Edge Plasmons Research Articles

Theory of plasmonic edge states in chiral bilayer systems

We analytically describe the plasmonic edge modes for an interface that involves the twisted bilayer graphene (TBG) or other similar Moire van der Waals heterostructure. For this purpose, we employ a spatially homogeneous, isotropic and frequency-dependent tensor conductivity which in principle accounts for electronic and electrostatic interlayer couplings. We predict that the edge mode dispersion relation explicitly depends on the chiral response even in the nonretarded limit, in contrast to the collective bulk plasmonic excitations in the TBG. We obtain a universal function for the dispersion of the optical edge plasmon in the paramagnetic regime. This implies a correspondence of the chiral-TBG optical plasmon to a magnetoplasmon of a single sheet, and chirality is interpreted as an effective magnetic field. The chirality also opens up the possibility of nearly undamped acoustic modes in the paramagnetic regime. Our results may guide future near-field nanoscopy for van der Waals heterostructures. In our analysis, we retain the long-range electrostatic interaction, and apply the Wiener-Hopf method to a system of integral equations for the scalar potentials of the two layers.

Optical N-invariant of graphene\u2019s topological viscous Hall fluid

Over the past three decades, graphene has become the prototypical platform for discovering topological phases of matter. Both the Chern Cin {mathbb{Z}} and quantum spin Hall upsilon in {{mathbb{Z}}}_{2} insulators were first predicted in graphene, which led to a veritable explosion of research in topological materials. We introduce a new topological classification of two-dimensional matter – the optical N-phases Nin {mathbb{Z}}. This topological quantum number is connected to polarization transport and captured solely by the spatiotemporal dispersion of the susceptibility tensor χ. We verify N ≠ 0 in graphene with the underlying physical mechanism being repulsive Hall viscosity. An experimental probe, evanescent magneto-optic Kerr effect (e-MOKE) spectroscopy, is proposed to explore the N-invariant. We also develop topological circulators by exploiting gapless edge plasmons that are immune to back-scattering and navigate sharp defects with impunity. Our work indicates that graphene with repulsive Hall viscosity is the first candidate material for a topological electromagnetic phase of matter.

Valley-Polarized Plasmonic Edge Mode Visualized in the Near-Infrared Spectral Range.

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.

Spin current generation by edge plasmons in graphene ribbons

We discuss the generation of a spin current by an edge plasmon in a graphene ribbon, which is a kind of surface plasmon that is localized near the edges of the ribbon. In contrast with a surface plasmon on the surface of a three-dimensional metal, the electric field of the edge plasmon rotates as a function of the time in the plane of graphene, which means that the optical spin-angular momentum of the edge plasmon is out of plane. We found that the electric-field-induced spin current flows by the inverse Faraday effect between the edges of the ribbon with spin polarization of electrons in the out-of-plane direction. The symmetric mode of the edge plasmon gives a larger magnitude of the spin current than the antisymmetric mode does. Moreover, the magnitude and direction of the spin current are tunable not only by the frequency of the edge plasmon, but also by the Fermi energy of graphene, which enables application to a spin-switching device controlled by a gate voltage.

A Nano‐Imaging Study of Graphene Edge Plasmons with Chirality‐Dependent Dispersions (Advanced Optical Materials 10/2021)

The graphene plasmons at the edges of a monolayer graphene have been demonstrated to exhibit superior electromagnetic ?eld con?nements. In article number 2100207, Huanjun Chen and co-workers show that, with a nano-imaging technique, the edge plasmon modes at zigzag and armchair edges exhibit chirality-dependent dispersions. In addition, due to the stronger molecule absorption ability of the zigzag edge, the associated plasmons exhibit a broader tuning range upon chemical doping via HNO3 exposure. This outcome highlights the potential of graphene zigzag edge in applications of nanoscale molecular sensing.

A Nano‐Imaging Study of Graphene Edge Plasmons with Chirality‐Dependent Dispersions

AbstractGraphene plasmons (GPs) have a variety of potential applications in nanophotonics and optoelectronics, such as room temperature mid‐infrared photodetectors, sensors, and modulators, due to their ultrahigh electromagnetic field confinements. In particular, the GPs at the edges of a monolayer graphene have been demonstrated to exhibit superior electromagnetic field confinements compared to the sheet plasmons. The graphene is terminated by two types of edges with different chiralities, that is, zigzag or armchair edge. Here, study of the plasmon modes at these two edges and their dispersions, is reported. The authors manage to visualize these two edges using a nano‐imaging technique, and show that edge plasmon behaviors are strongly dependent on chirality. The plasmon dispersions of these two edges can be modified upon chemical doping. Due to the stronger molecule absorption ability of the zigzag edge, the associated plasmons exhibit a broader tuning range.

