We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital angular momentum locked to the direction of propagation. They span a range of axial wavenumbers defined by the projections of two bulk Weyl points to a one-dimensional subspace, in a manner analogous to the formation of Fermi arc surface states. We use acoustic experiments to probe their dispersion relation, orbital angular momentum locked waveguiding, and ability to emit acoustic vortices into free space. These results point to new possibilities for creating and exploiting topological modes in three-dimensional structures through the interplay between band topology in momentum space and topological lattice defects in real space.
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 report manipulation of the magnetic states of elliptical cobalt magnetostrictive nanomagnets (of nominal dimensions ~ 340 nm x 270 nm x 12 nm) delineated on bulk 128° Y-cut lithium niobate with Surface Acoustic Waves (SAWs) launched from interdigitated electrodes. Isolated nanomagnets that are initially magnetized to a single domain state with magnetization pointing along the major axis of the ellipse are driven into a vortex state by surface acoustic waves that modulate the stress anisotropy of these nanomagnets. The nanomagnets remain in the vortex state until they are reset by a strong m…
In periodic media, despite the close relationship between geometrical effects in the bulk and topological surface states, the two are typically probed separately. We show that when beams in a Weyl medium reflect off an interface with a gapped medium, the trajectory is influenced by both bulk geometrical effects and the Fermi arc surface states. The reflected beam experiences a displacement, analogous to the Goos-Hänchen or Imbert-Fedorov shifts, that forms a half-vortex in the two-dimensional surface momentum space. The half-vortex is centered where the Fermi arc of the reflecting surface touc…
It was shown recently that Weyl fermions in a superconducting vortex lattice can condense into Landau levels. Here we study the chiral magnetic effect in the lowest Landau level: The appearance of an equilibrium current $I$ along the lines of magnetic flux $Φ$, due to an imbalance between Weyl fermions of opposite chirality. A universal contribution $dI/dΦ=(e/h)^2μ$ (at equilibrium chemical potential $μ$ relative to the Weyl point) appears when quasiparticles of one of the two chiralities are confined in vortex cores. The confined states are charge-neutral Majorana fermions.
Lorentz-violating type-II Weyl fermions, which were missed in Weyl's prediction of nowadays classified type-I Weyl fermions in quantum field theory, have recently been proposed in condensed matter systems. The semimetals hosting type-II Weyl fermions offer a rare platform for realizing many exotic physical phenomena that are different from type-I Weyl systems. Here we construct the acoustic version of type-II Weyl Hamiltonian by stacking one-dimensional dimerized chains of acoustic resonators. This acoustic type-II Weyl system exhibits distinct features in finite density of states and unique t…
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…
Weyl-like magnon excitations in ordered magnets have attracted significant recent attention. Despite of the tantalizing physics and application prospects, the experimental observation of Weyl magnons is still challenging owing to their extraordinarily high frequency that is not accessible to the microstrip antenna technique. Here we predict gigahertz Weyl excitations in the collective dynamics of dipolar-coupled magnetic vortices arranged in a three-dimensional stacked honeycomb lattice. It is found that the inversion symmetry breaking leads to the emergence of the type-II Weyl semimetal (WSM)…
Massless chiral fermions emergent in inversion symmetry-breaking Weyl semimetals (WSMs) reside in the vicinity of multiple low symmetry nodes and thus acquire strongly anisotropic dispersion. We investigate the longitudinal electromagnetic modes of two-component degenerate Weyl plasma relevant to the realistic band structure of type-I WSM. We show that the actual spectrum of three dimensional collective density excitations in TaAs family of WSM is gaples due to emergence of acoustic plasmons corresponding to out-of-phase oscillations of the plasma components. These modes exist around the [001]…
We theoretically study the modification of the energy spectrum of long-wavelength acoustic phonons due to the electron-phonon interaction in a three-dimensional topological Weyl semimetal under the influence of quantizing magnetic fields. We find that the dispersion and attenuation of phonons show striking oscillatory behaviors as varying the magnetic field at low temperatures. These oscillations are distinct when the Fermi energy is in different energy regimes. Moreover, the van Hove singularity of the Weyl spectrum can manifest as a transition between different oscillation patterns when incr…
