Topological phases of matter have been extensively investigated in solid state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain largely unexplored. Fractals, being nearly the same at different scales, are one of the intriguing complex geometries with non-integer dimensions. Here, we demonstrate acoustic Sierpiński fractal topological insulators with unconventional higher-order topological phenomena via consistent theory and experiments. We discover abundant topological edge and corner states emerging in our acoustic systems due to the rich edge and corner boundaries inside the fractals. Interestingly, the numbers of the edge and corner states scale the same as the bulk states with the system size and the exponents coincide with the Hausdorff fractal dimension of the Sierpiński carpet. Furthermore, the emergent corner states exhibit unconventional spectrum and wave patterns. Our study opens a pathway toward topological states in fractal geometries.
We describe the out-of-plane bending of chiral fractal lattices metamaterials by using a combination of theoretical models, full-scale finite elements and experimental tests representing the flexural behaviour of metamaterial beams under three-point bending. Good agreement is observed between the three sets of results. Parametric analyses show a linear log-log relation between bending modulus and aspect ratios of the unit cells, which are indicative of the fractal nature of the metamaterial. The ratio between the bending and in-plane tensile moduli of these chiral fractal metamaterials ranges …
Metamaterials have recently established a new paradigm for enhanced light absorption in state-of-the-art photodetectors. Here, we demonstrate broadband, highly efficient, polarization-insensitive, and gate-tunable photodetection at room temperature in a novel metadevice based on gold/graphene Sierpinski carpet plasmonic fractals. We observed an unprecedented internal quantum efficiency up to 100% from the near-infrared to the visible range with an upper bound of optical detectivity of $10^{11}$ Jones and a gain up to $10^{6}$, which is a fingerprint of multiple hot carriers photogenerated in g…
We introduce a class of Parity-Time symmetric elastodynamic metamaterials (Ed-MetaMater) whose Hermitian counterpart exhibits a frequency spectrum with unfolding (fractal) symmetries. Our study reveals a scale-free formation of exceptional points (EP) whose density is dictated by the fractal dimension of their Hermitian spectra. Demonstrated in a quasi-periodic Aubry-Harper, a geometric H-tree-fractal, and an aperiodic Fibonacci Ed-MetaMater, the universal route for EP-formation is established via a coupled mode theory model with controllable fractal spectrum. This universality will enable the…
Mechanical metamaterials are architected manmade materials that allow for unique behaviors not observed in nature, making them promising candidates for a wide range of applications. Existing metamaterials lack tunability as their properties can only be changed to a limited extent after the fabrication. In this paper, we present a new magneto-mechanical metamaterial that allows great tunability through a novel concept of deformation mode branching. The architecture of this new metamaterial employs an asymmetric joint design using hard-magnetic soft active materials that permits two distinct act…
Acoustic negative-index metamaterials show promise in achieving superlensing for diagnostic medical imaging. In spite of the recent progress made in this field, most metamaterials suffer from deficiencies such as low spatial symmetry, sophisticated labyrinth topologies and narrow-band features, which make them difficult to be utilized for symmetric subwavelength imaging applications. Here, we propose a category of robust multi-cavity metamaterials and reveal their common double-negative mechanism enabled by multi-polar (dipole, quadrupole and octupole) resonances in both two-dimensional (2D) a…
Double-negative acoustic metamaterials (AMMs) offer the promising ability of superlensing for applications in ultrasonography, biomedical sensing and nondestructive evaluation. Here, under the simultaneous increasing or non-increasing mechanisms, we develop a unified topology optimization framework considering the different microstructure symmetries, minimal structural feature sizes and dispersion extents of effective parameters. Then we apply the optimization framework to furnish the heuristic resonance-cavity-based and space-coiling metamaterials with broadband double negativity. Meanwhile, …
We numerically analyze the performance of labyrinthine acoustic metamaterials with internal channels folded along a Wunderlich space-filling curve to control low-frequency sound in air. In contrast to previous studies, we perform direct modeling of wave propagation through folded channels, not introducing effective theory assumptions. As a result, we reveal that metastructures with channels, which allow wave propagation in the opposite direction to incident waves, have different dynamics as compared to those for straight slits of equivalent length. The differences are attributed to activated t…
We propose a class of metamaterials in which propagation of acoustic waves is controlled magnetically through magnetoelastic coupling. The metamaterials are formed by a periodic array of thin magnetic layers ('resonators') embedded in a non-magnetic matrix. Acoustic waves carrying energy through the structure hybridize with the magnetic modes of the resonators ('Fano resonance'). This leads to a rich set of effects, enhanced by Bragg scattering and being most pronounced when the magnetic resonance frequency is close to or lies within acoustic band gaps. The acoustic reflection from the structu…
Symmetries crucially underlie the classification of topological phases of matter. Most materials, both natural as well as architectured, possess crystalline symmetries. Recent theoretical works unveiled that these crystalline symmetries can stabilize fragile Bloch bands that challenge our very notion of topology: while answering to the most basic definition of topology, one can trivialize these bands through the addition of trivial Bloch bands. Here, we fully characterize the symmetry properties of the response of an acoustic metamaterial to establish the fragile nature of the low-lying Bloch …
Nonlinear acoustic metamaterials (NAMs) open new freedoms in exploiting novel technologies for wave manipulations. Recently, the desired ultra-low and ultra-broad-band wave suppressions were achieved by the chaotic bands in NAMs [Nature Commun. 8, 1288 (2017)]. This work describes a remote interaction mechanism in NAMs-bridging coupling of nonlinear locally resonant bandgaps. Bridging bandgaps generate chaotic bands and share the negative mass between nonlinear resonators. The bandwidth and the efficiency for the wave reduction in chaotic bands can be manipulated effectively by modulating the …
In the past years classical wave-systems have constituted an excellent platform for emulating complex quantum phenomena. This approach has been especially fruitful in demonstrating topological phenomena in photonics and acoustics: from chiral edge states of Chern insulators and helical edge states of topological insulators to higher-dimensional topological states of quasiperiodic systems and systems with synthetic dimensions. Recently, a new class of topological states localized in more than one dimension of a D-dimensional system, referred to as higher-order topological (HOT) states, has been…
Tetrachiral materials are characterized by a cellular microstructure made by a periodic pattern of stiff rings and flexible ligaments. Their mechanical behaviour can be described by a planar lattice of rigid massive bodies and elastic massless beams. The periodic cell dynamics is governed by a monoatomic structural model, conveniently reduced to the only active degrees-of-freedom. The paper presents an explicit parametric description of the band structure governing the free propagation of elastic waves. By virtue of multiparametric perturbation techniques, sensitivity analyses are performed to…
A general process is proposed to experimentally design anisotropic inhomogeneous metamaterials obtained through a change of coordinate in the Helmholtz equation. The method is applied to the case of a cylindrical transformation that allows to perform cloaking. To approximate such complex metamaterials we apply results of the theory of homogenization and combine them with a genetic algorithm. To illustrate the power of our approach, we design three types of cloaks composed of isotropic concentric layers structured with three types of perforations: curved rectangles, split rings and crosses. The…
Using transfer-matrix methods, we investigate the response of a multilayered metamaterial system containing defects to an incident acoustic plane wave at normal or oblique incidence. The transmission response is composed of pass-bands with oscillatory behaviour, separated by band gaps and covers a wide frequency range. The presence of gain and loss in the layers leads to the emergence of symmetry breaking and re-entrant phases. In the general case, a system containing defects will display a more general property, pseudo-Hermiticity (PH), of which $\mathcal{PT}$ systems are a subset. In the PH-…