Plasmons in two-dimensional topological insulators

We analyze collective excitations in models of two-dimensional topological insulators using the random phase approximation. In a two-dimensional extension of the Su-Schrieffer-Heeger model, edge plasmonic excitations with induced charge-density distributions localized at the boundaries of the system are found in the topologically non-trivial phase, dispersing similarly as one-dimensional bulk plasmons in the conventional Su-Schrieffer-Heeger chain. For two-dimensional bulk collective modes, we reveal regimes of enhanced inter-band wave function correlations, leading to characteristic hardening and softening of inter- and intra-band bulk plasmonic branches, respectively. In the two-dimensional Haldane Chern insulator model, chiral, uni-directional edge plasmons in nano-ribbon architectures are observed, which can be characterized by an effective Coulomb interaction cross section. Bulk collective excitations in the two-dimensional Haldane model are shown to be originated by single-particle band structure details in different topological phases.

Edge diffraction, plasmon launching, and universal absorption enhancement in two-dimensional junctions

Diffraction of light at lateral inhomogenities is a central process in the near-field studies of nanoscale phenomena, especially the propagation of surface waves. Theoretical description of this process is extremely challenging due to breakdown of plane-wave methods. Here, we present and analyze an exact solution for electromagnetic wave diffraction at the linear junction between two-dimensional electron systems (2DES) with dissimilar surface conductivities. The field at the junction is a combination of three components with different spatial structure: free-field component, non-resonant edge component, and surface plasmon-polariton (SPP). We find closed-form expressions for efficiency of photon-to-plasmon conversion by the edge being the ratio of electric fields in SPP and incident wave. Particularly, the conversion efficiency can considerably exceed unity for the contact between metal and 2DES with large impedance. Our findings can be considered as a first step toward quantitative near-field microscopy of inhomogeneous systems and polaritonic interferometry.

Illuminating the Electronic Properties of WS2 Polytypism with Electron Microscopy

AbstractTailoring the specific stacking sequence (polytypes) of layered materials represents a powerful strategy to identify and design novel physical properties. While nanostructures built upon transition‐metal dichalcogenides (TMDs) with either the 2H or 3R crystalline phases have been routinely studied, knowledge of TMD nanomaterials based on mixed 2H/3R polytypes is far more limited. In this work, mixed 2H/3R free‐standing WS2 nanostructures displaying a flower‐like configuration are fingerprinted by means of state‐of‐the‐art transmission electron microscopy. Their rich variety of shape‐morphology configurations is correlated with relevant local electronic properties such as edge, surface, and bulk plasmons. Machine learning is deployed to establish that the 2H/3R polytype displays an indirect band gap of . Further, high resolution electron energy‐loss spectroscopy reveals energy‐gain peaks exhibiting a gain‐to‐loss ratio greater than unity, a property that can be exploited for cooling strategies of atomically‐thin TMD nanostructures and devices built upon them. The findings of this work represent a stepping stone towards an improved understanding of TMD nanomaterials based on mixed crystalline phases.

Plasmonic Dirac Cone in Twisted Bilayer Graphene.

We discuss plasmons of biased twisted bilayer graphene when the Fermi level lies inside the gap. The collective excitations are a network of chiral edge plasmons (CEP) entirely composed of excitations in the topological electronic edge states that appear at the AB-BA interfaces. The CEP form a hexagonal network with a unique energy scale ε_{p}=(e^{2})/(ε_{0}εt_{0}) with t_{0} the moiré lattice constant and ε the dielectric constant. From the dielectric matrix we obtain the plasmon spectra that has two main characteristics: (i)a diverging density of states at zero energy, and (ii)the presence of a plasmonic Dirac cone at ℏω∼ε_{p}/2 with sound velocity v_{D}=0.0075c, which is formed by zigzag and armchair current oscillations. A network model reveals that the antisymmetry of the plasmon bands implies that CEP scatter at the hexagon vertices maximally in the deflected chiral outgoing directions, with a current ratio of 4/9 into each of the deflected directions and 1/9 into the forward one. We show that scanning near-field microscopy should be able to observe the predicted plasmonic Dirac cone and its broken symmetry phases.

