Research advances in acoustic metamaterials and topological phononic crystals

<sec><p indent="0mm">Acoustic metamaterials and phononic crystals are new acoustic artificial materials developed in the last <sc>30 years.</sc> These artificial materials, generally composed of meta-atoms, possess unique properties (e.g., negative refractive index) that are not found in nature or previously believed to be impossible. Due to their exceptional properties, such artificial materials can lead to intriguing phenomena, such as acoustic cloaks, sound abnormal refraction/reflection and sound self-bending, providing a novel research pathway and a promising application opportunity for the precise and controllable modulation of acoustic vibrations. Nowadays, acoustic metamaterials and phononic crystals have been used to explore some interesting and intricate physics, such as nonreciprocal, topological and moiré physics, because of their flexibility in fabrication and manipulation. The combination of novel physics with these two acoustic artificial materials can significantly broaden their range of practical applications. </sec><sec> In this paper, we mainly outline the research history and recent progress of acoustic metamaterials and topological phononic crystals by presenting representative achievements, including effective acoustic parameters and nontrivial properties. First, we roughly classify the acoustic metamaterials into two types according to the structural characteristics of the meta-atoms. The first type is resonant acoustic metamaterials containing resonant meta-atoms, such as locally resonant structures, resonant membranes, and Helmholtz resonators. The second type is non-resonant acoustic metamaterials, which are composed of non-resonant meta-atoms, such as space-coiled and coupled filter-element structures. Then, based on this classification and according to the dimensional periodicity, the unique physical properties (such as negative mass density and negative bulk modulus) of different acoustic metamaterials and their ability to regulate the acoustic fields (such as acoustic cloak, super-resolution imaging, and abnormal sound transmission) are briefly reviewed. Second, we introduce the topological properties and construction methods of topological phononic crystals. The topological phononic crystals can be classified into two types according to their topological nature: Conventional topological phononic crystals and higher-order topological phononic crystals, which are characterized by the first-order (e.g., Chern numbers) and higher-order (e.g., quadrupole moments) topological invariants, respectively. In general, D-dimensional conventional phononic crystals host (D-1)-dimensional topological states at the boundaries of the systems. However, different from the conventional topological cases, the hallmark of the D-dimensional <italic>n</italic>-order higher-order phononic crystals is the existence of topological modes at (D-<italic>n</italic>)-dimensional boundaries of the systems, e.g., zero-dimensional corner modes of a two-dimensional system and one-dimensional hinge modes of a three-dimensional system. Under this background, the different topological phononic crystals, such as (higher-order) acoustic topological insulators and (higher-order) acoustic topological semimetals, and their potential applications are briefly reviewed. The development of topological phononic crystals has brought numerous unprecedented effects into acoustics, such as topological reflection, topological negative refraction, topological ‘sasers’ (i.e. the phononic analog of lasers) and non-Hermitian topological phononic crystals. Finally, we discuss the applications and existing challenges of acoustic metamaterials and topological phononic crystals, and provide an overview of future directions in the field. </sec>