Topological Phononic Logic

Science Bulletin, 2021

The recent discovery and realizations of higher-order topological insulators enrich the fundamental studies on topological phases. Here, we report three-dimensional (3D) wave-steering capabilities enabled by topological boundary states at three different orders in a 3D phononic crystal with nontrivial bulk topology originated from the synergy of mirror symmetry of the unit cell and a non-symmorphic glide symmetry of the lattice. The multitude of topological states brings diverse possibility of wave manipulations. Through judicious engineering of the boundary modes, we experimentally demonstrate two functionalities at different dimensions: 2D negative refraction of sound wave enabled by a firstorder topological surface state with negative dispersion, and a 3D acoustic interferometer leveraging on second-order topological hinge states. Our work showcases that topological modes at different orders promise diverse wave steering applications across different dimensions.

Entirely new, more exotic applications in electronics, including quantum computers, are also conceivable. The research was published in Nature Communications. [35] Researchers have succeeded in controllably propagating sound waves along the boundaries of topological metamaterials using a modulation technique that breaks timereversal symmetry. [34] NUS physicists have found a new way to create and tune the topological edge states in two-dimensional (2-D) topological insulators (TIs) for potential spintronic device applications. [33] With their insensitivity to decoherence, Majorana particles could become stable building blocks of quantum computers. [32]

Physical Review B

The Berry phase generally plays a key role in characterizing the topological phase for quantum and classic systems. However, topological edge states in a two-dimensional acoustic system are generally characterized by nonzero Berry curvature. Here we achieve the topological phase transition characterized by zero Berry curvature, based on the phononic crystal composed of 8-metaatomic composite metamolecules. We demonstrate that the phase transition can be induced through either modulating the intervals between the adjacent metaatoms or changing their sizes. The nontrivial Zak phase ensures the existence of the acoustic topological edge states, confining sound waves along the boundaries of finite sonic crystal rather than transmitting along the interface between the two structures possessing opposite topological phases. Furthermore, the multiple topological phase transitions are simply realized thanks to the two limbic metaatoms introduced. Although the eigenfrequencies of topological edge states, which appear in the partial band gap, overlap with the bulk states, we still numerically observe the topological edge states selectively through modulating the wavenumber in real space. The proposed acoustic topological insulator may have potential applications in acoustic waveguiding and isolating.

arXiv (Cornell University), 2022

Topological physics has revolutionised materials science, introducing topological insulators and superconductors with applications from smart materials to quantum computing. Bulk-boundary correspondence (BBC) is a core concept therein, where the non-trivial topology of a material's bulk predicts localized topological states at its boundaries. However, edge states also exist in systems where BBC is seemingly violated, leaving any topological origin unknown. For finitefrequency mechanical metamaterials, BBC has hitherto been described in terms of displacements, necessitating fixed boundaries to identify topologically protected edge modes. Herein, we introduce a new family of finite-frequency mechanical metamaterials whose topological properties emerge in strain coordinates for free boundaries. We show two examples, the first being the canonical massdimer, where BBC in strain coordinates reveals the previously unknown topological origin of its edge modes. Second, we introduce a new mechanical analog of the Majorana-supporting Kitaev chain. We theoretically and experimentally show that this Kitaev chain supports edge states for both free and fixed boundaries, wherein BBC is established in strains and displacements, respectively. Our findings suggest a previously undiscovered class of topological edge modes may exist, including within other settings such as electrical circuits and optics, and for more complex, tailored boundaries with coordinates other than strain.

Journal of the Mechanics and Physics of Solids, 2019

We propose a computational methodology to perform inverse design of quantum spin hall effect (QSHE)-based phononic topological insulators. We first obtain twofold degeneracy, or a Dirac cone, in the band structure using a level set-based topology optimization approach. Subsequently, four-fold degeneracy, or a double Dirac cone, is obtained by using zone folding, after which breaking of translational symmetry, which mimics the effect of strong spin-orbit coupling and which breaks the four-fold degeneracy resulting in a bandgap, is applied. We use the approach to perform inverse design of hexagonal unit cells of C 6 and C 3 symmetry. The numerical examples show that a topological domain wall with two variations of the designed metamaterials exhibit topologically protected interfacial wave propagation, and also demonstrate that larger topologically-protected bandgaps may be obtained with unit cells based on C 3 symmetry.