Plasmonic Edge, Centre and Breathing Modes in Two-Dimensional Disks

Recently, plasmonic edge and breathing modes are obtained by electron energy loss spectroscopy in aluminum nanotriangles and silver nanodisks. In this article, based on the free-electron gas model and the linear response theory, we have derived the energy absorption spectrum and charge distributions under applied external fields to study the plasmons sustained by two-dimensional disks. Plasmonic edge, center and breathing modes are further observed by the charge distributions. In addition, with the help of energy absorption spectrum, the evolutionary characteristics of plasmon modes with the system parameters such as size, atomic separation and electron filling are further confirmed, and the effect of different applied external fields on plasmon excitations is displayed.

Simultaneous Quantification of Protein Binding Kinetics in Whole Cells with Surface Plasmon Resonance Imaging and Edge Deformation Tracking.

Most drugs work by binding to receptors on the cell surface. Quantification of binding kinetics between drug and membrane protein is an essential step in drug discovery. Current methods for measuring binding kinetics involve extracting the membrane protein and labeling, and both have issues. Surface plasmon resonance (SPR) imaging has been demonstrated for quantification of protein binding to cells with single-cell resolution, but it only senses the bottom of the cell and the signal diminishes with the molecule size. We have discovered that ligand binding to the cell surface is accompanied by a small cell membrane deformation, which can be used to measure the binding kinetics by tracking the cell edge deformation. Here, we report the first integration of SPR imaging and cell edge tracking methods in a single device, and we use lectin interaction as a model system to demonstrate the capability of the device. The integration enables the simultaneous collection of complementary information provided by both methods. Edge tracking provides the advantage of small molecule binding detection capability, while the SPR signal scales with the ligand mass and can quantify membrane protein density. The kinetic constants from the two methods were cross-validated and found to be in agreement at the single-cell level. The variation of observed rate constant between the two methods is about 0.009 s−1, which is about the same level as the cell-to-cell variations. This result confirms that both methods can be used to measure whole-cell binding kinetics, and the integration improves the reliability and capability of the measurement.

Tunable terahertz dual-band band-stop filter based on surface magnetoplasmons in graphene sheet array

Magnetically tunable terahertz dual-band band-stop filters are proposed based on the surface magnetoplasmons of graphene. The magnetoplasmons of a graphene rectangular sheet array can be attributed to the combination effects of the two edge plasmons along the length and width directions. Under external magnetic field the two plasmonic resonances are respectively blue-shifted and red-shifted, leading to different dips in the vertical transmission spectrum through the graphene array. Following this mechanism, narrow-band and wider-band band-stop filters with dual stop bands are theoretically obtained in composite structures consisting of graphene sheet array layers and semiconductor substrate layer. The influence brought by structural parameters and the chemical potential of graphene on the filtering performance are analyzed. Numerical results show the center frequencies of the two stop bands of the filters can be efficiently tuned by the intensity of the magnetic field.

Graphene plasmonic-assisted enhancement of linear and nonlinear optical properties of conic-shaped InAs/GaAs quantum dots with wetting layer

Graphene plasmonic (GP) in terahertz spectral range has been used to enhance the linear and nonlinear optical properties of conic-shaped InAs/GaAs quantum dots (QDs) coupled to wetting layer. Single layer graphene flakes with rectangular geometry in three configurations were located beneath the wetting layer (WL) and by exciting the plasmonic edge modes the transition dipole moments (TDMs) of S-to-P transition were calculated. Optimization on distance and thickness has been done to reach highest TDM. The results showed that the real and imaginary parts of linear susceptibility were enhanced ten and eighteen times, respectively. For third-order susceptibility, seven hundred and twelve thousand times enhancements have been observed for real and imaginary parts, respectively. • Graphene plasmonic has been used in quantum dots. • Plasmonic edge modes of graphene were excited in emission frequency of quantum dot. • Huge enhancements in optical properties were observed in linear and third-order susceptibilities.

Probing the Radiative Electromagnetic Local Density of States in Nanostructures with a Scanning Tunneling Microscope

A novel technique for the investigation of the radiative contribution to the electromagnetic local density of states is presented. The inelastic tunneling current from a scanning tunneling microscope (STM) is used to locally and electrically excite the plasmonic modes of a triangular gold platelet. The radiative decay of these modes is detected through the transparent substrate in the far field. Emission spectra, which depend on the position of the STM excitation, as well as energy-filtered emission maps for particular spectral windows are acquired using this technique. The STM-nanosource spectroscopy and microscopy results are compared to those obtained from spatially resolved electron energy loss spectroscopy (EELS) maps on similar platelets. While EELS is known to be related to the total projected electromagnetic local density of states, the light emission from the STM-nanosource is shown here to select the radiative contribution. Full electromagnetic calculations are carried out to explain the experimental STM data, and provide valuable insight into the radiative nature of the different contributions of the breathing and edge plasmon modes of the nanoparticles. Our results introduce the STM-nanosource as a tool to investigate and engineer light emission at the nanoscale.

