Frequency-selective valley edge routing of elastic wave in topological phononic crystals with different symmetries.

The control of propagation direction or path of edge states is difficult when the chirality of the excitation source and the boundary structures are determined. Here, we studied a frequency-selective routing for elastic wave based on two types of topological phononic crystals (PnCs) with different symmetries. By constructing multiple types of interfaces between different PnCs structures with distinct valley topological phases, the valley edge states of elastic wave could be realized at different frequencies in the band gap. Meanwhile, based on the simulation of topological transport, it is found that the routing path of elastic waves valley edge states highly depends on the operating frequency and the inputting port of the excitation source. By varying the excitation frequency, the transport path can be switched. The results provide a paradigm for the control of elastic wave propagation paths that could be employed for designing the frequency-dependent ultrasonic division devices.

Recent advances in topological elastic metamaterials.

Topological elastic metamaterials have emerged as a new frontier in the quest of topological phases in condensed matter physics. Their exotic topological properties open a wealth of promising engineering-oriented applications that are difficult to realize with traditional elastic metamaterials, such as robust and defect insensitive waveguiding, signal sensing, and splitting. In this review, we retrospectively examine the underlying physical concept of topologically ordered states of elastic waves, starting from the one-dimensional example based on the Su-Schrieffer-Heeger model. We then move on to two-dimensional topological metamaterials, discussing elastic analogues of quantum Hall, pseudospin-Hall, valley-Hall phases. Finally, we survey the latest developments in the field including three-dimensional elastic topological phases and higher-order topological insulators. Altogether, this paper provides a comprehensive overview of the flourishing research frontier on topological elastic metamaterials, and highlights prominent future directions in this field.

Pseudospins and topological edge states for fundamental antisymmetric Lamb modes in snowflakelike phononic crystal slabs.

The topological transport of Lamb wave in phononic crystal slabs provides a great potential in reinforcing nondestructive testing, high sensitivity sensing, and information processing. In this paper, the authors investigate the pseudospins edge states of fundamental antisymmetric Lamb waves in a snowflakelike phononic slab. Significantly, the fourfold Dirac degeneracy for antisymmetric Lamb mode is accidentally formed at the Γ point with the critical angle of the snowflakelike holes, which does not require the folding of the lattices. Meanwhile, based on the rotating-scatterer mechanism, the mirror symmetry is broken and the topological multipole phase transitions are well induced during the gradual change of the scattering strength among the scatterers with the rotation angle. The topologically protected edge states and its unidirectional robust propagation are further demonstrated. The proposed topological phononic slabs will be a more hopeful option to apply in engineering practices.

Thermally tunable topological edge states for in-plane bulk waves in solid phononic crystals.

The remarkable properties of topological insulators have inspired numerous studies on topological transport for bulk waves, but the demonstrations of topological edge states with tunable frequency are few attempts. Here, we report on the active frequency tunability of topologically protected edge states for in-plane bulk waves by applying a thermal field. We find that the center frequency of topological band gap is shifted down and the band width is enlarged as the temperature increases. Meanwhile, the frequency range of topologically protected edge states is also shifted to low frequency region with the higher temperature. Furthermore, the robust propagation of in-plane bulk waves along a desired path is demonstrated within different frequency bands. The tunable frequency for both topological band gaps and topologically protected edge states achieves the active control of the transport for in-plane bulk waves, which may dramatically facilitate practical applications of novel phononic devices.

Topologically protected edge states for out-of-plane and in-plane bulk elastic waves.

Topological phononic insulators (TPnIs) show promise for application in the manipulation of acoustic waves for the design of low-loss transmission and perfectly integrated communication devices. Since solid phononic crystals exist as a transverse polarization mode and a mixed longitudinal-transverse polarization mode, the realization of topological edge states for both out-of-plane and in-plane bulk elastic waves is desirable to enhance the controllability of the edge waves in solid systems. In this paper, a two-dimensional (2D) solid/solid hexagonal-latticed phononic system that simultaneously supports the topologically protected edge states for out-of-plane and in-plane bulk elastic waves is investigated. Firstly, two pairs of two-fold Dirac cones, respectively corresponding to the out-of-plane and in-plane waves, are obtained at the same frequency by tuning the crystal parameters. Then, a strategy of zone folding is invoked to form double Dirac cones. By shrinking and expanding the steel scatterer, the lattice symmetry is broken, and band inversions induced, giving rise to an intriguing topological phase transition. Finally, the topologically protected edge states for both out-of-plane and in-plane bulk elastic waves, which can be simultaneously located at the frequency range from 1.223 to 1.251 MHz, are numerically observed. Robust pseudospin-dependent elastic edge wave propagation along arbitrary paths is further demonstrated. Our results will significantly broaden its practical application in the engineering field.

Multi-objective optimization of asymmetric acoustic transmission with periodical structure.

Asymmetric acoustic wave propagation is important for control and manipulation of the acoustic wave signals in various devices. However, previous approach to find optimal asymmetric acoustic transmission (AAT) is through repeatedly adjusting the geometrical parameters, thus causing time-consuming. Here we propose a study on the multi-objective optimization of the AAT, aiming to achieve the widest working frequency range (fr) and the highest transmittance peak (η) with regard to the design variables. For this purpose, the Radial Basis Function (RBF) neural work and finite element (FE) method are applied to obtain the valuable data in the procedure. Furthermore, local sensitivity analysis of design parameters on the fr and η are analyzed. Ultimately, the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is adapted for getting the Pareto-optimal solutions. The optimization results show great improvement for the overall performance of the AAT, which could be potentially significant in designing various sound devices.

Simultaneous multi-band valley-protected topological edge states of shear vertical wave in two-dimensional phononic crystals with veins.

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.