Although topological mechanical metamaterials have been extensively studied from a theoretical perspective, their experimental characterization has been lagging. To address this shortcoming, we present a systematic, laser-assisted experimental characterization of topological kagome lattices, aimed at elucidating their in-plane phononic and topological characteristics. We specifically explore the continuum elasticity limit, which is established when the ideal hinges that appear in the theoretical models are replaced by ligaments capable of supporting bending deformation, as observed for instance in realistic physical lattices. We reveal how the zero-energy floppy edge modes predicted for ideal configurations morph into finite-frequency phonon modes that localize at the edges. By probing the lattices with carefully designed excitation signals, we are able to extract and characterize all the features of a complex, low-frequency acoustic regime in which bulk modes and topological edge modes overlap and entangle in response. The experiments provide unequivocal evidence of the existence of strong asymmetric wave transport regimes at finite frequencies.

Recent progress in topological mechanics has revealed a family of Maxwell lattices that exhibit topologically protected floppy edge modes. These modes lead to a strongly asymmetric elastic wave response. In this paper, we show how topological Maxwell lattices can be used to realize nonreciprocal transmission of elastic waves. Our design leverages the asymmetry associated with the availability of topological floppy edge modes and the geometric nonlinearity built into the mechanical systems' response to achieve the desired nonreciprocal behavior, which can be further utilized to form a phonon diode via the addition of on-site pinning potentials that blocks the linear transmission and only allows the signal to transmit in one way. Finally, the nonreciprocal wave transmission can be switched on and off via topological phase transitions, paving the way to the design of cellular metamaterials that can serve as tunable topologically protected phonon diodes.

In this work, we investigate theoretically and demonstrate experimentally the existence of valley Hall edge states in the in-plane dynamics of honeycomb lattices with bivalued strut thickness. We exploit these states to achieve nontrivial waveguiding of optical modes that is immune to backscattering from sharp corners. We also present how different types of interfaces can be combined into multibranch junctions to form complex waveguide paths and realize a variety of structural logic designs with unconventional wave-transport capabilities. We illustrate this potential with two applications. The first is a direction-selective energy-splitting waveguide tree featuring a pronounced asymmetric wave-transport behavior. The second is an internal waveguide loop along which the energy can be temporarily trapped and periodically released, effectively working as a signal delayer. The modal complexity of in-plane elasticity has important consequences for the regime of manifestation of the edge states, as the availability of viable total band gaps is shifted to higher frequencies compared to the out-of-plane counterpart problem. It also poses additional experimental challenges, associated with proper acquisition and deciphering of the in-plane modes, the solution of which requires a systematic use of in-plane laser vibrometry.

Phononic crystals (PnCs) and acoustic metamaterials (AMMs) are artificially architected materials endowed with the capabilities of wave manipulation. This review specifically covers the theoretical fundamentals and recent development of PnCs and AMMs at the micro‐ and nanoscales due to their potential significance in modern electronic applications. Similarities and differences in phonon transport at these two scales are discussed. Research gaps between the macro‐ and small‐scale PnC and AMM development are identified from a theoretical point of view. A future outlook is also presented to propose possible applications of micro‐ and nano‐PnCs and AMMs, including advancing quantum information processing technologies, such as quantum computing.

Topological insulators hold promises to realize exotic quantum phenomena in electronic, photonic, and phononic systems. Conventionally, topological indices, such as winding numbers, have been used to predict the number of topologically protected domain-wall states (TPDWSs) in topological insulators, a signature of the topological phenomenon called bulk-edge correspondence. Here, we demonstrate theoretically and experimentally that the number of TPDWSs in a mechanical Su-Schrieffer-Heeger (SSH) model can be higher than the winding number depending on the strengths of beyond-nearest-neighbor interactions, revealing the breakdown of the winding number prediction. Alternatively, we resort to the Berry connection to accurately characterize the number and spatial features of TPDWSs in SSH systems, further confirmed by the Jackiw-Rebbi theory proving that the multiple TPDWSs correspond to the bulk Dirac cones. Our findings deepen the understanding of complex network dynamics and offer a generalized paradigm for precise TPDWS prediction in potential applications involving localized vibrations, such as drug delivery and quantum computing.