Edges Of Lattice Research Articles

Plasmonic topological insulators for topological nanophotonics.

Photonic topological insulators are optical structures supporting robust propagation of light at their edges that are topologically protected from scattering. Here we propose the concept of plasmonic topological insulators (PTI) that not only topologically protect light at the lattice edges but also enable their confinement and guidance at the deep-subwavelength scale. The suggested PTI are composed of an evanescently coupled array of metallic nanowires that are modulated periodically along the light propagation direction. The intrinsic loss associated with the PTI is found not to deteriorate their topological protection on the edge modes. The proposed PTI may find interesting applications in nanophotonics, where the tolerance to the fabrication disorders for device applications are essential.

Robust edge states in amorphous gyromagnetic photonic lattices

We numerically study amorphous analogues of a two-dimensional photonic Chern insulator. The amorphous lattices consist of gyromagnetic rods that break time-reversal symmetry, with the lattice sites generated by a close-packing algorithm. The level of short-range order is adjustable, and there is no long-range order. The topologically nontrivial gaps of the photonic Chern insulator are found to persist into the amorphous regime, so long as there is sufficient short-range order. Strongly nonreciprocal robust transmission occurs via edge states, which are shown to propagate ballistically despite the absence of long-range order, and to be exponentially localized along the lattice edge. Interestingly, there is an enhancement of nonreciprocal transmission even at very low levels of short-range order, where there are no discernable spectral gaps.

Influence of nanoscale deformation twins near a slant edge crack tip on crack blunting in nanocrystalline metals

A theoretical model is developed that discusses the effect of nanoscale deformation twins on dislocation emission from the tip of slant edge crack in nanocrystalline materials. By combining complex variable method of Muskhelishvili and conformal mapping technique, the explicit solutions of complex potentials are obtained analytically. The critical stress intensity factors (SIFs) for the emission of first lattice edge dislocation from a slant edge crack tip are calculated. The effects of vital parameters such as the crack length, the inclined angle of the crack, the relative thickness of the nanotwin on critical SIFs for dislocation emission are evaluated in detail. The results show that the emission of lattice dislocation from the slant edge crack tip is significantly influenced by nanoscale deformation twins. The smaller the inclined angle is, the more difficult it is for dislocation emission from the slant edge crack tip. Particularly, the dislocation near the tip of slant edge crack is prone to emit when the inclined angle of the crack is about 45°. As a special case, when the inclined angle of slant edge crack is 0°, the present results will reduce to those of the problem of nanoscale deformation twins interacting with mode I straight crack.

Interconnected Phosphorus and Nitrogen Codoped Porous Exfoliated Carbon Nanosheets for High-Rate Supercapacitors.

Carbon-based supercapacitors have high power density and long cycle life; however, they are known to suffer from problems related to low energy density and high inner resistance. Here, we report a novel hierarchically porous functional carbon that is made up of interconnected exfoliated carbon nanosheets with thickness of a few nanometers. Notably, these porous carbon nanosheets are doped with abundant nitrogen (N) dopants in the basal plane and phosphorus (P) functional groups at the edge of the graphene lattice. The specific surface chemistry and pore structure of the synthesized sample, combined with its large specific surface area, make it a high-performance active material for supercapacitor electrode. The obtained supercapacitor made with the optimized sample showed a high specific capacitance (265 F g-1 at 0.5 A g-1) as well as long-term stability (94% capacitance retention after 5000 cycles). Particularly, the enhanced electrochemical characteristics were maintained even at high electrode mass loading (time constant (τ0) is 1.10 s for an electrode mass loading of 12.38 mg cm-2 compared to 1.61 s for a mass loading of 4.17 mg cm-2 for commercial activated carbon), which is important for a high packing factor of the capacitor.

Endocytic proteins are partitioned at the edge of the clathrin lattice in mammalian cells.