Building on the discovery that a Weyl superconductor in a magnetic field supports chiral Landau level motion along the vortex lines, we investigate its transport properties out of equilibrium. We show that the vortex lattice carries an electric current $I=\tfrac{1}{2}(Q_{\rm eff}^2/h)(Φ/Φ_0) V$ between two normal metal contacts at voltage difference $V$, with $Φ$ the magnetic flux through the system, $Φ_0$ the superconducting flux quantum, and $Q_{\rm eff}<e$ the renormalized charge of the Weyl fermions in the superconducting Landau level. Because the charge renormalization is energy dependent…
The question whether the mixed phase of a gapless superconductor can support a Landau level is a celebrated problem in the context of \textit{d}-wave superconductivity, with a negative answer: The scattering of the subgap excitations (massless Dirac fermions) by the vortex lattice obscures the Landau level quantization. Here we show that the same question has a positive answer for a Weyl superconductor: The chirality of the Weyl fermions protects the zeroth Landau level by means of a topological index theorem. As a result, the heat conductance parallel to the magnetic field has the universal v…
Vortex waves, which carry orbital angular momentum, have found use in a range of fields from quantum communications to particle manipulation. Due to their widespread influence, significant attention has been paid to the methods by which vortex waves are generated. For example, active phased arrays generate diverse vortex modes at the cost of electronic complexity and power consumption. Conversely, analog apertures, such as spiral phase plates, metasurfaces, and gratings require separate apertures to generate each mode. Here we present a new class of metamaterial-based acoustic vortex generator…
The Letter reports an experimental observation of the classical version of valley polarized states in a two-dimensional hexagonal sonic crystal, where the inversion-symmetry breaking of scatterers induces an omnidirectional frequency gap. The acoustic valley states, which carry specific linear momenta and orbital angular momenta, were selectively excited by external Gaussian beams and conveniently confirmed by the pressure distribution outside the crystal, according to the criterion of momentum conservation. The vortex nature of such intriguing crystal states was directly characterized by scan…
We theoretically study the interplay between bulk Weyl electrons and magnetic topological defects, including magnetic domains, domain walls, and $\mathbb{Z}_6$ vortex lines, in the antiferromagnetic Weyl semimetals \mnsn\ and Mn$_3$Ge with negative vector chirality. We argue that these materials possess a hierarchy of energies scales which allows a description of the spin structure and spin dynamics using a XY model with $\mathbb{Z}_6$ anisotropy. We propose a dynamical equation of motion for the XY order parameter, which implies the presence of $\mathbb{Z}_6$ vortex lines, the double-domain p…
Higher-order topological phases have raised widespread interest in recent years with the occurrence of the topological boundary states of dimension two or more less than that of the system bulk. The higher-order topological states have been verified in gapped phases, in a wide variety of systems, such as photonic and acoustic systems, and recently also observed in gapless semimetal phase, such as Weyl and Dirac phases, in systems alike. The higher-order topology is signaled by the hinge states emerging in the common bandgaps of the bulk states and the surface states. In this Letter, we report …
We find that the vortex bound states in superconducting topological semimetals are gapless owing to topological massless excitations in their normal states. We demonstrate this universal result in a variety of semimetals including Dirac and Weyl semimetals, threefold degenerate spin-1 fermions, spin-3/2 Rarita-Schwinger-Weyl fermion semimetals and other exotic fermion semimetals. The formation of these gapless bound states are closely related to their Andreev specular reflection and propagating Andreev modes in $π$ phase superconductor-normal metal-superconductor (SNS) junctions. We further de…
Inspired by the discovery of quantum hall effect and topological insulator, topological properties of classical waves start to draw worldwide attention. Topological non-trivial bands characterized by non-zero Chern numbers are realized with external magnetic field induced time reversal symmetry breaking or dynamic modulation. Due to the absence of Faraday-like effect, the breaking of time reversal symmetry in an acoustic system is commonly realized with moving background fluids, and hence drastically increases the engineering complexity. Here we show that we can realize effective inversion sym…
We present a calculation of the low lying spectrum of a rotating Bose-Einstein condensate. We show that in a cylindrical geometry, there exist two linear branches, one associated to usual acoustic excitation, the other corresponding to a twisting mode of the vortex lattice. Using a hydrodynamical approach we derive the elasticity coefficient of the vortex lattice and calculate the spectrum of condensate in a three dimensionnal harmonic trap with cylindrical symmetry.
