arXiv subjects

Georgios Theocharis

Publications and source records attributed to Georgios Theocharis.

36 records · Page 2Linked to original sources

arXiv2022

Duality of Topological Edge States in a Mechanical Kitaev Chain

We theoretically investigate and experimentally demonstrate the existence of topological edge states in a mechanical analog of the Kitaev chain with a non-zero chemical potential. Our system is a one-dimensional monomer system involving two coupled degrees of freedom, i.e., transverse displacement and rotation of elastic elements. Due to the particle-hole symmetry, a topologically nontrivial bulk leads to the emergence of edge states in a finite chain with fixed boundaries. In contrast, a topologically trivial bulk also leads to the emergence of edge states in a finite chain, but with free boundaries. We unravel a duality in our system that predicts the existence of the latter edge states. This duality involves the iso-spectrality of a subspace for finite chains, and as a consequence, a free chain with topologically trivial bulk maps to a fixed chain with a nontrivial bulk. Lastly, we provide the conditions under which the system can exhibit perfectly degenerate in-gap modes, akin to Majorana zero modes. These findings suggest that mechanical systems with fine-tuned degrees of freedom can be fertile testbeds for exploring the intricacies of Majorana physics.

cond-mat.mes-hall↗

arXiv2022

Wave-packet spreading in disordered soft architected structures

We study the dynamical and chaotic behavior of a disordered one-dimensional elastic mechanical lattice which supports translational and rotational waves. The model used in this work is motivated by the recent experimental results of B. Deng et al., Nat. Commun. 9, 3410 (2018). This lattice is characterized by strong geometrical nonlinearities and the coupling of two degrees-of-freedom (DoFs) per site. Although the linear limit of the structure consists of a linear Fermi-Pasta-Ulam-Tsingou lattice and a linear Klein-Gordon (KG) lattice whose DoFs are uncoupled, by using single site initial excitations on the rotational DoF, we evoke the nonlinear coupling between the system's translational and rotational DoFs. Our results reveal that such coupling induces rich wave-packet spreading behavior in the presence of strong disorder. In the weakly nonlinear regime, we observe energy spreading only due to the coupling of the two DoFs (per site) which is in contrast to what is known for KG lattices with a single DoF per lattice site, where the spreading occurs due to chaoticity. Additionally, for strong nonlinearities, we show that initially localized wave-packets attain near ballistic behavior in contrast to other known models. We also reveal persistent chaos during energy spreading, although its strength decreases in time as quantified by the evolution of the system's finite-time maximum Lyapunov exponent. Our results show that flexible, disordered and strongly nonlinear lattices are a viable platform to study energy transport in combination with multiple DoFs (per site), also present an alternative way to control energy spreading in heterogeneous media.

nlin.CD↗

arXiv2022

Bulk-edge correspondence in the trimer Su-Schrieffer-Heeger model

A remarkable feature of the trimer Su-Schrieffer-Heeger (SSH3) model is that it supports localized edge states. Although Zak's phase remains quantized for the case of a mirror-symmetric chain, it is known that it fails to take integer values in the absence of this symmetry and thus it cannot play the role of a well-defined bulk invariant in the general case. Attempts to establish a bulk-edge correspondence have been made via Green's functions or through extensions to a synthetic dimension. Here we propose a simple alternative for SSH3, utilizing the previously introduced sublattice Zak's phase, which also remains valid in the absence of mirror symmetry and for non-commensurate chains. The defined bulk quantity takes integer values, is gauge invariant, and can be interpreted as the difference of the number of edge states between a reference and a target Hamiltonian. Our derivation further predicts the exact corrections for finite open chains, is straightforwadly generalizable, and invokes a chiral-like symmetry present in this model.

