Valley interface states, resulting in acoustic valley Hall topological insulators, have recently become a hot topic in the study of acoustic systems. On the basis of structural diversity and potential applications, we construct a two-dimensional triangular-lattice phononic crystal with $C_{3v}$-symmetric scatterers, and obtain two distinct valley Hall phases with nonvanishing valley Chern indices by rotating the scatterers. We numerically calculate the dispersion relations of these valley Hall phases including two kinds of interfaces, and find that valley interface states exist at not only the zigzag interface but also the armchair interface. We demonstrate the acoustic splitting and merging of valley interface states in the cross-waveguides, and numerically achieve the xor and or logic functions. We also design three complicated waveguides by assembling phononic crystals with distinct valley Hall phases. By experimental measurements in these waveguides, we successfully implement one-, two-, and three-channel topological transport. This research possibly provides a design route exploiting valley interface states to fabricate multichannel acoustic communication devices.

The acoustic analogy of topological insulators is a hot field of materials research. On one-dimensional acoustic systems, many researchers have lately paid their attention to the applications of the Su-Schrieffer-Heeger (SSH) model, which can support topologically nontrivial phases. In this paper, we design a supercell composed of two identical hollow cylinders with a side split immersed in the air background. The supercell is arranged in a line to form a SSH model, which has three bandgaps including two zone-folding-induced gaps and a local resonant gap in the subwavelength region. By analyzing the eigenstates and calculating the Zak phases, we find that a topological phase transition takes place only in the zone-folding-induced gaps when we rotate the split-cylinders. Thus, a finite-size array, made of two sublattices with distinct topological properties, inevitably produces topological interface states on their interface. In addition, we demonstrate that the topological interface states can be adjusted in a wide frequency range by rotating the cylinders that control the coupling strength between two split-cylinders in one supercell. These tunable topological interface states may have potential application prospects in wave filtering, wave detecting, and so on.

Backscattering immunity of valley edge states for a monolayer sonic crystal provides a basis for designing devices with unconventional functions. Recently, the valley edge state of a bilayer sonic crystal, regarded as a new degree of freedom, gives a powerful platform for manipulating acoustic waves. In this Letter, we realize valley spin insulators in a bilayer sonic crystal and find that the layer-mixed, layer-polarized, and layer-locked edge states exist on both zigzag and armchair interfaces. There are significant differences between the armchair edge states and the zigzag edge states at the interfaces formed by two domains of distinct acoustic layer-valley Hall phases. Based on the projected dispersion relations for a bilayer sonic crystal, we achieve theoretically and experimentally bilayer multichannel transmission with different layers locking. This paper provides a design approach for applications of bilayer acoustic multichannel communication devices.

Synthesized three-dimensional space provides us with a platform to explore the intriguing acoustic valley Hall insulator. In this paper, a rotational degree of freedom is introduced to construct a synthetic three-dimensional space. Based on simulations, our results show that Weyl points and Fermi arcs and topologically nontrivial edge modes appear in a synthetic space. Not only rotational operation but also boundary truncation can modulate the frequencies of nontrivial edge states, which result in two completely different edge states at the upper and lower boundaries. Using frequencies of edge states protected by Weyl points, we devise two different acoustic topological rainbow devices. The two devices are able to trap states with different frequency components at different spatial positions: one device is capable of capturing low-frequency components at close range, while the other has the ability to confine low-frequency components at long distances. This work may boost further the development of topological rainbow devices in a synthetic space related to the acoustic valley Hall insulator.

Effective modulation of electronic and optical properties for van der Waals heterostructures is beneficial to spintronics and optoelectronic devices. We use first-principle calculations to investigate the effects of intralaminar biaxial strain on the Rashba spin splitting and optical absorption of MoSSe/WSe $$_2$$2 heterostructures. First, considering the different stacking manners, the most stable configuration is confirmed from six heterostructures. The results show that this is in type II energy band alignment, which effectively reduces the carrier recombination rate. Second, Rashba splitting strength can be effectively modulated by biaxial strain, and splitting occurs at the $$\Gamma $$Γ point, in which the tensile and compressive strains can suppress and promote the strength, respectively. Third, we calculate the dielectric constant and optical absorption of the MoSSe/WSe $$_2$$2 heterostructure and find a higher optical absorption coefficient in visible light scope than two monolayers, and the maximum value can reach 6.11 $$\times $$× $$10^5$$10 5 cm $$^{-1}$$- 1 . The first absorption peak of the heterostructure increases with increasing tensile strain and the absorption edge is red shifted. On the contrary, there is an opposite effect under compressive strain. These results suggest that MoSSe/WSe $$_2$$2 heterostructures have potential applications in strain-tunable spintronic and optoelectronic devices.

Higher-order topological insulators, providing a horizon beyond the conventional bulk-interface correspondence, have zero-dimensional topological corner states at different corners, such as a right-angled corner. Here, we numerically demonstrate a hierarchy of band topology in a two-dimensional square-lattice sonic crystal. In our system, the acoustic bulk bands mimic the quantum spin Hall effect, while gapped interface states emerge in the bulk gap due to symmetry reduction and carry quantized Zak phases, which result in zero-dimensional topological corner states in the interface gap. By direct acoustic measurement, we observe that zero-dimensional topological corner states are confined at not only the right-angled corner, but also the straight-angled corner. Our results present this type of topological shape-dependent corner state, which possibly possesses potential application in controlling and localizing acoustic waves.