Weyl points and Fermi arcs in a chiral phononic crystal

Abstract

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...

Topological Phononics: From Fundamental Models to Real Materials

“…3D phononic topological states include phononic topological nodal lines, phononic Weyl points, and phononic TIs. The phononic topological nodal lines have been proposed in mechanical metacrystals, and phononic Weyl points have been found in acoustic systems, Maxwell frames, and non‐centrosymmetric materials …”

“…Phononic Weyl points have been found in other systems including chiral phononic crystals, stacked acoustic dimerized chains, and non‐centrosymmetric solid‐state materials . One hallmark of phononic Weyl points is the existence of surface Fermi arc states.…”

“…One hallmark of phononic Weyl points is the existence of surface Fermi arc states. Li et al observed the surface Fermi arc states in a chiral phononic crystal . In 2018, Li et al first reported the prediction of phononic single Weyl point and their surface phononic arc states in solid‐state 3D materials TiS, ZrSe, and HfTe .…”

“…Recently, there is growing research of interest in exploring topological states of phonons. Various topological phononic states have been proposed/realized in acoustic systems, mechanical metamaterials, Maxwell frames, and solid‐state materials . Topological phononic states are characterized by nonzero topological invariants.…”

Breaking the barriers: advances in acoustic functional materials

“…Weyl points are robust and can only be annihilated in pairs with opposite charges. In acoustics, Weyl points were first realized by incorporating chiral interlayer couplings or unequal onsite couplings in the staked honeycomb lattice [27,103]. A plane cut with a fixed k z in the 3D Brillouin zone could acquire net Berry flux due to the existence of the Weyl point, resulting in a nonzero Chern number.…”