cond-mat.mes-hall↗

arXiv2022

Topological state transfer in Kresling origami

Topological mechanical metamaterials have been widely explored for their boundary states, which can be robustly isolated or transported in a controlled manner. However, such systems often require pre-configured design or complex active actuation for wave manipulation. Here, we present the possibility of in-situ transfer of topological boundary modes by leveraging the reconfigurability intrinsic in twisted origami lattices. In particular, we employ a dimer Kresling origami system consisting of unit cells with opposite chirality, which couples longitudinal and rotational degrees of freedom in elastic waves. The quasi-static twist imposed on the lattice alters the strain landscape of the lattice, thus significantly affecting the wave dispersion relations and the topology of the underling bands. This in turn facilitates an efficient topological state transfer from one edge to the other. This simple and practical approach of energy transfer in origami-inspired lattices can thus inspire a new class of efficient energy manipulation devices.

cond-mat.mes-hall↗

arXiv2022

Acoustic Su-Schrieffer-Heeger lattice: Direct mapping of acoustic waveguides to Su-Schrieffer-Heeger model

Topological physics strongly relies on prototypical lattice model with particular symmetries. We report here on a theoretical and experimental work on acoustic waveguides that is directly mapped to the one-dimensional Su-Schrieffer-Heeger chiral model. Starting from the continuous two dimensional wave equation we use a combination of monomadal approximation and the condition of equal length tube segments to arrive at the wanted discrete equations. It is shown that open or closed boundary conditions topological leads automatically to the existence of edge modes. We illustrate by graphical construction how the edge modes appear naturally owing to a quarter-wavelength condition and the conservation of flux. Furthermore, the transparent chirality of our system, which is ensured by the geometrical constraints allows us to study chiral disorder numerically and experimentally. Our experimental results in the audible regime demonstrate the predicted robustness of the topological edge modes.

cond-mat.mes-hall↗

arXiv2021

Subwavelength Su-Schrieffer-Heeger topological modes in acoustic waveguides

Topological systems furnish a powerful way of localizing wave energy at edges of a structured material. Usually this relies on Bragg scattering to obtain bandgaps with nontrivial topological structures. However, this limits their applicability to low frequencies since that would require very large structures. A standard approach to address the problem is to add resonating elements inside the material to open gaps in the subwavelength regime. Unfortunately, one usually has no precise control on the properties of the obtained topological modes, such as their frequency or localization length. In this work, we propose a new construction to couple acoustic resonators such that acoustic modes are mapped exactly to the eigenmodes of the Su-Schrieffer-Heeger model. The relation between energy in the lattice model and the acoustic frequency is controlled by the characteristics of the resonators. This allows us to obtain Su-Schrieffer-Heeger topological modes at any given frequency, for instance in the subwavelength regime. We also generalize the construction to obtain well-controlled topological edge modes in alternative tunable configurations.

physics.class-ph↗

arXiv2021

Nonlinear Topological Edge States: from Dynamic Delocalization to Thermalization

We consider a mechanical lattice inspired by the Su-Schrieffer-Heeger model along with cubic Klein-Gordon type nonlinearity. We investigate the long-time dynamics of the nonlinear edge states, which are obtained by nonlinear continuation of topological edge states of the linearized model. Linearly unstable edge states delocalize and lead to chaos and thermalization of the lattice. Linearly stable edge states also reach the same fate, but after a critical strength of perturbation is added to the initial edge state. We show that the thermalized lattice in all these cases shows an effective renormalization of the dispersion relation. Intriguingly, this renormalized dispersion relation displays a unique symmetry, i.e., its square is symmetric about a finite squared frequency, akin to the chiral symmetry of the linearized model.

nlin.CD↗

arXiv2021

Topological two-dimensional Su-Schrieffer-Heeger analogue acoustic networks: Total reflection at corners and corner induced modes

In this work, we investigate some aspects of an acoustic analogue of the two-dimensional Su-Schrieffer-Heeger model. The system is composed of alternating cross-section tubes connected in a square network, which in the limit of narrow tubes is described by a discrete model coinciding with the two-dimensional Su-Schrieffer-Heeger model. This model is known to host topological edge waves, and we develop a scattering theory to analyze how these waves scatter on edge structure changes. We show that these edge waves undergo a perfect reflection when scattering on a corner, incidentally leading to a new way of constructing corner modes. It is shown that reflection is high for a broad class of edge changes such as steps or defects. We then study consequences of this high reflectivity on finite networks. Globally, it appears that each straight part of edges, separated by corners or defects, hosts localized edge modes isolated from their neighbourhood.

