Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session N66: Metamaterials and Hyperbolic LatticesRecordings Available

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Sponsoring Units: DCMP Chair: Andreas Riemann, Western Washington University Room: Hyatt Regency Hotel Grant Park D 
Wednesday, March 16, 2022 11:30AM  11:42AM 
N66.00001: Wearable Mechanical Textile Metamaterials David Farrell, Connor McCann, Antonio Elia Forte, Reza Sourki, Conor Walsh, Katia Bertoldi Textiles are ubiquitous in our daily lives and appear everywhere from apparel to wearable robots. On one hand, stretchable knits are used in clothing for comfort and their ability to conform to our body. On the other hand, stiff woven textiles are utilized in functional garments to direct forces and support loads (e.g. backpack straps). Here, we combine a stretchable knit and a stiff woven to realize textile metamaterials that are comfortable but capable of directing forces to target locations. We use inverse design tools to identify spatially varying architectures that can manipulate forces across the fabric, while leaving desired areas undeformed. Furthermore, we show that our metamaterials can be engineered to support target deformation modes such as dimples that can be exploited to realize a new generation of wearable devices. 
Wednesday, March 16, 2022 11:42AM  11:54AM 
N66.00002: Terahertz Beam Steering with Phase Change Based Metasurfaces Zizwe A Chase, Riad Yahiaoui, Xi Wang, Zhixiang Huang, Thomas A Searles We demonstrate dynamic control of beam steering applications by using a phase change material, VO_{2}, to form a 2gap split ring resonators supported on a sapphire substrate. A combination of a series of terahertz metadeflectors comprised of geometrically optimized 2gap split ring resonators were employed to achieve a phase shift that covers a broad range of 02π. This device will operate in the linear crosspolarization regime within the 0.21 THz frequency band. The use of VO_{2} allows for a dynamically controlled on/off state that manipulates the angle of deflection of the transmitted beam. The scheme could be exploited for developing novel highly efficient switchable THz polarization beam deflectors. 
Wednesday, March 16, 2022 11:54AM  12:06PM 
N66.00003: Tunable nonlinear metasurfaces for controlling the propagation of nonlinear waves Majid Kheybari, Osama R Bilal Metamaterials which are often periodic arrangement of unit cells, are artificial materials that can manipulate waves in a desirable manner. These metamaterials can be designed in various shapes and geometries to possess band gaps, or frequency regions, where waves are not allowed to propagate. Once a unit cell geometry is realized, its properties along with its operational frequencies are fixed. Having tunable metamaterials with ondemand property change is desirable. Here, we present a class of metamaterials that takes advantage of geometric and magnetic nonlinearities to tune the propagation of nonlinear waves. The tuning takes place on the level of each unit cell individually, giving rise to vast space of applications. 
Wednesday, March 16, 2022 12:06PM  12:18PM 
N66.00004: Experimental Study on the Effects of Hierarchical Handedness on Auxetic Chiral Mechanical Metamaterial under Different Temperatures Siyao Liu, Yaning Li Periodic mechanical metamaterials with hierarchical handedness are designed. Specifically, four hierarchical representative volume elements (RVE) are developed: design A has a righthanded chiral core in the center of a lefthanded chiral cell; design B has a lefthanded chiral core in the center of a lefthanded chiral cell; designs C and D are the multimaterial versions of design A and design B, respectively, by adding soft corners at critical locations. Specimens of the four designs are fabricated via a multimaterials 3D printer (Stratasys Connex3). Uniaxial tension experiments are conducted under various temperatures in a thermal chamber. The effective mechanical properties including the effective stiffness, the effective Poisson’s ratio, rotation efficiency, ultimate strength, and fracture strain of the designs are obtained from the mechanical experiments. In addition, 3D finite element models of the designs are developed in ABAQUS to support the experiments. Design guidelines for desired properties related to auxeticity, rotation efficiency, effective stiffness, and the shearnormal coupling effects will be provided. The experimental and numerical results show that the core handedness and stiffness ratio can significantly influence the effective mechanical properties of hierarchical chiral designs. 
Wednesday, March 16, 2022 12:18PM  12:30PM 
N66.00005: Extreme dynamics from transition waves in bistable metastructures Myungwon Hwang, Andres F Arrieta Metastructures with underlying bistable microstructure have shown strongly nonlinear interaction between the transition waves and the structural modes, resulting in inputindependent frequency conversion. The studied architecture has also provided a new paradigm for designing metamaterials and metastructures by breaking the strong correlation between the unit cell structures and the apparent macroscopic dynamics. In this study, the reciprocal behavior of the same architecture is explored, such that excitations at the macroscopic structural level induce transition waves within the microstructure. The constituting unit cell has a wide variety of tunable parameters, which can be adjusted to match the operating conditions or alter the response characteristics. Notably, the lattice discreteness can control the amount of radiated energy in the form of phonons trailing main transition waves. Thus, the studied architecture can be used to redirect and dissipate the energy from potentially dangerous ambient sources or power core infrastructures with integrated energy transduction mechanisms. Furthermore, the induced transition waves can still alter the macroscopic response of the metastructures, disrupting or neutralizing any unwanted input sources. 
