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Diatomic chain consisting of spring-mass system forms an attenuation bandgap due to the formation of the standing wave when the wavelength matches with the periodicity, known as Bragg-scattering. Edge-state phenomenon can be obtained by breaking the periodicity of the diatomic chain. Owing to this edge state phenomenon, the waves, and in turn the energy, is localized at the point of the asymmetry. In this work, an efficient vibrational energy harvesting technique is proposed exploiting this edge-state energy localization by inserting piezo-electric harvester at the junction of the asymmetry. To illustrate the performance of the proposed harvester under the broad-band noise, voltage-frequency curve for three different diatomic chain configurations, having same mass and stiffness, are analyzed. The performance metric, defined as the area under the voltage-frequency curve, shows 21.5 times higher performance can be obtained just by breaking the symmetry of a conventional diatomic chain. As it is also observed that the attenuation properties of the symmetric and asymmetric chain remain same; thus, the proposed edge-state energy harvester has a significant promise toward simultaneous energy harvesting and vibration control. [ABSTRACT FROM AUTHOR]

We consider the effect of time-periodic forcing on a one-dimensional Schrödinger equation with a topologically protected defect (edge) mode. The unforced system models a domain wall or dislocation defect in a periodic structure, and it supports a defect mode which bifurcates from the Dirac point (linear band crossing) of the underlying bulk medium. We study the robustness of this state against time-periodic forcing of the type that arises in the study of Floquet topological insulators in condensed matter, photonics, and cold-atoms systems. Our numerical simulations demonstrate that under time-periodic forcing of sufficiently high frequency, the defect state undergoes radiative leakage of its energy away from the interface into the bulk; the time-decay is exponential on a time scale proportional to the inverse square of the forcing amplitude. The envelope dynamics of our Floquet system are approximately governed, on long time scales, by an effective (homogenized) periodically forced Dirac equation. Multiple scale analysis of the effective envelope dynamics yields an expansion of the radiating solution, which shows excellent agreement with our numerical simulations. [ABSTRACT FROM AUTHOR]

We propose a scheme to investigate and witness edge modes of general one-dimensional photonic trimers in a circuit quantum electrodynamic lattice. These in-gap edge modes are strictly and analytically solved and the criteria for their emergence are indicated respectively. Moreover, the energy spectrum of the system shows two different regimes characterized by a discrepancy in the number of edge modes. Specifically, while there are always a couple of edge modes only present at one single boundary in both the regimes, one of the regimes also shows another pair of edge modes localized on the opposite boundary. Furthermore, these edge modes are witnessed with the aid of continuous-time quantum walks and average photon number measurements. Our scheme provides a comprehensive method for studying the edge modes of matter.

For a triangular lattice of particles, with nearest neighbour interactions and a traction free boundary, there exists a surface wave band for out-of-plane motion. Interactions between such a surface wave and stationary crack tip in mode III are investigated. The discrete Helmholtz equation for scattered waves, that incorporates an anisotropy parameter for unequal spring constants in horizontal versus slant directions, is solved exactly. The coefficient of transmission from one crack face to another, as well as that owing to reflection on the same face, is obtained in a closed form; the same leads to an estimate of energy fraction of incident wave that is leaked at the crack tip via bulk waves. It is found, in terms of surface wave band, that the transmission coefficient attains its maximum magnitude above the mid-band while the energy leak is minimum at the upper-band limit. Besides surface wave propagation across crack tip, surface wave excitation due to incident bulk wave is also discussed. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'. [ABSTRACT FROM AUTHOR]

Metal nanostructures have attracted attention because of their unique optical characteristics derived from localized surface plasmon resonance. In this study, gold nanoholes with edge structures were designed and characterized to possess two plasmon bands at different wavelengths. These bands were assigned to the plasmon modes that generated a concentrated electric field at the tip of the individual edge structures. Furthermore, wavelengths of these bands were independently tuned from the visible to near-infrared wavelengths with shape and size of the gold nanoholes and edge structures as variables. To demonstrate wavelength tuning, a gold nanostructure with edge plasmon bands at wavelengths of approximately 785 and 1064 nm (typical laser wavelengths for surface-enhanced Raman scattering and optical tweezers, respectively) was successfully obtained via optical simulation. The results indicate that the structure designed in this study provides a guideline for the design of optical devices with efficient multiple optical functions.