cond-mat.mes-hall↗

arXiv2021

Disorder-induced topological phase transition in a 1D mechanical system

We numerically investigate the topological phase transition induced purely by disorder in a spring-mass chain. We employ two types of disorders - chiral and random types - to explore the interplay between topology and disorder. By tracking the evolution of real space topological invariants, we obtain the topological phase diagrams and demonstrate the bilateral capacity of disorder to drive topological transitions, from topologically nontrivial to trivial and vice versa. The corresponding transition is accompanied by the realization of a mechanical Topological Anderson Insulator. The findings from this study hint that the combination of disorder and topology can serve as an efficient control knob to manipulate the transfer of mechanical energy.

physics.app-ph↗

arXiv2020

Robustness of topological corner modes against disorder and application to acoustic networks

We study the two-dimensional extension of the Su-Schrieffer-Heeger model in its higher order topological insulator phase, which is known to host corner states. Using the separability of the model into a product of one-dimensional Su-Schrieffer-Heeger chains, we analytically describe the eigen-modes, and specifically the zero-energy level, which includes states localized in corners. We then consider networks with disordered hopping coefficients that preserve the chiral (sublattice) symmetry of the model. We show that the corner mode and its localization properties are robust against disorder if the hopping coefficients have a vanishing flux on appropriately defined super plaquettes. We then show how this model with disorder can be realised using an acoustic network of air channels, and confirm the presence and robustness of corner modes.

cond-mat.mes-hall↗

arXiv2020

Stability of topological edge states under strong nonlinear effects

We examine the role of strong nonlinearity on the topologically-robust edge state in a one-dimensional system. We consider a chain inspired from the Su-Schrieffer-Heeger model, but with a finite-frequency edge state and the dynamics governed by second-order differential equations. We introduce a cubic onsite-nonlinearity and study this nonlinear effect on the edge state's frequency and linear stability. Nonlinear continuation reveals that the edge state loses its typical shape enforced by the chiral symmetry and becomes generally unstable due to various types of instabilities that we analyze using a combination of spectral stability and Krein signature analysis. This results in an initially-excited nonlinear-edge state shedding its energy into the bulk over a long time. However, the stability trends differ both qualitatively and quantitatively when softening and stiffening types of nonlinearity are considered. In the latter, we find a frequency regime where nonlinear edge states can be linearly stable. This enables high-amplitude edge states to remain spatially localized without shedding their energy, a feature that we have confirmed via long-time dynamical simulations. Finally, we examine the robustness of frequency and stability of nonlinear edge states against disorder, and find that those are more robust under a chiral disorder compared to a non-chiral disorder. Moreover, the frequency-regime where high-amplitude edge states were found to be linearly stable remains intact in the presence of small amount of disorder of both types.

nlin.PS↗

arXiv2020

Corner states in second-order mechanical topological insulator

We numerically and experimentally study corner states in a continuous elastic plate with em-bedded bolts in a hexagonal pattern. While preserving C6 crystalline symmetry, the system can transition from a topologically trivial to a non-trivial configuration. We create interfacial corners of 60° and 120° by adjoining trivial and non-trivial topological configurations. Due to the rich interaction between the bolts and the continuous elastic plate, we find a variety of corner states with and without topological origin. Notably, some of the corner states are highly localized and tunable. By taking advantage of this property, we experimentally demonstrate one-way corner localization in a Z-shaped domain wall.

cond-mat.mes-hall↗

arXiv2019

Multi-functional resonant acoustic networks for wave routing

We demonstrate that asymmetric 3-port devices can be used to design a multi-functional set-up operating as a symmetric combiner and splitter at the same frequency. For a concrete implementation of the proposed multi-functionality protocol, we employ a resonant acoustic 3-port device operating in a subwavelength regime, showing splitting/combining abilities with nearly perfect transmission in presence of losses, induced by the interactions of the system's resonances. Finally, as an extension of the 3-port multi-functionality concept, we propose a new type of 4-port networks, consisting in an assembly of 3-port unit cells with combining/splitting properties, capable to achieve various wave guiding features with perfect transmission depending on the phase of the inputs.