Dozens of proteins capture, polymerize and reshape the clathrin lattice during clathrin-mediated endocytosis (CME). How or if this ensemble of proteins is organized in relation to the clathrin coat is unknown. Here, we map key molecules involved in CME at the nanoscale using correlative super-resolution light and transmission electron microscopy. We localize 19 different endocytic proteins (amphiphysin1, AP2, β2-arrestin, CALM, clathrin, DAB2, dynamin2, EPS15, epsin1, epsin2, FCHO2, HIP1R, intersectin, NECAP, SNX9, stonin2, syndapin2, transferrin receptor, VAMP2) on thousands of individual clathrin structures, generating a comprehensive molecular architecture of endocytosis with nanoscale precision. We discover that endocytic proteins distribute into distinct spatial zones in relation to the edge of the clathrin lattice. The presence or concentrations of proteins within these zones vary at distinct stages of organelle development. We propose that endocytosis is driven by the recruitment, reorganization and loss of proteins within these partitioned nanoscale zones.

Grand-canonical solution of semiflexible self-avoiding trails on the Bethe lattice.

We consider a model of semiflexible interacting self-avoiding trails (sISATs) on a lattice, where the walks are constrained to visit each lattice edge at most once. Such models have been studied as an alternative to the self-attracting self-avoiding walks (SASAWs) to investigate the collapse transition of polymers, with the attractive interactions being on site as opposed to nearest-neighbor interactions in SASAWs. The grand-canonical version of the sISAT model is solved on a four-coordinated Bethe lattice, and four phases appear: non-polymerized (NP), regular polymerized (P), dense polymerized (DP), and anisotropic nematic (AN), the last one present in the phase diagram only for sufficiently stiff chains. The last two phases are dense, in the sense that all lattice sites are visited once in the AN phase and twice in the DP phase. In general, critical NP-P and DP-P transition surfaces meet with a NP-DP coexistence surface at a line of bicritical points. The region in which the AN phase is stable is limited by a discontinuous critical transition to the P phase, and we study this somewhat unusual transition in some detail. In the limit of rods, where the chains are totally rigid, the P phase is absent and the three coexistence lines (NP-AN, AN-DP, and NP-DP) meet at a triple point, which is the endpoint of the bicritical line.

Topological frustration of artificial spin ice

Frustrated systems, typically characterized by competing interactions that cannot all be simultaneously satisfied, display rich behaviours not found elsewhere in nature. Artificial spin ice takes a materials-by-design approach to studying frustration, where lithographically patterned bar magnets mimic the frustrated interactions in real materials but are also amenable to direct characterization. Here, we introduce controlled topological defects into square artificial spin ice lattices in the form of lattice edge dislocations and directly observe the resulting spin configurations. We find the presence of a topological defect produces extended frustration within the system caused by a domain wall with indeterminate configuration. Away from the dislocation, the magnets are locally unfrustrated, but frustration of the lattice persists due to its topology. Our results demonstrate the non-trivial nature of topological defects in a new context, with implications for many real systems in which a typical density of dislocations could fully frustrate a canonically unfrustrated system.

