Tunable Topological Surface States of Three-Dimensional Acoustic Crystals

Abstract

Topological design for band structures of artificial materials such as acoustic crystals provides a powerful tool to manipulate wave propagating in a robust and symmetry-protected way. In this paper, based on the band folding and breaking mechanism by building blocks with acoustic atoms, we construct a three-dimensional topological acoustic crystal with a large complete bandgap. At a mirror-symmetry domain wall, two gapped symmetry and anti-symmetry surface states can be found in the bandgap, originated from two opposite Su-Schrieffer-Heeger chains. Remarkably, by enforcing a glide symmetry on the domain wall, we can tune the original gapped surface states in a gapless fashion at the boundaries of surface Brillouin zone, acting as omnidirectional acoustic quantum spin Hall effect. Our tunable yet straightforward acoustic crystals offer promising potentials in realizing future topological acoustic devices.

Various topological phases and their abnormal effects of topological acoustic metamaterials

“…Another construction method is based on 1D SSH chains to shape a NaCl‐like 3D structure (Figure 10B). [ 81 ] The original zero‐dimensional (0D) edge states will expand into 2D in momentum space. Considering there exists a glide symmetry for a 2D domain‐wall, for example, $${{\boldsymbol{G}}}_{{\boldsymbol{y}}}$$: ( x , y , z ) → ( x + a /2, − y , z ), we have $${{\boldsymbol{G}}}_{{\boldsymbol{y}}}^{{\bf{2}}}$$: ( x , y , z ) → ( x + a , y , z ).…”

“…chains to shape a NaCl-like 3D structure (Figure 10B). [81] The original zero-dimensional (0D) edge states will expand into 2D in momentum space. Considering there exists a glide symmetry for a 2D domain-wall, for example, G y : (x, y, z) → (x+ a/2, −y, z), we have G y 2 : (x, y, z) → (x+ a, y, z).…”

Acoustic metasurfaces with Frieze symmetries

“…3,4 The effects of symmetry, and its strategic breaking, have been utilized across wave physics, from the passive beam-steering applications to topological surfaces and insulators. [5][6][7][8][9][10] There has been a recent interest in the design of reconfigurable one-dimensional (1D) waveguiding structures, [11][12][13][14] whereby the symmetries of the unit cell are used, or broken, to tailor the dispersion of supported modes. Glide-symmetry has been extensively investigated in the electromagnetic regime, [15][16][17][18] with notable studies done by Hessel et al in 1973 19 with periodically loaded waveguides.…”

Localization of edge state in acoustic topological insulators by curvature of space

“…In the past several decades, TIs have constituted an expanding research field in condensed matter, and the robust transport effect of boundary states against disorders has attracted intense interest in classical systems [7][8][9][10][11][12]. Inspired by these concepts, analogous topological optics/acoustic are becoming a hot notion throughout physics in a variety of frontier domains [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], such as one-way propagation [13,14], communications [15,16], and acoustic-noise reduction [17] and so on. Similar to the electrons propagating in a crystal, sound in the phononic crystal will also experience a periodic potential [18][19][20], and the physical performance can be delineated by the energy band structure, such as the concept of topology [21][22][23].…”

“…Usually, if there are two bands can be adiabatically transformed each other, it can be regard as topologically equivalent [25], and will appear band gap remains open by connected two equivalent TIs [26]. Typically, the gapless boundary modes is protected by the topology, and the modes in the boundary possess robust characteristics which are insensitive to structural disturbance [27][28][29].…”