Research ArticleAPPLIED PHYSICS

Experimental demonstration of acoustic semimetal with topologically charged nodal surface

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Science Advances  21 Feb 2020:
Vol. 6, no. 8, eaav2360
DOI: 10.1126/sciadv.aav2360
  • Fig. 1 Charged nodal surface and a tight-binding model realization.

    (A) Berry flux density distributions of a Weyl point. (B) The same as (A) but for a charged nodal surface. The orange sphere and transparent red plane indicate the Weyl point and nodal surface, respectively. The arrows represent the orientation and amplitude of the Berry flux density. (C) Sketch of the tight-binding model. Each unit cell consists of two sublattices (color spheres). Their projections onto the x-y plane form a hexagonal lattice with a lattice constant a. The lattice constant along the z direction is h, and the red and blue spheres are located on the planes z = nh and z = (n + 1/2)h, respectively, with n being an integer. The cyan and black bonds represent hopping between different sites, associated with hopping strengths tc and t0, respectively. This model exhibits C˜2z symmetry with broken inversion symmetry. (D) The first Brillouin zone and its projection onto the kx-kz plane. The orange spheres represent Weyl points with topological charges +1, and the cyan surfaces at kz = ± π/h represent the nodal surfaces with charges −2.

  • Fig. 2 A 3D phononic crystal designed with a charged nodal surface.

    (A) Unit cell geometry of the phononic crystal. The solid ingredient (colored) is acoustically rigid for airborne sound. The structure parameters are a = 16.0 mm, h = 2u = 9.6 mm, r = 5.0 mm, d = 4.8 mm, and w = 2.2 mm. (B) Bulk band structure simulated along several high symmetry directions of the first Brillouin zone. (C) Left: Gapless surface dispersions (color lines) for a phononic slab periodic in the x-z plane but finite along the y direction (see the right), simulated at a fixed kz = 0.5π/h. The shadow regions are projected from the bulk bands. Right: Schematic view of the phononic crystal slab specified with truncation details for both the surfaces XZ1 and XZ2, where l1 = (d + w)/2 and l3=a/23. Note that l2=53a, and thus, the slab has a thickness more than five structural periods along the y direction.

  • Fig. 3 Experimental detection of the topological surface states.

    (A) An image of the experimental setup. The insets give the details for the cover plate with holes opened (top) or sealed (bottom). The plugs that seal the holes will be removed one by one during the measurement. Photo credit: Liping Ye, Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University. (B) The measured in-plane dispersions (bright color) for the XZ1 surface, in good agreement with the simulated surface arcs (white curves) and bulk band projections (gray regions). The orange spheres label the projected Weyl points K and K′, and the arrows indicate the main propagating directions of the surface acoustic waves. Note that 9.43 kHz corresponds to the Weyl point frequency, and 9.75 kHz falls into the frequency range of the nodal surface. Since the (bulk) nodal surface bands are flat, their projections are narrow for 9.75 kHz. (C) The same as (B) but measured for the XZ2 surface. Trivial surface states (black curves) appear in this case. (D) Experimentally measured surface dispersions (bright color) at kz = 0.5π/h for the sample surfaces XZ1 and XZ2, which reproduce excellently the simulation results (white curves).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/8/eaav2360/DC1

    Supplementary Text

    Section S1. Nodal surfaces with higher charges

    Section S2. Tight-binding model

    Section S3. Transition between topologically nontrivial and trivial nodal surfaces

    Fig. S1. Tight-binding model.

    Fig. S2. Chern number as a function of kz.

    Fig. S3. Topological charge distributions before and after the topological transition.

    Movie S1. Topological transition process.

    References (3640)

  • Supplementary Materials

    The PDF file includes:

    • Supplementary Text
    • Section S1. Nodal surfaces with higher charges
    • Section S2. Tight-binding model
    • Section S3. Transition between topologically nontrivial and trivial nodal surfaces
    • Fig. S1. Tight-binding model.
    • Fig. S2. Chern number as a function of kz.
    • Fig. S3. Topological charge distributions before and after the topological transition.
    • References (3640)

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.avi format). Topological transition process.

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