Session M10: Metamaterials and Hyperbolic Lattices

Observation of Ordinary and High-order van Hove Singularities in Macroscopic Non-local Metamaterials

The van Hove singularity is a prominent phenomenon in periodic systems, attributed to the presence of maxima, minima, and undulation points of bands in the energy dispersion in momentum space. In this context, we report direct observations of ordinary and high-order van Hove singularity in macroscopic vibro-elastic metamaterials, achieved through one-dimensional discrete chains with designed nonlocal interactions. One experiment identifies a new feature - a stationary inflection point on the dispersion curve, which is indicative of a second-order van Hove singularity, where waves neither propagate nor spread in metamaterials. Another experiment demonstrates a maxon-roton-like dispersion relation, in which group velocity direction changes between given frequencies, resulting in three different coexisting acoustical modes at one frequency. This study demonstrates unprecedented phenomena of wave propagation. It accomplishes the accurate tailoring of fundamental dispersion bands and enables precise manipulation of waves by metamaterials.   

Multimodal higher-order topological metamaterial for multifunctional elastic wave-based computing

Elastic metamaterials have emerged as a promising platform for the realization of wave-based computing in mechanical devices that mimic electronic computing operations. Higher-order topological metamaterials are a specific class of elastic metamaterials that takes inspiration from condensed matter physics to confine elastic waves through waveguides across a hierarchy of unique dimensions. However, higher-order topological metamaterials have yet to be explored in the context of elastic wave-based computing. To address this research opportunity, this research proposes a 2D higher-order topological metamaterial that harnesses multiband 0D topological corner states to create multifunctional elastic wave-based computing elements. The proposed metamaterial is a 2D thin plate with embedded resonators that are geometrically configured to enable multimodal resonances. Eigenfrequency studies uncover 0D corner states that emerge in four different frequency ranges and have unique displacement field characteristics. Frequency response simulations illustrate how the diverse attributes of the multiband 0D corner states can be employed to create Boolean logic gates. A design scheme is created such that each of the fundamental Boolean logic gates can be realized in the metamaterial, which has versatile modes of operation that depend on the excitation frequency and phase. The outcomes from this study reveal the potential of higher-order topological phases for wave-based mechanical computing.   

Directly layer-resolved observation of flat-band in phononic magic-angle twisted bilayer graphene

In recent years, twistronics has gradually become an exciting upsurging topic. Among them, with the flat bands of the quasiparticle excitations, magic-angle twisted bilayer graphene can lead to exotic phenomena, including superconductivity, Mott insulating phases, and topological-related states. Many phenomena have been experimentally observed in magic-angle twisted bilayer graphene. However, the microscopic and layer-resolved excitations within the flat bands are still not directly probed. Such excitation is critical to provide a direct understandings of the coherent coupling between the two layers with subtle interlayer interactions, which is technically limited in condensed matter systems due to the lack of minimally invasive probes between the two layers of material, e.g., graphene. Here, by utilizing a phononic analog of magic-angle twisted bilayer graphene (PTBG), we directly measure excitations of each layer at the magic twist angle, enabling in situ layer resolution of the flat-band behavior. Supported by theoretical modeling, our layer-resolved measurement provides a direct understanding and interpretation of the perturbations inside the PTBG system. In magic-angle PTBG, the perturbation created by interlayer coupling is significant and highly nontrivial, strongly reshaping the low-energy states of each layer. In large-angle PTBG, low-energy states are only mildly affected by the moiré effect and can be approximated as two decoupled Dirac cones from individual layers. This work extends twistronics to artificial crystals and provides new approaches to investigate fundamental physics.   

Exploration of Angle-Dependent Klein Tunneling in Snowflake-Shaped AlN Thin Film Phononic Crystals

This study focuses on design fabrication of snowflake-shaped Aluminum Nitride (AlN) thin film phononic crystals. In the suspended configuration, these structures exhibit the Klein Tunneling effect, allowing reflection-free wave transmission. Notably, the interdigital transducer's angle modulates the angle-dependency of this effect. Employing the impedance-matching microscope (TMIM) for detailed analysis, we deciphered the phononic behavior influenced by the Klein Tunneling phenomenon. Our findings spotlight the potential of snowflake-shaped AlN phononic crystals in advanced wave manipulation applications.   