We present a model of a topological semimetal in three dimensions (3D) whose energy spectrum exhibits a nodal line acting as a vortex ring; this in turn is linked by a pseudospin structure akin to that of a smoke ring. Contrary to a Weyl point node spectrum, the vortex ring gives rise to skyrmionic pseudospin patterns in cuts on both sides of the nodal ring plane; this pattern covers the full Brillouin zone, thus leading to a new, `maximal', anomalous Hall effect in a 3D semimetal. Tuning a model parameter shrinks the vortex ring until it vanishes, giving way to a pair of Weyl nodes of opposit…
The notion of higher-order topological insulators has endowed materials with topological states beyond the first order. Particularly, a three-dimensional (3D) higher-order topological insulator can host topologically protected 1D hinge states, referred to as the second-order topological insulator, or 0D corner states, referred to as the third-order topological insulator. Similarly, a 3D higher-order topological semimetal can be envisaged if it hosts states on the 1D hinges. Here we report the realization of a second-order topological Weyl semimetal in a 3D-printed acoustic crystal, which posse…
The phonon magnetochiral effect consists of a nonreciprocity in the velocity or attenuation of acoustic waves when they propagate parallel and antiparallel to an external magnetic field. The first experimental observation of this effect has been reported recently in a chiral magnet and ascribed to the hybridization between acoustic phonons and chiral magnons. Here, we predict a potentially measurable phonon magnetochiral effect of electronic origin in chiral Weyl semimetals. Caused by the Berry curvature and the orbital magnetic moment, this effect is enhanced for longitudinal phonons by the c…
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 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 …
Weyl semimetal, a three-dimensional electronic system with relativistic linear energy dispersion around gapless points carrying nontrivial Berry charge, is predicted to exhibit a wealth of unique response and transport properties.A crucial question is whether those properties are robust against disorder and whether Anderson localization occurs.In this work, the effects of nonperturbative topological (vortex loop) excitations and Berry phase in disordered time-reversal invariant 3d Weyl semimetal are studied.It is shown that the chiral symmetry is restored in the nonlinear sigma model describin…
Topological phases have recently been realised in bosonic systems. The associated boundary modes between regions of distinct topology have been used to demonstrate robust waveguiding, protected from defects by the topology of the surrounding bulk. A related type of topologically protected state that is not propagating but is bound to a defect has not been demonstrated to date in a bosonic setting. Here we demonstrate numerically and experimentally that an acoustic mode can be topologically bound to a vortex fabricated in a two-dimensional, Kekulé-distorted triangular acoustic lattice. Such lat…
Majorana bound states exist inside a core of half-quantum vortex in spin-triplet superconductors. Despite intense efforts, they have not been discovered in any spin-triplet superconductor candidate materials. After the success of topological insulator, another route to achieve Majorana fermions has been suggested: heterostructures of s-wave superconductors and topological insulator or semimetal with strong spin-orbit coupling provide an effective spinless $p+ip$ pairing which supports Majorana bound states in a single vortex. This theoretical observation has stimulated both experimental and th…
Spin-1 Weyl point is formed by three bands touching at a single point in the three dimensional (3D) momentum space, with two of which show cone-like dispersion while the third band is flat. Such a triply degenerate point carries higher topological charge $\pm2$2 and can be described by a three-band Hamiltonian. We first propose a tight-binding model of a 3D Lieb lattice with chiral interlayer coupling to form the Spin-1 Weyl point. Then we design a chiral phononic crystal that carries these spin-1 Weyl points and special straight-type acoustic Fermi arcs. We also computationally demonstrate th…
Recently, intense efforts have been devoted to realizing classical analogues of various topological phases of matter. In this Letter, we explore the intriguing Weyl physics by a simple one-dimensional sonic crystal, in which two extra structural parameters are combined to construct a synthetic three-dimensional space. Based on our underwater ultrasonic experiments, we have not only observed the synthetic Weyl points directly, but also probed the novel reflection phase singularity that connects inherently with the topological robustness of Weyl points. As a smoking gun evidence of the topologic…