Wednesday, March 16, 2022 12:30PM  12:42PM 
N66.00006: The surface plasmonic waves in multicoaxial negativeindex metamaterial cables Manvir S Kushwaha, Bahram DjafariRouhani By using an elegant response function theory, which does not require matching of the messy boundary conditions, we investigate the surface plasmon excitations in the multicoaxial cylindrical cables made up of negativeindex metamaterials. The multicoaxial cables with dispersive metamaterial components exhibit a rather richer (and complex) plasmon spectrum with each interface supporting two modes: one TM and the other TE for m0 (the integer order of the Bessel function). The cables with nondispersive metamaterial components bear a different tale: they do not support simultaneously both TM and TE modes over the whole range of propagation vector. The computed local and total density of states enable us to substantiate spatial positions of the modes in the spectrum. Such quasionedimensional systems as studied here should prove to be the milestones of the emerging optoelectronics and telecommunications systems. 
Wednesday, March 16, 2022 12:42PM  12:54PM 
N66.00007: Topological hyperbolic band insulators David M Urwyler, Patrick M Lenggenhager, Titus Neupert, Tomas Bzdusek The recently formulated hyperbolic band theory allows to describe singleparticle energy states of tightbinding models in negatively curved spaces. The most salient feature of this theory is the unusually large dimension of the momentum space: the spectrum of particles on a twodimensional hyperbolic lattice necessitates a characterization with an at least fourdimensional Brillouin zone. Such higherdimensional momentum spaces imply the existence of a larger set of topological band invariants than for the Euclidean lattices, suggesting potentially new types of topological hyperbolic matter. 
Wednesday, March 16, 2022 12:54PM  1:06PM 
N66.00008: Automorphic Bloch theorems for hyperbolic lattices Joseph Maciejko, Steven Rayan Hyperbolic lattices are a new form of synthetic quantum matter in which particles effectively hop on a discrete tessellation of twodimensional hyperbolic space, a nonEuclidean space of uniform negative curvature. To describe the singleparticle eigenstates and eigenenergies for hopping on such a lattice, a hyperbolic generalization of band theory was previously constructed, based on ideas from algebraic geometry. In this hyperbolic band theory, eigenstates are automorphic functions, and the Brillouin zone is a higherdimensional torus, the Jacobian of the compactified unit cell understood as a highergenus Riemann surface. Three important questions were left unanswered: (1) whether a band theory can be expected to hold for a nonEuclidean lattice, where translations do not generally commute; (2) whether a formal Bloch theorem can be rigorously established; and (3) whether hyperbolic band theory can describe finite lattices realized in experiment. In the present work, we address all three questions simultaneously. By formulating periodic boundary conditions for finite but arbitrarily large lattices, we show that a generalized Bloch theorem can be rigorously proved, but may or may not involve higherdimensional irreducible representations (irreps) of the nonabelian translation group, depending on the lattice geometry. Higherdimensional irreps corrrespond to points in a moduli space of higherrank stable holomorphic vector bundles, which further generalizes the notion of Brillouin zone beyond the Jacobian. For a large class of finite lattices, only onedimensional irreps appear, and the hyperbolic band theory previously developed becomes exact. 
Wednesday, March 16, 2022 1:06PM  1:18PM 
N66.00009: Hofstadter's butterfly in the hyperbolic plane Alexander Stegmaier, Lavi K Upreti, Ronny Thomale, Igor Boettcher Applying a magnetic field to an electron in a twodimensional crystal lattice produces a spectrum that is widely known as Hofstadter's butterfly. Hofstadter's results however only apply to lattices that are embedded in flat (Euclidean) space. In light of the recent interest in hyperbolic lattices, we reconsider Hofstadter's problem on hyperbolic {p,q} lattices beyond the Euclidean {4,4} square lattice of the original calculation. For this, we implement periodic boundaries in hyperbolic space, eliminating the extensive edge mode contributions that would otherwise cloud the spectrum. We present the resulting magnetic spectra for a variety of {p,q} lattices and observe distinct features of these hyperbolic Hofstadter butterflies such as the loss of fractality and a systematic dependence between the type of lattice and spectral features. 
Wednesday, March 16, 2022 1:18PM  1:30PM 
N66.00010: Electriccircuit realization of a hyperbolic drum Patrick M Lenggenhager, Alexander Stegmaier, Lavi K Upreti, Tobias Hofmann, Tobias Helbig, Achim Vollhardt, Martin Greiter, Ching Hua Lee, Stefan Imhof, Hauke Brand, Tobias Kießling, Igor Boettcher, Titus Neupert, Ronny Thomale, Tomas Bzdusek The recent development of hyperbolic band theory, which describes energy spectra of particles on hyperbolic lattices, revived interest in crystalline models embedded in negatively curved spaces and sparked the search for suitable experimental realizations. We argue that electric circuits offer a highly versatile and easily fabricable platform to test this theory and to investigate a wide range of hyperbolic tightbinding models, while providing direct access to local degrees of freedom. To demonstrate this flexibility, we emulate a diskshaped sample of the hyperbolic {3,7} lattice (i.e., the regular tessellation where seven equilateral triangles meet at each vertex), for which the lowenergy modes are effectively described by the LaplaceBeltrami operator. Using this system, which we call “hyperbolic drum”, we reveal evidence of the negative curvature in both static and dynamical experiments. First, we measure the spectral ordering of the Laplacian eigenstates which is universally different in hyperbolic vs. flat twodimensional spaces. Second, we verify signal propagation along curved geodesics. Our experiments showcase that electric circuits can be utilized to explore the propagation dynamics in curved spaces and to realize models of topological hyperbolic matter.

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