Abstract
The introduction of the concept of valley pseudospin to phononic crystals has made a remarkable topologically protected interface transport of sound, which opens a novel research area referred to as valley Hall topological insulators. Here, we demonstrate the simultaneous multi-band edge states of shear vertical waves in two-dimensional phononic crystals with veins. The multi-band edge states are topologically valley-protected and are obtained by simultaneously gapping multiple Dirac points at K (or K′) under the inversion symmetry breaking. As the relative radius of the two adjacent steel columns varies, the band diagram undergoes a topological transition which can be characterized by topological charge distributions and opposite valley Chern numbers. Subsequently, the vortex chirality of the bulk valley modes is unveiled. With numerical simulations, simultaneous multi-band valley dependent edge states and the associated valley-protected backscattering suppression around the curved waveguide are further demonstrated. Our work could become a promising platform for applications of multi-functional topological acoustic devices.
Highlights
The discoveries of quantum Hall effect[1], quantum spin Hall effects[2, 3], and topological insulators[4, 5] have opened a new door for the understanding of condensed matter physics
Lu et al have reported the experimental observation of topological valley transport of sound by breaking rotating symmetry relying on the quantum valley Hall effects[24, 31]
We demonstrate the existence of topological transition as the radii of the two adjacent steel columns varies, which is characterized by topological charge distributions and opposite valley Chern numbers
Summary
The discoveries of quantum Hall effect[1], quantum spin Hall effects[2, 3], and topological insulators[4, 5] have opened a new door for the understanding of condensed matter physics. The topological properties of one-way elastic edge state[22], acoustic topological insulator[23], and topological valley transport[24] that are immune to backscattering in the presence of imperfections and impurities including localized defects and sharp corners are being studied by some scientists Achieving these topologically protected acoustic propagations is mainly depending on two categories of mechanisms. Based on the acoustic quantum spin Hall effect, the robust pseudospin-dependent one-way edge sound transport[23, 28,29,30] has been successfully demonstrated in time-reversal invariant systems. Valley-protected backscattering suppressions of SV waves propagating along the straight waveguide and the curved waveguide are demonstrated in multiple frequency ranges
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