Fig. 3: Acoustic crystal design and the observation of drumhead surface states.
From: Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal
a Experimental sample for measuring the surface states (SSs). The lattice constants in the xy plane and along the z direction are a = 140 mm and az = 70 mm, respectively. b Unit cell of the acoustic crystal, with tubes enabling positive and negative couplings colored in purple and blue, respectively. The dimensions of the cuboid cavities are l = 56 mm, w = 28 mm and h = 7 mm. The width parameters of the tubes are dx1 = 3.2 mm, dx2 = 7.8 mm, dy = 6 mm, dz1 = 3.2 mm and dz2 = 4.8 mm. The acoustic crystal is filled with air and surrounded by hard walls. c Equi-frequency surface of the acoustic crystal in b at 3020 Hz (slightly below the frequency range of the nodal ring) calculated from full-wave simulations. d Experimentally measured SS dispersion at 3045 Hz (inside the frequency range of the nodal ring). The solid blue curves denote the projections of the nodal rings. e, f Experimentally measured SS dispersion along the horizontal (vertical) white dashed line in d. The gray and red dots represent simulated eigenfrequencies of the bulk and SSs, respectively. The blue dots denote the projections of the bulk nodal points.