Carrier Density Tunable CdO Thin Film Heterostructures by Ion Beam Irradiative Patterning for Mid-IR Plasmonic Metamaterials

Epitaxial cadmium oxide (CdO) thin films grown by high-power impulse magnetron sputtering (HiPIMS) are premier platforms for low-loss mid-IR optoelectronic devices. Herein, defect engineering and dopant activation for optically sharp, laterally patterned CdO heterostructures are executed by modulated carrier density profiles via ion beam irradiation. Low- (30 keV) to high-energy (1-3 MeV) ion irradiation are facilities to define CdO carrier density grating arrays unlike conventional TCO methods. Nanometer periodicity at 30 keV and micrometer resolution at 1-3 MeV are achievable. While optimal thermal activation, defect site imaging by TEM, and spectral analysis by micro-FTIR are ongoing, preliminary data indicate FIB-produced gratings by Ga³⁺ are locally activated by peak shifts and narrowing according to free carrier generation and mobility enhancement by Raman spectroscopy. Although defects affect local microstructure, epitaxy is maintained post-irradiation. Ion irradiation at 1-3 MeV develops a carrier density window of 2.5 x 10¹⁹ - 2.5 x 10²⁰ cm^-3 and mobilities upwards of 200 cm²V^-1s^-1 relative to displacement damage dose (DDD). Near- and far-field optical measurements identify local carrier density and mobility effects, as well as plasmon dispersion maps by ATR pair simulation to experimental data. Overall, these ion-beam modification methods show promising capabilities to design new lateral patterning techniques for spatially coherent CdO metamaterials in the mid-IR.   

Analysis of metal-dielectric structures for broadband light manipulation

Metal-dielectric composites exhibit unique optical properties in the visible wavelength range. The use of plasmonic/dielectric composites was previously studied for the design of light absorbers [1], [2] .  Multiple metal-dielectric layers have thicknesses from several nm to tens of nm. This work presents solutions for effective optical properties of Ag/SiO₂ metamaterial structures. We specifically explore effects of aperiodic layer thicknesses. Our theoretical model is supplemented wirh computations. Desired broadband optical properties are obtained by optimizing  structure dimensions. Incident light can be linearly polarized or unpolarized. Applications of this research include antireflection coatings and light-trapping structures.

[1] N.Mattiucci , M. J. Bloemer , N. Akozbek. G. D’Aguanno, Impedance matched thin metamaterials make metals absorbing, Scientific Reports, 3:3203, 2013.

[2] Christian Harris, Dongxia Wei, Stephanie Law, Andrey  Semichaevsky, Semiconductor-based mid-IR metamaterials: experimental and theoretical studies, APS March Meeting, Baltimore, MD, March 14, 2016   

GNN-based Inverse Design of Three-Dimensional Aperiodic Metamaterials Enabling Programmable Shapes

Artificially structured materials including metamaterials can exhibit unique or target properties via the rationally designed microstructures. Compared with the periodic design of metamaterials, an aperiodic configuration enables a more flexible design space and more sophisticated responses, which shows promise for many engineering applications. However, the corresponding complex modelling method and expensive calculation cost make the inverse design of big metamaterial-based system a big challenge. Here, an aperiodic design method of three-dimensional (3D) lattice metamaterials that enables tunable morphing distributions is proposed. First, we develop a theoretical model for arbitrary curled truss microstructures which are then assembled into the lattice metamaterials in three dimensions. Next, the constitutive relation and Poisson's ratio of the 3D metamaterial are predicted by the proposed model along with the validations of finite-element analysis (FEA) and mechanical experiment. Furthermore, by a parametric design modelling considering deep learning (DL), a GNN-trained database of the structure-property relationship is constructed. Finally, given a certain size of metamaterials with target shape under external load, the optimal geometry parameters are identified via an improved particle swarm algorithm. Our work shows an effective and efficient inverse design framework to program the shape of 3D metamaterials.   

Breakdown of Conventional Winding Number Calculation in One-Dimensional Lattices with Interactions Beyond Nearest Neighbors

Topological indices, such as winding numbers, have been conventionally used to predict the number of topologically protected edge states (TPESs) in topological insulators, a signature of the topological phenomenon called bulk-edge correspondence. In this work, we theoretically and experimentally demonstrate that the number of TPESs at the domain boundary of a Su-Schrieffer-Heeger (SSH) model can be higher than the winding number depending on the strengths of beyond-nearest neighbors, revealing the breakdown of the winding number prediction. Hence, we resort to the Berry connection to accurately count the number of TPESs in an SSH system with a domain boundary. Moreover, the Berry connection can elucidate wavelengths of the TPESs, which is further confirmed using the Jackiw Rebbi theory. We analytically prove that each of the multiple TPES modes at the domain boundary corresponds to a bulk Dirac cone, asserting the robustness of the Berry connection method, which offers a generalized paradigm for TPES prediction.   