Topological zero-energy modes in time-reversal-symmetry-broken systems

The well-known Su-Schrieffer-Heeger (SSH) model predicts that a chain of sites with alternating coupling constant exhibits two topological distinct phases, and at the truncated edge of the topological nontrivial phase there exists topologically protected edge modes. Such modes are named zero-energy modes as their eigenvalues are located exactly at the midgaps of the corresponding bandstructures. The previous publications have reported a variety of photonic realizations of the SSH model, however, all of these studies have been restricted in the systems of time-reversal-symmetry (TRS), and thus the important question how the breaking of TRS affects the topological edge modes has not been explored. In this work, to the best of our knowledge, we study for the first time the topological zero-energy modes in the systems where the TRS is broken. The system used here is semiconductor microcavities supporting exciton-polariton quasi-particle, in which the interplay between the spin-orbit coupling stemming from the TE-TM energy splitting and the Zeeman effect causes the TRS to break. We first study the topological edge modes occurring at the edge of one-dimensional microcavity array that has alternative coupling strengths between adjacent microcavity, and, by rigorously solving the Schrdinger-like equations (see Eq.(1) or Eq.(2) in the main text), we find that the eigen-energies of topological zero-energy modes are no longer pinned at the midgap position:rather, with the increasing of the spin-orbit coupling, they gradually shift from the original midgap position, with the spin-down edge modes moving toward the lower band while the spin-up edge modes moving towards the upper band. Interestingly enough, the mode profiles of these edge modes remain almost unchanged even they are approaching the bulk transmission bands, which is in sharp contrast to the conventional defect modes that have an origin of bifurcation from the Bloch mode of the upper or lower bands. We also study the edge modes in the two-dimensional microcavity square array, and find that the topological zero modes acquire mobility along the truncated edge due to the coupling from the adjacent arrays. Importantly, owing to the breaking of the TRS, a pair of counterpropagating edge modes, of which one has a momentum k and the other has -k, is no longer of energy degeneracy; as a result the scattering between the forward-and backward-propagating modes is greatly suppressed. Thus, we propose the concept of the one-dimensional topological zero-energy modes that are propagating along the two-dimensional lattice edge, with extremely weak backscattering even on the collisions of the topological zero-energy modes with structural defects or disorder.

Modulational instability and solitary waves in polariton topological insulators

Optical microcavities supporting exciton–polariton quasi-particles offer one of the most powerful platforms for the investigation of the rapidly developing area of topological photonics in general, and of photonic topological insulators in particular. Energy bands of the microcavity polariton graphene are readily controlled by a magnetic field and influenced by the spin-orbit (SO) coupling effects, a combination leading to the formation of linear unidirectional edge states in polariton topological insulators as very recently predicted. In this work we depart from the linear limit of non-interacting polaritons and predict instabilities of the nonlinear topological edge states resulting in the formation of the localized topological quasi-solitons, which are exceptionally robust and immune to backscattering wave packets propagating along the graphene lattice edge. Our results provide a background for experimental studies of nonlinear polariton topological insulators and can influence other subareas of photonics and condensed matter physics, where nonlinearities and SO effects are often important and utilized for applications.

Edge Solitons in Nonlinear-Photonic Topological Insulators.

We show theoretically that a photonic topological insulator can support edge solitons that are strongly self-localized and propagate unidirectionally along the lattice edge. The photonic topological insulator consists of a Floquet lattice of coupled helical waveguides, in a medium with local Kerr nonlinearity. The soliton behavior is strongly affected by the topological phase of the linear lattice. The topologically nontrivial phase gives a continuous family of solitons, while the topologically trivial phase gives an embedded soliton that occurs at a single power and arises from a self-induced local nonlinear shift in the intersite coupling. The solitons can be used for nonlinear switching and logical operations, functionalities that have not yet been explored in topological photonics. We demonstrate using solitons to perform selective filtering via propagation through a narrow channel, and using soliton collisions for optical switching.

ZIF-8 Derived, Nitrogen-Doped Porous Electrodes of Carbon Polyhedron Particles for High-Performance Electrosorption of Salt Ions.

Three-dimensional (3-D) ZIF-8 derived carbon polyhedrons with high nitrogen (N) content, (denoted as NC-800) are synthesized for their application as high-performance electrodes in electrosorption of salt ions. The results showed a high specific capacitance of 160.8 F·g−1 in 1 M NaCl at a scan rate of 5 mV·s−1. Notably, integration of 3-D mesopores and micropores in NC-800 achieves an excellent capacitive deionization (CDI) performance. The electrosorption of salt ions at the electrical double layer is enhanced by N-doping at the edges of a hexagonal lattice of NC-800. As evidenced, when the initial NaCl solution concentration is 1 mM, the resultant NC-800 exhibits a remarkable CDI potential with a promising salt electrosorption capacity of 8.52 mg·g−1.