We introduce a theoretical framework for the new concept of three-dimensional (3D) twistronics by developing a generalized Bloch band theory for 3D layered systems with a constant twist angle $θ$ between successive layers. Our theory employs a nonsymmorphic symmetry that enables a precise definition of an effective out-of-plane crystal momentum, and also captures the in-plane moiré pattern formed between neighboring twisted layers. To demonstrate the novel topological physics that can be achieved through 3D twistronics, we present two examples. In the first example of chiral twisted graphite, …
Inspired by the newly emergent valleytronics, great interest has been attracted to the topological valley transport in classical metacrystals. The presence of nontrivial domain-wall states is interpreted with a concept of valley Chern number, which is well defined only in the limit of small bandgap. Here, we propose a new visual angle to track the intricate valley topology in classical systems. Benefiting from the controllability of our acoustic metacrystals, we construct Weyl points in synthetic three-dimensional momentum space through introducing an extra structural parameter (rotation angle…
Weyl points (WPs) are isolated degeneracies carrying quantized topological charges, and are therefore robust against Hermitian perturbations. WPs are predicted to spread to the Weyl exceptional rings (WERs) in the presence of non-Hermiticity. Here, we use a one-dimensional (1D) Aubry-Andre-Harper (AAH) model to construct a Weyl semimetal in a 3D parameter space comprised of one reciprocal dimension and two synthetic dimensions. The inclusion of non-Hermiticity in the form of gain and loss produces a WER. The topology of the WER is characterized by both its topological charge and non-Hermitian …
Within the earlier developed high-energy-$\vec k\cdot \vec p$-Hamiltonian approach to describe graphene-like materials the simulations of non-Abelian Zak phases and band structure of the quasi-relativistic graphene model with a flavors number $N=3$ have been performed in approximations with %of zero- and non-zero values of and without gauge fields (flavors). It has been shown that a Zak-phases set for non-Abelian Majorana-like excitations (modes) in Dirac valleys of the quasirelativistic graphene model is the cyclic group $\mathbf{Z}_{12}$. This group is deformed into $\mathbf{Z}_8$ at suffici…
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…
Low-energy electrons near Dirac/Weyl nodal points mimic massless relativistic fermions. However, as they are not constrained by Lorentz invariance, they can exhibit tipped-over type-II Dirac/Weyl cones which provide highly anisotropic physical properties and responses, creating unique possibilities. Recently, they have been observed in several quantum and classical systems. Yet, there is still no simple and deterministic strategy to realize them since their nodal points are accidental degeneracies, unlike symmetry-guaranteed type-I counterparts. Here, we propose a band-folding scheme for const…
We study surface superconductivity involving the `drumhead' surface states of (doped) Weyl loop materials. The leading weak coupling instability in the bulk is toward a chiral superconducting order, which fully gaps the Fermi surface. In this state the surface also becomes superconducting, with $p+ip$ symmetry. We show that the surface SC state is "topological" as long as it is fully gapped, and the system traps Majoarana modes wherever a vortex line enters or exits the bulk. In contrast to true 2D $p+ip$ superconductors, these Majorana zero modes arise even in the "strong pairing" regime wher…
We provide a systematic study of non-Hermitian topologically charged systems. Starting from a Hermitian Hamiltonian supporting Weyl points with arbitrary topological charge, adding a non-Hermitian perturbation transforms the Weyl points to one-dimensional exceptional contours. We analytical prove that the topological charge is preserved on the exceptional contours. In contrast to Hermitian systems, the addition of gain and loss allows for a new class of topological phase transition: when two oppositely charged exceptional contours touch, the topological charge can dissipate without opening a g…
Weyl semimetals and nodal line semimetals are characterized by linear electronic bands touching at zero-dimensional points and one-dimensional lines, respectively. Recently, it has been predicted that nodal line semimetals can be driven into tunable Floquet-Weyl semimetals by circularly polarized light. Here, we study the occurrence of interface states between two regions of a nodal line semimetal shined by two beams of light with opposite circular polarizations. Within a minimal model, we find remarkable modifications of the energy structure by tuning the polarized light, such as the possible…
A monopole harmonic superconductor is a novel topological phase of matter with topologically protected gap nodes that result from the non-trivial Berry phase structure of Cooper pairs. In this work we propose to realize a monopole superconductor by the proximity effect between a time-reversal broken Weyl semi-metal and an $s$-wave superconductor. Furthermore, we study the zero-energy vortex bound states in this system by projection methods and by exact solutions. The zero modes exhibit a non-trivial phase winding in real space as a result of the non-trivial winding of the order parameter in mo…