Frontiers in Materials, 2021

Many engineering applications leverage metamaterials to achieve elastic wave control. To enhance the performance and expand the functionalities of elastic waveguides, the concepts of electronic transport in topological insulators have been applied to elastic metamaterials. Initial studies showed that topologically protected elastic wave transmission in mechanical metamaterials could be realized that is immune to backscattering and undesired localization in the presence of defects or disorder. Recent studies have developed tunable topological elastic metamaterials to maximize performance in the presence of varying external conditions, adapt to changing operating requirements, and enable new functionalities such as a programmable wave path. However, a challenge remains to achieve a tunable topological metamaterial that is comprehensively adaptable in both the frequency and spatial domains and is effective over a broad frequency bandwidth that includes a subwavelength regime. To advance the state of the art, this research presents a piezoelectric metamaterial with the capability to concurrently tailor the frequency, path, and mode shape of topological waves using resonant circuitry. In the research presented in this manuscript, the plane wave expansion method is used to detect a frequency tunable subwavelength Dirac point in the band structure of the periodic unit cell and discover an operating region over which topological wave propagation can exist. Dispersion analyses for a finite strip illuminate how circuit parameters can be utilized to adjust mode shapes corresponding to topological edge states. A further evaluation provides insight into how increased electromechanical coupling and lattice reconfiguration can be exploited to enhance the frequency range for topological wave propagation, increase achievable mode localization, and attain additional edge states. Topological guided wave propagation that is subwavelength in nature and adaptive in path, localization, and frequency is illustrated in numerical simulations of thin plate structures. Outcomes from the presented work indicate that the easily integrable and comprehensively tunable proposed metamaterial could be employed in applications requiring a multitude of functions over a broad frequency bandwidth.

Laser & Photonics Reviews

Photonic topological insulators supporting unidirectional topologically protected edge states represent attractive platform for realization of disorder-and backscatteringimmune transport of edge excitations in both linear and nonlinear regimes. In many realizations of topological insulators structured periodic materials are used, since they may admit specific Dirac degeneracy in the spectrum, around which unidirectional edge states appear under the action of physical effects breaking time-reversal symmetry. While properties of the edge states at unclosed interfaces of two bulk media with different topology are known, the existence of the edge states in practical finite-dimensional topological insulators fully immersed in nontopological environment remains largely unexplored. In this work using as an example realistic polariton topological insulators built from small-size honeycomb arrays of microcavity pillars, we illustrate how topological properties of the system build up upon gradual increase of its dimensionality. To account for dissipative nature of polariton condensate forming in the array of microcavity pillars, we consider the impact of losses and resonant pump leading to rich bistability effects in this system. We describe the mechanism in accordance with which trivial-phase pump "selects" and excites specific nonlinear topological edge states circulating along the periphery of the structure in the azimuthal direction dictated by the direction of the external applied magnetic field. We also show the possibility of utilization of vortex pump with different topological charges for selective excitation of different edge currents.

Proceedings of the National Academy of Sciences, 2020

Topological edge modes are excitations that are localized at the materials’ edges and yet are characterized by a topological invariant defined in the bulk. Such bulk–edge correspondence has enabled the creation of robust electronic, electromagnetic, and mechanical transport properties across a wide range of systems, from cold atoms to metamaterials, active matter, and geophysical flows. Recently, the advent of non-Hermitian topological systems—wherein energy is not conserved—has sparked considerable theoretical advances. In particular, novel topological phases that can only exist in non-Hermitian systems have been introduced. However, whether such phases can be experimentally observed, and what their properties are, have remained open questions. Here, we identify and observe a form of bulk–edge correspondence for a particular non-Hermitian topological phase. We find that a change in the bulk non-Hermitian topological invariant leads to a change of topological edge-mode localization ...

Nature Photonics, 2014

The application of topology, the mathematics studying conserved properties through continuous deformations, is creating new opportunities within photonics, bringing with it theoretical discoveries and a wealth of potential applications. This field was inspired by the discovery of topological insulators, in which interfacial electrons transport without dissipation even in the presence of impurities. Similarly, the use of carefully-designed wave-vector space topologies allows the creation of interfaces that support new states of light with useful and interesting properties. In particular, it suggests the realization of unidirectional waveguides that allow light to flow around large imperfections without back-reflection. The present review explains the underlying principles and highlights how topological effects can be realized in photonic crystals, coupled resonators, metamaterials and quasicrystals.

Scientific reports, 2014

Condensed matter systems with topological order and metamaterials with left-handed chirality have attracted recently extensive interests in the fields of physics and optics. So far the topological order and chirality of electromagnetic wave are two independent concepts, and there is no work to address their connection. Here we propose to establish the relation between the topological order in condensed matter systems and the chirality in metamaterials, by mapping explicitly Maxwell's equations to the Dirac equation in one dimension. We report an experimental implement of the band inversion in the Dirac equation, which accompanies change of chirality of electromagnetic wave in metamaterials, and the first microwave measurement of topological excitations and topological phases in one dimension. Our finding provides a proof-of-principle example that electromagnetic wave in the metamaterials can be used to simulate the topological order in condensed matter systems and quantum phenomena in relativistic quantum mechanics in a controlled laboratory environment. OPEN SUBJECT AREAS: METAMATERIALS TOPOLOGICAL INSULATORS