An atomistic study of resistance offered by twist grain boundaries to incoming edge dislocation in FCC metals

We explored 45 twist grain boundaries (GBs), spanning a broad range of misorientation angles (0°<θ<180°), to quantify the resistance offered to incoming lattice edge dislocation in different FCC metals (Al, Cu and Ni). The results provide corroborative evidence of the fact that GBs with higher energy offer strong resistance to incoming edge dislocation. Consequently, it has been found that: (1) the dislocation absorption resistance (stress at which dislocation is absorbed in the GB) follows a power-law relationship with the grain boundary energy, (2) grain boundary absorption resistance in FCC materials follow a simple statistical distribution, (3) the absorption resistance for the particular material is governed by the non-dimensional parameter γs/μbp, where γs is the stacking fault energy, μ is the shear modulus and bp is the Burgers vector of partial dislocations. It is envisioned that crystal plasticity based models could use this information to choose and define more realistic constitutive equations for grain boundaries.

Electron Counting and a Large Family of Two-Dimensional Semiconductors

In comparison with conventional semiconductors, most two-dimensional semiconductor (2DSC) materials are dissimilar in structure and composition. Herein, we use electron-counting rules to propose a large family of 2DSCs, which all adopt the same structure and are composed of solely main group elements. Advanced density functional theory calculations are used to predict a number of novel 2DSCs, and we show that they span a large range of lattice constants, band gaps, and band edge states. As a result, they are good candidate materials for heterojunctions. This family of two-dimensional materials may be instrumental in the fabrication of 2DSC devices that may rival the currently employed 3D semiconductors.

Dilute oriented loop models

We study a model of dilute oriented loops on the square lattice, where each loop is compatible with a fixed, alternating orientation of the lattice edges. This implies that loop strands are not allowed to go straight at vertices, and results in an enhancement of the usual symmetry to . The corresponding transfer matrix acts on a number of representations (standard modules) that grows exponentially with the system size. We derive their dimension and those of the centralizer by both combinatorial and algebraic techniques. A mapping onto a field theory permits us to identify the conformal field theory governing the critical range, . We establish the phase diagram and the critical exponents of low-energy excitations. For generic n, there is a critical line in the universality class of the dilute model, terminating in an point. The case n = 1 maps onto the critical line of the six-vertex model, along which exponents vary continuously.

Slow Relaxation of Shape and Orientational Texture in Membrane Gel Domains.

Gel domains in lipid bilayers are structurally more complex than fluid domains. Growth dynamics can lead to noncircular domains with a heterogeneous orientational texture. Most model membrane studies involving gel domain morphology and lateral organization assume the domains to be static. Here we show that rosette shaped gel domains, with heterogeneous orientational texture and a central topological defect, after early stage growth, undergo slow relaxation. On a time scale of days to weeks domains converge to circular shapes and approach uniform texture. 1,2-Dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) enriched gel domains are grown by cooling 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC):DPPC bilayers into the solid-liquid phase coexistence region and are visualized with fluorescence microscopy. The relaxation of individual domains is quantified through image analysis of time-lapse image series. We find a shape relaxation mechanism which is inconsistent with Ostwald ripening and coalescence as observed in membrane systems with coexisting liquid phases. Moreover, domain texture changes in parallel with the changes in domain shape, and selective melting and growth of particular subdomains cause the texture to become more uniform. We propose a relaxation mechanism based on relocation of lipids from high-energy lattice positions, through evaporation-condensation and edge diffusion, to low-energy positions. The relaxation process is modified significantly by binding Shiga toxin, a bacterial toxin from Shigella dysenteriae, to the membrane surface. Binding alters the equilibrium shape of the gel domains from circular to eroded rosettes with disjointed subdomains. This observation may be explained by edge diffusion while evaporation-condensation is restricted, and it provides further support for the proposed overall relaxation mechanism.