Abstract With the development of science and technology, phononic crystals can be fabricated at nanoscale. The advancement yields significant applications in thermo-electric, acousto-optical and electron-phonon devices. At nanoscale, the surface heterogeneity of structures is a result of the differences between the arrangement and environment of the surface atoms and those of their counterparts in the body. This characteristic plays an important role in determining the mechanical properties of the structures. The effects of surface heterogeneity on band structures of the phononic crystals at nanoscale are studied in this paper. We also investigate the topological properties of phononic nanobeams through theoretical and numerical approaches. The topological edge mode, which is affected by the surface heterogeneity, is observed. Particularly, a theoretical method based on the plane wave expansion method is proposed to conveniently calculate the Zak phase, which is an important constant describing the topological properties. The numerical results show that surface heterogeneity mainly influences the response frequency for the dispersion relations and the topological behaviors in the phononic nanobeam. The study may be beneficial for the understanding of the size-dependent behaviors of phononic crystals at nanoscale and for the design of nanodevices based on the dispersion and topological properties of phononic crystals. [ABSTRACT FROM AUTHOR]

Edge mode could disturb the ultra-subtle mass detection for graphene resonators. Herein, classical molecular dynamics simulations are performed to investigate the effect of edge mode on mass sensing for a doubly clamped strained graphene resonator. Compared with the fundamental mode, the localized vibration of edge mode shows a lower frequency with a constant frequency gap of 32.6 GHz, despite the mutable inner stress ranging from 10 to 50 GPa. Furthermore, the resonant frequency of edge mode is found to be insensitive to centrally located adsorbed mass, while the frequency of the fundamental mode decreases linearly with increasing adsorbates. Thus, a mass determination method using the difference of these two modes is proposed to reduce interferences for robust mass measurement. Moreover, molecular dynamics simulations demonstrate that a stronger prestress or a higher width–length ratio of about 0.8 could increase the low-quality factor induced by edge mode, thus improving the performance in mass sensing for graphene resonators.

Abstract Photonic graphene, a photonic crystal with honeycomb structures, has been intensively studied in both theoretical and applied fields. Similar to graphene which admits Dirac Fermions and topological edge states, photonic graphene supports novel and subtle propagating modes (edge modes) of electromagnetic waves. These modes have wide applications in many optical systems. In this paper, we propose a novel gradient recovery method based on Bloch theory for the computation of topological edge modes in photonic graphene. Compared to standard finite element methods, this method provides higher order accuracy with the help of gradient recovery technique. This high order accuracy is desired for constructing the propagating electromagnetic modes in applications. We analyze the accuracy and prove the superconvergence of this method. Numerical examples are presented to show the efficiency by computing the edge mode for the P -symmetry and C -symmetry breaking cases in honeycomb structures. [ABSTRACT FROM AUTHOR]

We study the evolution of the one-particle entanglement spectrum for the one-dimensional dimerized chain in the presence of impurities. When the system quenches from a topologically nontrivial phase to a trivial phase with disorder, the spectrum features the split of two zero-energy edge modes due to their interaction with impurities. Our observations demonstrate the feasibility of using entanglement spectrum to study the quench dynamics of topological systems. [ABSTRACT FROM AUTHOR]

The problem of vibrations of an ice sheet with a rectilinear crack on the surface of an ideal incompressible fluid of finite depth under the action of a time-periodic local load is solved analytically using the Wiener-Hopf technique. Ice cover is simulated by two thin elastic semi-infinite plates of constant thickness. The thickness of the plates may be different on the opposite sides of the crack. Various boundary conditions on the edges of the plates are considered. For the case of contact of plates of the same thickness, a solution in explicit form is obtained. The asymptotics of the deflection of the plates in the far field is studied. It is shown that in the case of contact of two plates of different thickness, predominant directions of wave propagation at an angle to the crack can be identified in the far field. In the case of contact of plates of the same thickness with free edges and with free overlap, an edge waveguide mode propagating along the crack is excited. It is shown that the edge mode propagates with maximum amplitude if the vertical wall is in contact with the plate. Examples of calculations are given. [ABSTRACT FROM AUTHOR]

