singularities. By investigating two minimal models, we show that they originate from energy saddle points located between Weyl points with opposite chiralities, and we illustrate their topological nature through their magnetotransport properties in the ballistic regime. We exemplify the relation between van Hove singularities and topological phase t…
The Weyl semimetal is a new quantum state of topological semimetal, of which topological surface states -- the Fermi arcs exist. In this paper, the Fermi arcs in Weyl semimetals are classified into two classes -- class-1 and class-2. Based on a tight-binding model, the evolution and transport properties of class-1/2 Fermi arcs are studied via the tilting strength of the bulk Weyl cones. The (residual) anomalous Hall conductivity of topological surface states is a physical consequence of class-1 Fermi arc and thus class-1 Fermi arc becomes a nontrivial topological property for hybrid or type-II…
We consider theoretically surface plasmon polaritons in Weyl semimetals. These materials contain pairs of band touching points - Weyl nodes - with a chiral topological charge, which induces an optical anisotropy and anomalous transport through the chiral anomaly. We show that these effects, which are not present in ordinary metals, have a direct fundamental manifestation in the surface plasmon dispersion. The retarded Weyl surface plasmon dispersion depends on the separation of the Weyl nodes in energy and momentum space. For Weyl semimetals with broken time-reversal symmetry, the distance bet…
Weyl fermions1 do not appear in nature as elementary particles, but they are now found to exist 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 of these topological points which are frequently perceived as monopoles in momentum space. Here, we demonstrate that generalized Weyl points can exist in a parameter space and we report the first observation of such nodal points in one-dimensional photonic crystals in the optical range. The reflection phase inside the band gap of a truncated …
In this work we explore the effects of nonlinearity on three-dimensional topological phases. Of particular interest are the so-called Weyl semimetals, known for their Weyl nodes, i.e., point-like topological charges which always exist in pairs and demonstrate remarkable robustness against general perturbations. It is found that the presence of onsite nonlinearity causes each of these Weyl nodes to break down into nodal lines and nodal surfaces at two different energies while preserving its topological charge. Depending on the system considered, additional nodal lines may further emerge at high…