Four-wave mixing of topological edge plasmons in graphene metasurfaces.

We study topologically protected four-wave mixing (FWM) interactions in a plasmonic metasurface consisting of a periodic array of nanoholes in a graphene sheet, which exhibits a wide topological bandgap at terahertz frequencies upon the breaking of time reversal symmetry by a static magnetic field. We demonstrate that due to the significant nonlinearity enhancement and large life time of graphene plasmons in specific configurations, a net gain of FWM interaction of plasmonic edge states located in the topological bandgap can be achieved with a pump power of less than 10 nW. In particular, we find that the effective nonlinear edge-waveguide coefficient is about γ ≃ 1.1 × 1013 W-1 m-1, i.e., more than 10 orders of magnitude larger than that of commonly used, highly nonlinear silicon photonic nanowires. These findings could pave a new way for developing ultralow-power-consumption, highly integrated, and robust active photonic systems at deep-subwavelength scale for applications in quantum communications and information processing.

Plasmonic Emission of Bullseye Nanoemitters on Bi2Te3 Nanoflakes.

Topological insulators, such as Bi2Te3, have been confirmed to exhibit plasmon radiation over the entire visible spectral range. Herein, we fabricate bullseye nanoemitters, consisting of a central disk and concentric gratings, on the Bi2Te3 nanoflake. Due to the existence of edge plasmon modes, Bi2Te3 bullseye nanostructures are possible to converge light towards the central disk. Taking advantage of the excellent spatial resolution of cathodoluminescence (CL) characterization, it has been observed that plasmonic behaviors depend on the excitation location. A stronger plasmonic intensity and a wider CL spectral linewidth can be obtained at the edge of the central disk. In order to further improve the focusing ability, a cylindrical Pt nanostructure has been deposited on the central disk. Additionally, the finite element simulation indicates that the electric-field enhancement originates from the coupling process between the plasmonic emission from the Bi2Te3 bullseye and the Pt nanostructure. Finally, we find that enhancement efficiency depends on the thickness of the Pt nanostructure.

Attomolar SERS detection of organophosphorous pesticides using silver mirror-like micro-pyramids as active substrate.

Surface-enhanced Raman spectroscopy (SERS) is gaining importance as an ultrasensitive analytical tool for routine high-throughput analysis of a variety of molecular compounds. One of the main challenges is the development of robust, reproducible and cost-effective SERS substrates. In this work, we study the SERS activity of 3D silver mirror-like micro-pyramid structures extended in the z-direction up to 3.7μm (G0 type substrate) or 7.7μm (G1 type substrate), prepared by Si-based microfabrication technologies, for trace detection of organophosphorous pesticides, using paraoxon-methyl as probe molecule. The average relative standard deviation (RSD) for the SERS intensity of the peak displayed at 1338cm-1 recorded over a centimetre scale area of the substrate is below 13% for pesticide concentrations in the range 10-6 to 10-15molL-1. This data underlies the spatial uniformity of the SERS response provided by the microfabrication approach. According to finite-difference time-domain (FDTD) simulations, such remarkable feature is mainly due to the contribution on electromagnetic field enhancement of edge plasmon polaritons (EPPs), propagating along the pyramid edges where the pesticide molecules are preferentially adsorbed. Graphical abstract.

Coupled edge modes supported by a microwave metasurface

Microwave metasurfaces comprising overlapping layers of circular patches arranged in a hexagonal array are found to support edge modes akin to edge plasmons. The coupling of these edge modes across small gaps between two such arrays is explored. This phenomenon, well known at optical frequencies, is verified here for the first time, to the best of our knowledge, at microwave frequencies.

Edge-Plasmon Whispering-Gallery Modes in Nanoholes

Metallic apertures support a rich variety of widely investigated electromagnetic phenomena, which are the basis of many optical devices. Research on edge plasmons in these structures is scarce, though, and limited to dipolar resonances. This study shows that nanoholes additionally support high-order edge plasmons, in the form of whispering-gallery modes. Notably, the excited orders are determined by the lattice symmetries, are very sensitive to the environment, and exhibit highly tailorable features. These results shed light on the physics of metallic nanoholes and point to applications in nanophotonics and plasmonics.