Topological phase transitions of a two-dimensional topologically nontrivial polaritonic system are studied. A generic model of semiconductor excitons strongly coupled with tailored photonic modes is considered. We introduce a pseudospin operator, measuring the polariton polarization between photonic-like and excitonic-like. The associated pseudospin spectrum and pseudospin Chern numbers are calculated. It is shown that the pseudospin Chern number phase diagram exhibits certain features resembling the topological phase of quantum-spin-Hall-like. Moreover, a series of topological phase transitions may occur with the closing of the bulk energy gap or the pseudospin spectrum gap. In a tight-binding form, the edge-mode simulation is done numerically to confirm the analytically results. [ABSTRACT FROM AUTHOR]

A monolayer-graphene-based concentric-double-rings (CDR) structure is reported to achieve broadband plasmon-induced transparency (PIT) on the strength of edge mode in the mid-infrared regime. The theoretical analysis and simulation results reveal that the structure designed here has two plasmonic resonance peaks at 39.1 and 55.4 THz, and a transparency window with high transmission amplitude at the frequency of 44.1 THz. Based on the edge mode coupling between neighbor graphene ribbons, PIT phenomenon is produced through the interference between different (bright and dark) modes. The frequency and bandwidth of the transparency window and slow light time could be effectively adjusted and controlled via changing geometrical parameters of graphene or applying different gate voltages. Additionally, this structure is insensitive to the polarization and incident angle. This work has potential application on the optical switches and slow light modulators.

Spin waves propagation in 1D magnonic crystals is investigated theoretically. Mathematical model based on plane wave expansion method is applied to different types of magnonic crystals, namely bi-component magnonic crystal with symmetric/asymmetric boundaries and ferromagnetic film with periodically corrugated top surface. It is shown that edge modes in magnonic crystals may exhibit nonreciprocal behaviour at much lower frequencies than in homogeneous films. [ABSTRACT FROM AUTHOR]

• The gold nanostructure was designed to have two edge plasmon modes whose wavelengths are independently tunable. • Wavelength-tunable range was from approximately 800 to 1800 nm. • The optimal design for application using 785 and 1064 nm laser was successfully suggested. • The electric field enhancement of optimal design reached 1.5 × 104 and 7.7 × 103 for 785 and 1064 nm. Metal nanostructures have attracted attention because of their unique optical characteristics derived from localized surface plasmon resonance. In this study, gold nanoholes with edge structures were designed and characterized to possess two plasmon bands at different wavelengths. These bands were assigned to the plasmon modes that generated a concentrated electric field at the tip of the individual edge structures. Furthermore, wavelengths of these bands were independently tuned from the visible to near-infrared wavelengths with shape and size of the gold nanoholes and edge structures as variables. To demonstrate wavelength tuning, a gold nanostructure with edge plasmon bands at wavelengths of approximately 785 and 1064 nm (typical laser wavelengths for surface-enhanced Raman scattering and optical tweezers, respectively) was successfully obtained via optical simulation. The results indicate that the structure designed in this study provides a guideline for the design of optical devices with efficient multiple optical functions. [ABSTRACT FROM AUTHOR]

In this article, the existence of thickness-edge modes in a semi-infinite hexagonal (6 mm) magneto-electro-elastic plate is analyzed. Each surface of the plate is traction-free, but subjected to four different types of electromagnetic boundary conditions. It is found that when the two major surfaces of the plate are electrically open and magnetically closed, three types of electromagnetic boundary conditions on the minor surface of the plate allow the existence of thickness-edge modes. The frequencies of the thickness-edge modes for the three cases of the existence are given explicitly. [ABSTRACT FROM AUTHOR]

