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Topologically protected one-way transportation of sound, mimicking the topological properties of the condensed matter, has received greatly attentions. Thus far, the topological phases and the topological edge states of sound are yielded in the vicinity of the Dirac cones fixed at the high symmetric points of the Brillouin zone. Here, we present a new type of the phononic topological insulator in the square lattice with position-variational Dirac cones along the high symmetric lines. The emergence of such Dirac cones, characterized by the vortex structure in a momentum space, is attributed to the unavoidable band crossing protected by the mirror symmetry. By rotating the square columns, these Dirac points are lifted and a complete band gap is induced because of the mirror-symmetry-breaking. Along the topological domain wall between the phononic crystals (PhCs) with the distinct topological phases stemming from the mirror symmetry inversion, we obtain a topological edge state for the neutral scalar sound which is absence of the intrinsic polarization and is uncoupled from an external field. Within a wide rotational range of the square column, the topological edge state in our PhCs evolves from a gapless one into a gapped one with a robust edge transport against cavities and disorders. Our excellent results are promising for the exploration of the new topological phenomena in the PhCs beyond the hexagonal lattices. Furthermore, the flexibility of the rotational square columns provides an interesting platform for the design of tunable topological acoustic devices., Comment: 26 pages and 5 figures

Quasi-lossless and asymmetric sound transports, which are exceedingly desirable in various modern physical systems, are almost based on nonlinear or angular-momentum biasing effects with extremely high power levels and complex modulation schemes. A practical route for the steerable sound transport along any arbitrary acoustic pathway, especially in a 3D acoustic network, could revolutionize the sound power flow and the sound communication. Here, we design an acoustic device consisting of a regular-tetrahedral cavity with four cylindrical waveguides. A smaller regular-tetrahedral solid in this cavity is eccentrically emplaced to break its spatial symmetry. The numerical and experimental results show that the sound power flow can unimpededly transport between two waveguides away from the eccentric solid within a wide frequency range. Furthermore, in the vicinity of eigenmode, the sound waves from various waveguides can transport to different waveguides, respectively along the compressed and broadened pathways without mutually interference. Endowed with these quasi-lossless and asymmetric transport characteristics, we construct a 3D acoustic network, in which the sound power flow can flexibly propagate along arbitrary sound pathways defined by our acoustic devices with eccentrically-emplaced regular-tetrahedral solids., Comment: 16 pages and 6 figures

Topological phononic states, facilitating acoustic unique transports immunizing to defects and disorders, have significantly revolutionized our scientific cognition of acoustic wave systems. Up to now, the theoretical and experimental demonstrations of topologically protected one-way transports with pseudospin states in a phononic crystal beyond the graphene lattice with C6v symmetry are still unexploited. Furthermore, the tunable topological states, in form of robust reconfigurable acoustic pathways, have been evaded in the topological phononic insulators. Here, we realize a topological phase transition in the double Dirac degenerate cone of rotatable triangular phononic crystals with C3v symmetry, by introducing the zone folding mechanism. Along a topological domain wall between two portions of phononic crystals with distinct topological phases, we experimentally observe the quantum spin Hall (QSH) effect for sound, characterized by the robust pseudospin-dependent one-way edge model. As the triangular phononic crystals can freely rotate, we straightforward reconfigure an arbitrary contour defined by the topological domain wall along which the acoustic waves can unimpededly transport. Our research develops a new route for the exploration of the topological phenomena in experiments and provides an excellent framework for freely steering the acoustic immune-backscattering propagation within topological phononic structures., Comment: 21 pages and 5 figures