The quantum spin Hall effect lays the foundation for the topologically protected manipulation of waves, but is restricted to one-dimensional-lower boundaries of systems and hence limits the diversity and integration of topological photonic devices. Recently, the conventional bulk-boundary correspondence of band topology has been extended to higher-order cases that enable explorations of topological states with codimensions larger than one such as hinge and corner states. Here, we demonstrate a higher-order quantum spin Hall effect in a two-dimensional photonic crystal. Owing to the non-trivial higher-order topology and the pseudospin-pseudospin coupling, we observe a directional localization of photons at corners with opposite pseudospin polarizations through pseudospin-momentum-locked edge waves, resembling the quantum spin Hall effect in a higher-order manner. Our work inspires an unprecedented route to transport and trap spinful waves, supporting potential applications in topological photonic devices such as spinful topological lasers and chiral quantum emitters.

Stable and efficient guided waves are essential for information transmission and processing. Recently, topological valley-contrasting materials in condensed matter systems have been revealed as promising infrastructures for guiding classical waves, for they can provide broadband, non-dispersive and reflection-free electromagnetic/mechanical wave transport with a high degree of freedom. In this work, by designing and manufacturing miniaturized phononic crystals on a semi-infinite substrate, we experimentally realized a valley-locked edge transport for surface acoustic waves (SAWs). Critically, original one-dimensional edge transports could be extended to quasi-two-dimensional ones by doping SAW Dirac “semimetal” layers at the boundaries. We demonstrate that SAWs in the extended topological valley-locked edges are robust against bending and wavelength-scaled defects. Also, this mechanism is configurable and robust depending on the doping, offering various on-chip acoustic manipulation, e.g., SAW routing, focusing, splitting, and converging, all flexible and high-flow. This work may promote future hybrid phononic circuits for acoustic information processing, sensing, and manipulation.

Topological materials for classical waves, e.g., electromagnetic and acoustic waves, have attracted growing interest, mainly due to the robustness, low loss, and new artificial degree of freedom conferred by their boundaries. Surface acoustic waves (SAWs), as widely used information carriers of microdevice relevance, are ubiquitous in today’s wireless communication and sensing networks. Herein, we report the implementation of a SAW topological insulator based on a monolithically integrated platform. By using a miniature acoustic resonator array working tens of megahertz on a piezoelectric half-space, we successfully endow electrically pumped Rayleigh-type SAWs with the “spin-momentum locking” feature, enabling solid-state acoustic waves on the “one-dimensional interface of the two-dimensional surface on the three-dimensional volume” detour arbitrarily and pass through defects and intersections with much smaller losses than those incurred with any other solutions. These revolutionary topological SAWs may open an avenue for monolithic electronic-(photonic)-phononic circuits with ultrahigh performance and advanced functionalities in, e.g., future mobile communicating, sensing, and quantum-information processing.

Waveguides and resonators are core components in the large-scale integration of electronics, photonics and phononics, both in existing and future scenarios. In certain situations, there is critical coupling of the two components; i.e. no energy passes through the waveguide after the incoming wave couples into the resonator. The transmission spectral characteristics resulting from this phenomenon are highly advantageous for signal filtering, switching, multiplexing and sensing. In the present study, adopting an elastic-wave platform, we introduce topological insulator (TI), a remarkable achievement in condensed matter physics over the past decade, into a classical waveguide-ring-resonator configuration. Along with basic similarities with classical systems, a TI system has important differences and advantages, mostly owing to the spin-momentum locked transmission states at the TI boundaries. As an example, a two-port TI waveguide resonator can fundamentally eliminate upstream reflections while completely retaining useful transmission spectral characteristics, and maximize the energy in the resonator, with possible applications being novel signal processing, gyro/sensing, lasering, energy harvesting and intense wave–matter interactions, using phonons, photons or even electrons. The present work further enhances confidence in using topological protection for practical device performance and functionalities, especially considering the crucial advantage of introducing (pseudo)spins to existing conventional configurations. More in-depth research on advancing phononics/photonics, especially on-chip, is foreseen.

Precisely engineered gigahertz surface acoustic wave (SAW) trapping enables diverse and controllable interconnections with various quantum systems, which are crucial to unlocking the full potential of phonons. The topological rainbow based on synthetic dimension presents a promising avenue for facile and precise localization of SAWs. In this study, we successfully developed a monolithic gigahertz SAW topological rainbow by utilizing a nanoscale translational deformation as a synthetic dimension. We observed a gapless topological boundary state, which originates from a 2π phase winding in the Zak phase during translation. These boundary states enable on-chip single-mode rainbowlike filters with an extensive range of adjustable operating frequencies. Furthermore, we construct nanoscale wedge-shaped grooves, realizing the Born-von-Karman interface. The interface generates topological rainbow resonators with high quality and small mode volume, which can trap topological phononic states of different frequencies into different positions. This study underscores the immense potential of topological acoustics in synthetic dimensions for microwave acoustics, providing a robust design framework for the precise manipulation of SAWs.