physics.class-ph↗

arXiv2019

Self-induced topological transition in phononic crystals by nonlinearity management

A new design paradigm of topology has recently emerged to manipulate the flow of phonons. At its heart lies a topological transition to a nontrivial state with exotic properties. This framework has been limited to linear lattice dynamics so far. Here we show a topological transition in a nonlinear regime and its implication in emerging nonlinear solutions. We employ nonlinearity management such that the system consists of masses connected with two types of nonlinear springs, "stiffening" and "softening" types, alternating along the length. We show, analytically and numerically, that the lattice makes a topological transition simply by changing the excitation amplitude and invoking nonlinear dynamics. Consequently, we witness the emergence of a new family of finite-frequency edge modes, not observed in linear phononic systems. We also report the existence of kink solitons at the topological transition point. These correspond to heteroclinic orbits that form a closed curve in the phase portrait separating the two topologically-distinct regimes. These findings suggest that nonlinearity can be used as a strategic tuning knob to alter topological characteristics of phononic crystals. These also provide fresh perspectives towards understanding a new family of nonlinear solutions in light of topology.

cond-mat.mes-hall↗

arXiv2019

Observation of edge waves in a two-dimensional Su-Schrieffer-Heeger acoustic network

In this work, we experimentally report the acoustic realization the two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model in a simple network of air channels. We analytically study the steady state dynamics of the system using a set of discrete equations for the acoustic pressure, leading to the 2D SSH Hamiltonian matrix without using tight binding approximation. By building an acoustic network operating in audible regime, we experimentally demonstrate the existence of topological band gap. More supremely, within this band gap we observe the associated edge waves even though the system is open to free space. Our results not only experimentally demonstrate topological edge waves in a zero Berry curvature system but also provide a flexible platform for the study of topological properties of sound waves.

physics.class-ph↗

arXiv2019

Granular Graphene: direct observation of zigzag and armchair edge waves

We propose a mechanical granular graphene obtained by replacing the carbon atoms with macroscopic spherical stainless steel beads in contact. The experimental measured dispersion relation is presented, in conjunction with evidence of the Dirac points. In addition, wave propagation along the zigzag and a robust turning effect of edge waves from the zigzag to the armchair boundary is experimentally revealed, even in the absence of a full band gap for bulk modes. Our work shows that mechanical granular graphene can serve as an excellent experimental platform to study novel Dirac, topological and nonlinear wave phenomena.

physics.app-ph↗

arXiv2017

Bright and Gap Solitons in Membrane-Type Acoustic Metamaterials

We study analytically and numerically envelope solitons (bright and gap solitons) in a one-dimensional, nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear, dispersive and dissipative wave equation. Applying the multiple scales perturbation method, we derive an effective lossy nonlinear Schrödinger equation and obtain analytical expressions for bright and gap solitons. We also perform direct numerical simulations to study the dissipation-induced dynamics of the bright and gap solitons. Numerical and analytical results, relying on the analytical approximations and perturbation theory for solions, are found to be in good agreement.

nlin.PS↗

arXiv2014

Locally Resonant Granular Chain

We report the design and testing of a tunable and nonlinear mechanical metamaterial, called locally resonant granular chain. It consists of a one-dimensional array of hollow spherical particles in contact, containing local resonators. The resonant particles are made of an aluminium outer spherical shell and a steel inner mass connected by a polymeric plastic structure acting as a spring. We characterize the linear spectra of the individual particles and of one-dimensional arrays of particles using theory, numerical analysis, and experiments. A wide band gap is observed as well as tunability of the dispersive spectrum by changing the applied static load. Finally, we experimentally explore the nonlinear dynamics of the resonant particles. By using nonlinear acoustical techniques, we reveal a complex, nonclassical nonlinear dynamics.

cond-mat.mtrl-sci↗