Hyperbolic Weyl Point in Reciprocal Chiral Metamaterials

Xiao, Meng; Lin, Qiang; Fan, Shanhui

doi:10.1103/physrevlett.117.057401

Phys. Rev. Lett.

2016

DOI: 10.1103/physrevlett.117.057401

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Hyperbolic Weyl Point in Reciprocal Chiral Metamaterials

Meng Xiao

Qiang Lin

Shanhui Fan

Abstract: Abstract: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.

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Cited by 164 publications

(121 citation statements)

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“…Drastically different from previous proposals to obtain photonic equivalents of condensed matter topological insulators based on Bragg interferences181920212223242526272829 or homogenized metamaterials3031323334, our approach allows for an extension of photonic topological phases down to the deep subwavelength regime, exploiting multiple-scattering and spatial dispersion.…”

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confidence: 94%

Crystalline metamaterials for topological properties at subwavelength scales

et al. 2017

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The exciting discovery of topological condensed matter systems has lately triggered a search for their photonic analogues, motivated by the possibility of robust backscattering-immune light transport. However, topological photonic phases have so far only been observed in photonic crystals and waveguide arrays, which are inherently physically wavelength scaled, hindering their application in compact subwavelength systems. In this letter, we tackle this problem by patterning the deep subwavelength resonant elements of metamaterials onto specific lattices, and create crystalline metamaterials that can develop complex nonlocal properties due to multiple scattering, despite their very subwavelength spatial scale that usually implies to disregard their structure. These spatially dispersive systems can support subwavelength topological phases, as we demonstrate at microwaves by direct field mapping. Our approach gives a straightforward tabletop platform for the study of photonic topological phases, and allows to envision applications benefiting the compactness of metamaterials and the amazing potential of topological insulators.

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Crystalline metamaterials for topological properties at subwavelength scales

et al. 2017

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“…In addition to the standard Weyl points possessing a point-like Fermi surface (referred to as type-I), another type of Weyl point was more recently recognized, which has a conical Fermi surface (referred to as type-II) 13,[19][20][21] . Since the Weyl point or Weyl cone in Weyl semimetals represents a special dispersion of electrons moving in periodic potentials, the question naturally arises as to whether a similar dispersion or the Weyl point for classical waves propagating in artificial periodic structures exists [8][9][10][11][12][13][22][23][24][25][26][27][28] . Lu et al were the first to report the existence of Weyl points and the associated one-way SWs in photonic crystals based on double-gyroid structures 8,9 .…”

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confidence: 99%

Weyl points and Fermi arcs in a chiral phononic crystal

et al. 2017

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Topological semimetals are materials whose band structure contains touching points that are topologically nontrivial and can host quasiparticle excitations that behave as Dirac or Weyl fermions [1][2][3][4][5][6][7] . These so-called Weyl points not only exist in electronic systems, but can also be found in artificial periodic structures with classical waves, such as electromagnetic waves in photonic crystals [8][9][10][11] and acoustic waves in phononic crystals 12,13 . Due to the lack of spin and a di culty in breaking time-reversal symmetry for sound, however, topological acoustic materials cannot be achieved in the same way as electronic or optical systems. And despite many theoretical predictions 12,13 , experimentally realizing Weyl points in phononic crystals remains challenging. Here, we experimentally realize Weyl points in a chiral phononic crystal system, and demonstrate surface states associated with the Weyl points that are topological in nature, and can host modes that propagate only in one direction. As with their photonic counterparts, chiral phononic crystals bring topological physics to the macroscopic scale.Recently, interest in Weyl semimetals has been growing 1-7 . Weyl semimetals are materials in which the electrons have linear dispersions in all directions while being doubly degenerate at a single point, called the Weyl point, near the Fermi surface in threedimensional (3D) momentum space. In other words, the electrons in Weyl semimetals obey the Weyl equation and thus behave like Weyl fermions. The Weyl point is a source or sink of the Berry curvature flux in momentum space; in other words, it is a magnetic monopole with a topological charge, defined as the Berry curvature flux threading a sphere enclosing the Weyl point with a value of either +1 or −1, corresponding to the chirality of the Weyl fermion. The Weyl point and the associated topological invariants enable Weyl semimetals to exhibit a variety of unusual properties, including robust surface waves (SWs) [14][15][16] and chiral anomaly 17,18 . In addition to the standard Weyl points possessing a point-like Fermi surface (referred to as type-I), another type of Weyl point was more recently recognized, which has a conical Fermi surface (referred to as type-II) 13,[19][20][21] . Since the Weyl point or Weyl cone in Weyl semimetals represents a special dispersion of electrons moving in periodic potentials, the question naturally arises as to whether a similar dispersion or the Weyl point for classical waves propagating in artificial periodic structures exists [8][9][10][11][12][13][22][23][24][25][26][27][28] . Lu et al. were the first to report the existence of Weyl points and the associated one-way SWs in photonic crystals based on double-gyroid structures 8,9 . Weyl points were also observed in photonic crystals fabricated using conventional planar fabrication technology 10,11 . Following the developments of the Weyl photonic crystals, Weyl phononic crystals (PCs) with Weyl points for acoustic waves have also been proposed in graph...

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“…Here we consider a semi-infinite system and thus only the surface states localized at one surface [red curve in Fig. 4(c) [20,27], photonics [28][29][30][31][32][33], and polaritons [34][35][36].…”

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Acoustic Type-II Weyl Nodes from Stacking Dimerized Chains

Yang¹,

Zhang²

2016

Phys. Rev. Lett.

142

101

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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 transport properties of Fermi-arc-like surface states. In a certain momentum space direction, the velocity of these surface states are determined by the tilting direction of the type-II Weyl nodes, rather than the chirality dictated by the Chern number. Our study also provides an approach of constructing acoustic topological phases at different dimensions with the same building blocks. [7]. Following these developments, Weyl nodes for acoustic waves have also been proposed by applying on-site unequal coupling or chiral coupling on a graphite structure [8]. Both coupling approaches can enable the emergence of acoustic waves as Weyl quasiparticles in an acoustic crystal.Recently, type-II Weyl semimetals hosting fundamentally new type-II Weyl fermions have been proposed [9] and confirmed experimentally [10-13] with both the bulk fermions and Fermi arcs observed. A type-II Weyl node appears at the contact of electron and hole pockets and exhibits a strongly tilted cone spectrum with non-vanishing density of states (DOS), in contrast to a point-like Fermi surface at a type-I Weyl node [2] with vanishing DOS. The type-II Weyl fermions were in fact "missed" by Weyl because they violate the Lorentz symmetry. Therefore unlike the type-I case, the type-II Weyl fermions cannot be adiabatically connected back to the Lorentz-invariant Weyl fermions in Weyl's prediction.In the context of acoustics, the previous proposal based on the graphite structure [8] did not distinguish type-I and type-II Weyl Hamiltonians. Consequently, only acoustic topological surface states for type-I Weyl nodes have been studied. In this Letter, on a platform of stacked dimerized chains of acoustic resonators, we construct acoustic type-II Weyl nodes following the explicit type-II Weyl Hamiltonian [9]. Unique features of this acoustic type-II Weyl system

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Hyperbolic Weyl Point in Reciprocal Chiral Metamaterials

Cited by 164 publications

References 37 publications

Crystalline metamaterials for topological properties at subwavelength scales

Crystalline metamaterials for topological properties at subwavelength scales

Weyl points and Fermi arcs in a chiral phononic crystal

Acoustic Type-II Weyl Nodes from Stacking Dimerized Chains

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