In this paper, the edge mode vibration is studied with three different methods: the reciprocal work method, already used by Torvik [J. Acoust. Soc. Am. 41 (1967) 346] to model this phenomenon, the S-parameter method and a finite element model that are applied for the first time to the study of the edge resonance. Moreover, laser probe measurements of the edge mode have also been performed and compared to the numerical predictions. The good agreement between the numerical predictions and the experimental data allows full understanding of the resonant phenomenon. The edge resonance is linked to the strong increase in amplitude of two complex Lamb waves, and the edge mode is proved to radiate into the plate as the first symmetrical Lamb mode S0. Displacements at the edge and away from the edge have been computed and measured to evaluate the spatial and temporal behaviour of the edge mode. The dependence of the edge resonance frequency and amplitude on the Poisson coefficient has also been studied. [Copyright &y& Elsevier]

Because of the bulk gap, low energy physics in the quantum Hall effect is confined to the edges of the 2D electron liquid. The velocities of edge modes are key parameters of edge physics. They were determined in several quantum Hall systems from time-resolved measurements and high-frequency ac transport. We propose a way to extract edge velocities from dc transport in a point contact geometry defined by narrow gates. The width of the gates assumes two different sizes at small and large distances from the point contact. The Coulomb interaction across the gates depends on the gate width and affects the conductance of the contact. The conductance exhibits two different temperature dependencies at high and low temperatures. The transition between the two regimes is determined by the edge velocity. An interesting feature of the low-temperature I − V curve is current oscillations as a function of the voltage. The oscillations emerge due to charge reflection from the interface of the regions defined by the narrow and wide sections of the gates.

Some new properties of optical diodes were investigated, as well as compared with the known ones for the following three systems: 1) an isotropic magnetoactive layer, 2) a magnetophotonic crystal layer, and 3) a photonic crystal with a helical structure, assuming that these systems are in an external magnetic field and have giant parameters of magneto-optical activity. It is shown that these systems can be used as broadband ideal optical diodes. At giant values of the magneto-optical activity in the long-wavelength region of the spectrum, there appears a new photonic band gap (PBG) for helically structured photonic crystals. Accordingly, two PBGs and a transparent window between them appear in the whole spectral region. When magneto-optical activity parameter increases, this new (the second) PBG occupies the entire spectrum. Furthermore, the light localization at the edge modes is investigated. It is shown that an unusually strong light localization takes place at some modes. The trapped total light energy and the energy density peculiarities are investigated, too. Image 1 • Diode properties of isotropic magneto-active layer in the external magnetic field was investigated. • Diode properties of magnetophotonic crystal layer was investigated. • Diode properties of chiral structured photonic crystal being in external magnetic field was investigated. • Light localization peculiarities was investigated. [ABSTRACT FROM AUTHOR]

In this paper, topologically protected wave propagation in metastable structure has been investigated by mimicking the quantum valley Hall effect. Reconfigurable topological waveguides are achieved by switching the metastable states of the structure. First, a K-point Dirac cone, which is guaranteed by the C6 rotational symmetry of the metastable unit cell, is identified in the band structure. Then, by reconfiguring the bistable elements, the space inversion symmetry of the unit cell is broken and a topological bandgap opened. The topological non-triviality of this bandgap is verified by the values assumed by the Berry curvature and valley Chern number. Next, the topological edge modes localized at the interface are studied by analyzing the dispersion relation of a finite strip. The analysis results show that reconfigurable topologically protected waveguides, which are immune to backscattering at sharp corners and local defects, can be achieved utilizing the edge modes. [ABSTRACT FROM AUTHOR]