Hyperbolic lattices and two-dimensional Yang-Mills theory

Hyperbolic lattices are a new type of synthetic matter emulated in circuit quantum electrodynamics and electric-circuit networks, where particles coherently hop on a discrete tessellation of two-dimensional negatively curved space. While real-space methods and a reciprocal-space hyperbolic band theory have been recently proposed to analyze the energy spectra of those systems, discrepancies between the two sets of approaches remain. In this work, we reconcile those approaches by first establishing an equivalence between hyperbolic band theory and U(N) topological Yang-Mills theory on higher-genus Riemann surfaces. We then show that moments of the density of states of hyperbolic tight-binding models correspond to expectation values of Wilson loops in the quantum gauge theory and become exact in the large-N limit.   

HyperCells and HyperBloch: open-source software packages for studying hyperbolic lattices based on triangle groups

Hyperbolic lattices form the analogue of periodic structures in the hyperbolic plane and have been experimentally realized as networks in various metamaterial platforms such as coplanar-waveguide resonators and electric circuits. Naturally, the lattices possess discrete translation symmetry. However, due to the negative curvature, the resulting translation group is non-commutative which complicates not only the formulation of band theory but also the construction of periodic boundary conditions that converge to the thermodynamic limit. Both infinite lattices and finite clusters with periodic boundary conditions can be conveniently described in terms of triangle groups, which take the role of the space groups.

In this talk, I am going to introduce two recently released open source software packages, called HyperCells and HyperBloch, which provide convenient tools to construct connected and symmetric unit cells, including the associated translations, define arbitrary tight-binding models on them, and apply the recently developed supercell method for hyperbolic band theory to gain access at infinite-lattice eigenstates and -energies. The construction is based on an algebraic description of the lattice in terms of the corresponding triangle group, which facilitates a discussion of not only the translation symmetry but point-group symmetries as well. I will illustrate the scope and usage of both packages by discussing several examples and showing some recent results obtained using them.   

Hyperbolic non-Abelian semimetal

We extend the notions of topologically protected band crossings and semimetals to hyperbolic lattices in negatively curved space. Due to their distinct translation group structure, such lattices support non-Abelian Bloch states which, unlike conventional Bloch states, acquire a matrix-valued Bloch factor under lattice translations. By adapting the Hamiltonian of a four-dimensional quantum Hall insulator, we devise a hyperbolic tight-binding model whose non-Abelian Bloch states constitute a peculiar kind of two-dimensional topological semimetal. In particular, by combining diverse numerical and analytical approaches, we uncover a quartic scaling in the density of states at low energies, and illuminate a nodal manifold of codimension five inside the reciprocal space. The band crossing is topologically protected by a non-zero value of the second Chern number, reminiscent of the characterization of Weyl nodes by the first Chern number. We investigate the anomalous nonlinear topological response of this two-dimensional system that emanates from the novel type of semimetallic band structure.   

Spontaneous symmetry breaking on interacting Euclidean and hyperbolic non-Hermitian fermionic systems

Spontaneous symmetry breaking plays an important role in the dynamic mass generation of particles in the Standard model, known as the Anderson-Higgs mechanism. It can take place via a quantum phase transition at a finite strength of an appropriate interaction or even for infinitesimally strong interactions depending on the scaling of the density of states. In this talk, I will show that this concept is applicable even for non-Hermitian (NH) materials from extensive bipartite lattice-based self-consistent Hartree-Fock numerical analyses of the nearest-neighbor Coulomb repulsion model for spinless (taken only for simplicity) fermions. First, I will promote a general principle of constructing non-Hermitian operators on any bipartite lattice, embedded on flat Euclidean or curved hyperbolic space, that over an extended parameter regime is guaranteed to feature a real eigenvalue spectrum. Next, I will show that in such a parameter regime, the non-Hermitian parameter enhances the tendency of a charge-density-wave (CDW) ordering by spontaneously breaking the sublattice inversion symmetry, making it more prominent at weaker interactions in comparison to its counterpart in Hermitian systems. Nucleation of the CDW ordering dynamically develops mass gap for NH fermionic excitations. I will establish that this is a generic and robust phenomenon, which is operative on any flat Euclidean and curved hyperbolic bipartite lattice, supporting either vanishing (NH Dirac liquid), constant (NH Fermi liquid), or diverging (NH flat band) density of states. If time permits, I will also discuss the role of external magnetic fields on the dynamic mass generation in NH Dirac liquids.   

Anderson localization transition in disordered hyperbolic lattices

We study Anderson localization in disordered tight-binding models on hyperbolic lattices. Such lattices are geometries intermediate between ordinary two-dimensional crystalline lattices, which localize at infinitesimal disorder, and Bethe lattices, which localize at strong disorder. Using state-of-the-art computational group theory methods to create large systems, we approximate the thermodynamic limit through appropriate periodic boundary conditions and numerically demonstrate the existence of an Anderson localization transition on the {8,3} and {8,8} lattices. We find unusually large critical disorder strengths and determine critical exponents.