A mathematical model for plasticity and damage: A discrete calculus formulation

In this article we propose a discrete lattice model to simulate the elastic, plastic and failure behaviour of isotropic materials. Focus is given on the mathematical derivation of the lattice elements, nodes and edges, in the presence of plastic deformations and damage, i.e. stiffness degradation. By using discrete calculus and introducing non-local potential for plasticity, a force-based approach, we provide a matrix formulation necessary for software implementation. The output is a non-linear system with allowance for elasticity, plasticity and damage in lattices. This is the key tool for explicit analysis of micro-crack generation and population growth in plastically deforming metals, leading to macroscopic degradation of their mechanical properties and fitness for service. An illustrative example, analysing a local region of a node, is given to demonstrate the system performance.

Invisible surface defects in a tight-binding lattice

Surface Tamm states arise in one-dimensional lattices from some defects at the lattice edge and their energy generally falls in a gap of the crystal. The defects at the surface change rather generally the phase of propagative Bloch waves scattered off at the lattice edge, so that an observer, far from the surface, can detect the existence of edge defects from e.g. time-of-flight measurements as a delay or an advancement of a Bloch wave packet. Here we show that a special class of defects can sustain surface Tamm states which are invisible, in a sense that reflected waves acquire the same phase as in a fully homogeneous lattice with no surface state. Surface states have an energy embedded into the tight-binding lattice band and show a lower than exponential (algebraic) localization. Like most of bound states in the continuum of von Neumann - Wigner type, such states are fragile and decay into resonance surface states in presence of perturbations or lattice disorder. The impact of structural lattice imperfections and disorder on the invisibility of the defects is investigated by numerical simulations.

Experimental observation of bulk and edge transport in photonic Lieb lattices

We analyze the transport of light in the bulk and at the edge of photonic Lieb lattices, whose unique feature is the existence of a flat band representing stationary states in the middle of the band structure that can form localized bulk states. We find that transport in bulk Lieb lattices is significantly affected by the particular excitation site within the unit cell, due to overlap with the flat band states. Additionally, we demonstrate the existence of new edge states in anisotropic Lieb lattices. These states arise due to a virtual defect at the lattice edges and are not described by the standard tight-binding model.

Landau-Stark states in finite lattices and edge-induced Bloch oscillations

We consider the dynamics of a charged particle in a finite along the x-direction square lattice in the presence of a normal to the lattice plane magnetic field and an in-plane electric field aligned with the y-axis. For a vanishing magnetic field this dynamics would be common Bloch oscillations where the particle oscillates in the y-direction with an amplitude inverse proportional to the electric field. We show that a non-zero magnetic field crucially modifies this dynamics. Namely, the new Bloch oscillations consist of time intervals where the particle moves with constant velocity in the x-direction intermitted by intervals where it is accelerated or decelerated along the lattice edges. The analysis is done in terms of the Landau-Stark states which are eigenstates of a quantum particle in a two-dimensional lattice subject to (real or synthetic) electric and magnetic fields.

Floquet-Hubbard bound states in the continuum

We theoretically demonstrate that a type of robust two-particle bound state embedded in the continuum (BIC), which we call Floquet-Hubbard (FH) BIC, can be induced in a homogeneous (i.e., defect-free) Hubbard semilattice by an intense oscillating electric field. While single-particle BIC states are fragile states that exist solely for specially tailored potentials, FH BIC states are found in a wide range of parameter space, do not require fulfillment of resonance conditions, and are thresholdless. Analytical results are derived in the high-frequency limit of field modulation by a multiple-time-scale asymptotic analysis of the ac-driven Hubbard Hamiltonian in the two-particle sector. A FH BIC mode basically corresponds to a molecular state, in which the two particles bind together, undergoing correlated tunneling on the lattice. Localization of the molecular state is induced by the external oscillating field, which effectively attracts the molecular state at the edge of the semi-infinite lattice. Our results can pave the way for the study and interpretation of strong-field phenomena in correlated-particles physics.