Edge mode could disturb the ultra-subtle mass detection for graphene resonators. Herein, classical molecular dynamics simulations are performed to investigate the effect of edge mode on mass sensing for a doubly clamped strained graphene resonator. Compared with the fundamental mode, the localized vibration of edge mode shows a lower frequency with a constant frequency gap of 32.6 GHz, despite the mutable inner stress ranging from 10 to 50 GPa. Furthermore, the resonant frequency of edge mode is found to be insensitive to centrally located adsorbed mass, while the frequency of the fundamental mode decreases linearly with increasing adsorbates. Thus, a mass determination method using the difference of these two modes is proposed to reduce interferences for robust mass measurement. Moreover, molecular dynamics simulations demonstrate that a stronger prestress or a higher width–length ratio of about 0.8 could increase the low-quality factor induced by edge mode, thus improving the performance in mass sensing for graphene resonators. [ABSTRACT FROM AUTHOR]

Valley polarization has recently been adopted in optics, offering robust waveguiding and angular momentum sorting. The success of valley systems in photonic crystals suggests a plasmonic counterpart that can merge topological photonics and topological condensed matter systems, for instance, two-dimensional materials with the enhanced light-matter interaction. However, a valley plasmonic waveguide with a sufficient propagation distance in the near-infrared (NIR) or visible spectral range has so far not been realized due to ohmic loss inside the metal. Here, we employ gap surface plasmons for high index contrasting and realize a wide-bandgap valley plasmonic crystal, allowing waveguiding in the NIR-visible range. The edge mode with a propagation distance of 5.3 μm in the range of 1.31-1.36 eV is experimentally confirmed by visualizing the field distributions with a scanning transmission electron microscope cathodoluminescence technique, suggesting a practical platform for transferring angular momentum between photons and carriers in mesoscopic active devices.

Using a weak limit for the hopping integral in one direction in the Hofstadter model, we show that the fermion states in the gaps of the spectrum are determined within the Kitaev chain. The proposed approach allows us to study the behavior of Chern insulators (CI) in different classes of symmetry. We consider the Hofstadter model on the square and honeycomb lattices in the case of rational and irrational magnetic fluxes ϕ , and discuss the behavior of the Hall conductance at a weak magnetic field in a sample of finite size. We show that in the semiclassical limit at the center of the fermion spectrum, the Bloch states of fermions turn into chiral Majorana fermion liquid when the magnetic scale 1 ϕ is equal to the sample size N. We are talking about the dielectric–metal phase transition, which is determined by the behavior of the Landau levels in 2D fermion systems in a transverse magnetic field. When a magnetic scale, which determines the wave function of fermions, exceeds the size of the sample, a jump in the longitudinal conductance occurs. The wave function describes non-localized states of fermions, the sample becomes a conductor, the system changes from the dielectric state to the metallic one. It is shown, that at 1 ∕ ϕ > N the quantum Hall effect and the Landau levels are not realized, which makes possibility to study the behavior of CI in irrational magnetic fluxes. [ABSTRACT FROM AUTHOR]

In this paper, a new kind of graphene double-ribbon bend structure, which can support two edge graphene surface plasmons (EGSPs) modes, is proposed. In this double-ribbon bend, one edge mode can be partly converted into another one. We attribute the mode conversion mechanism to the interference between the two edge plasmonic modes. Based on the finite element method (FEM), we calculate the transmission and loss of EGSPs propagating along this graphene double-ribbon bend in the mid-infrared range under different parameters. [ABSTRACT FROM AUTHOR]

A monolayer-graphene-based concentric-double-rings (CDR) structure is reported to achieve broadband plasmon-induced transparency (PIT) on the strength of edge mode in the mid-infrared regime. The theoretical analysis and simulation results reveal that the structure designed here has two plasmonic resonance peaks at 39.1 and 55.4 THz, and a transparency window with high transmission amplitude at the frequency of 44.1 THz. Based on the edge mode coupling between neighbor graphene ribbons, PIT phenomenon is produced through the interference between different (bright and dark) modes. The frequency and bandwidth of the transparency window and slow light time could be effectively adjusted and controlled via changing geometrical parameters of graphene or applying different gate voltages. Additionally, this structure is insensitive to the polarization and incident angle. This work has potential application on the optical switches and slow light modulators. [ABSTRACT FROM AUTHOR]