Edge Plasmons Research Articles

Unidirectional plasmonic edge modes on general two-dimensional materials

We investigate the field and spin-momentum coupling of edge plasmons hosted by general two-dimensional materials and identify sweet spots depending on the polarisation plane, ellipticity and the position of an electric dipole relative to the plane and edge. Exciting the dipole at these sweet spots by propagating light leads to uni-directional propagating edge plasmons or edge modes suppression. We also extend previous approximate treatments (Fetter 1985 Phys. Rev. B 32 7676) to include anisotropy and hyperbolic systems, elucidating its predictions for the existence of edge modes. A thorough assessment of the approximate description is carried out, comparing its spin-momentum coupling features in the near field with exact results from Wiener–Hopf techniques. Simulations are also performed confirming the overall picture. Our results shed new light on the quest of chiral plasmonics in 2D materials and should be relevant for future experiments.

Electrically defined topological interface states of graphene surface plasmons based on a gate-tunable quantum Bragg grating

Abstract A periodic metagate is designed on top of a boron nitride-graphene heterostructure to modulate the local carrier density distribution on the monolayer graphene. This causes the bandgaps of graphene surface plasmon polaritons to emerge because of either the interaction between the plasmon modes, which are mediated by the varying local carrier densities, or their interaction with the metal gates. Using the example of a double-gate graphene device, we discuss the tunable band properties of graphene plasmons due to the competition between these two mechanisms. Because of this, a bandgap inversion, which results in a Zak phase switching, can be realized through electrostatic gating. Here we also show that an anisotropic plasmonic topological edge state exists at the interface between two graphene gratings of different Zak phases. While the orientation of the dipole moments can differentiate the band topologies of each graphene grating, the angle of radiation remains a tunable property. This may serve as a stepping stone toward active control of the band structures of surface plasmons for potential applications in optical communication, wave steering, or sensing.

Edge modes of chiral Berry plasmons in graphene nanoribbons

This study examines the edge modes of chiral Berry plasmons propagating along zigzag or armchair edges of a graphene nanoribbon under a finite Berry flux and Fermi pressure. A two-dimensional quantum hydrodynamic model is used to derive analytical expressions of the dispersion relation and transverse confinement length. Direction-dependent edge modes exist in armchair nanoribbons under antisymmetric or symmetric boundary conditions. A confined mode appears in the zigzag nanoribbon under hard-wall boundary conditions. The transverse confinement length of edge plasmons in the nanoribbon can be an order of magnitude shorter than that in the semi-infinite structure.

Manipulating acoustic and plasmonic modes in gold nanostars.

In this contribution experimental evidence of plasmonic edge modes and acoustic breathing modes in gold nanostars (AuNSs) is reported. AuNSs are synthesized by a surfactant-free, one-step wet-chemistry method. Optical extinction measurements of AuNSs confirm the presence of localized surface plasmon resonances (LSPRs), while electron energy-loss spectroscopy (EELS) using a scanning transmission electron microscope (STEM) shows the spatial distribution of LSPRs and reveals the presence of acoustic breathing modes. Plasmonic hot-spots generated at the pinnacle of the sharp spikes, due to the optically active dipolar edge mode, allow significant intensity enhancement of local fields and hot-electron injection, and are thus useful for size detection of small protein molecules. The breathing modes observed away from the apices of the nanostars are identified as stimulated dark modes – they have an acoustic nature – and likely originate from the confinement of the surface plasmon by the geometrical boundaries of a nanostructure. The presence of both types of modes is verified by numerical simulations. Both these modes offer the possibility of designing nanoplasmonic antennas based on AuNSs, which can provide information on both mass and polarizability of biomolecules using a two-step molecular detection process.

Tailoring absorption spectrum by inserting an epsilon-near-zero film into metal-dielectric-metal assembly

A method of tailoring the absorption band generated by metal-dielectric-metal (MDM) resonator is analytically proposed and numerically investigated in this paper. By inserting an epsilon-near-zero (ENZ) film into the MDM layers, the absorption bandwidth can be sufficiently widened due to the coupling from ENZ mode to localized edge plasmon mode. Theoretical instructions of how to design respective layer thickness to obtain optimized absorption rate are investigated with the guidance of vast simulations and the hybrid resonance characteristics by the coupling from ENZ mode are further inspected by monitoring the resonant electric and magnetic field. The meta-absorber can achieve high absorption with a large bandwidth under oblique incidence. The method and the structure proposed in this paper have potential views in highly integrated nanostructures in solar cells, photovoltaic and sensing application fields.

Multiple harmonics control of edge pseudomagnetoplasmons in strained graphene

Valley-resolved edge plasmons are relevant to nano-optics at subwavelength scales. However, less attention has been paid to their tunable properties in time domain. In this work we investigate edge pseudomagnetoplasmons in a strained graphene modulated by multiple harmonics with frequency in the THz regime. The edge plasmon is described by a set of nonlinear hydrodynamic equations, which are self-consistently solved by the flux-corrected transport method. Without the applied voltage, there exist two unidirectional-propagating edge-plasmon modes with weak valley polarization P. It is demonstrated that by varying the amplitude of multiple harmonics one can alter both the amplitude and the polarity of the valley polarization in the edge plasmon. One can achieve a full valley polarization P=1 at the instant of half cycle of the multiple harmonics and P=-1 at the instant of one cycle. The edge-plasmon density and the transverse velocity vanish for the frozen valley.

Plasmonic topological edge states in ring-structure gate graphene.

Topological photonic states exhibit unique robustness against defects, facilitating fault-tolerant photonic device applications. However, existing proposals either involve a sophisticated and bulky structure or can only operate in the microwave regime. We show a theoretical demonstration for highly confined topologically protected plasmonic states to be realized at infrared frequencies in monolayer graphene with a ring-structure gate. With a suitable bias voltage, the combined gate-graphene structure is shown to produce sufficiently strong Bragg scattering of graphene surface plasmons and to impart them with nontrivial topological properties. Our design is compact and could pave the way for dynamically reconfigurable, robust, nanoscale, integrated photonic devices.

Field-induced spin-polarized electronic and optical properties of armchair stanene nanoribbons

Electronic and optical properties of armchair stanene nanoribbons are studied within the sp3 tight-binding model including spin-orbit coupling in the presence of in-plane electric field. Electric field strongly modulates energy dispersions leading to a zero-gap transition, shift in edge-states, and exhibition of spin-splitting states. Then, the complex dielectric functions in the long wavelength limit is calculated from the gradient approximation. More field-induced transition channels exhibit richer optical spectra which further reveal spin-polarized feature at low frequency. Prominent plasmons in loss spectra come from π–σ mixing orbital. The plasmon peak frequency and height are tuned by field strength. Also, the threshold plasmon frequency linearly decreases as electric field increases and it vanishes at critical field. The reflectance exhibits oscillatory behaviors and shows dip structures with sharp plasmon edge, undergoing a red-shift with increasing field. The calculated results fully show that field-modulations of electronic and optical properties strongly depend on nanoribbon's geometry.

Probing plasmons on the edge of graphene nanoribbons under electric field

By using first principle method, we address the plasmon excitation in narrow zigzag and armchair graphene nanoribbons under the effect of the perpendicular electric field. We observed that the edge plasmons with very high one-dimensional confinement mainly originated from π transition peaks and along with increasing the ribbon width, edges contribute much less than in narrow ribbons. Applying electric field excites and hybrids distinct plasmon modes which indicate, the magnitude, intensity and type of plasmon modes within various momentum transfer range are dependent differently on the gating. The key role of charge polarization at the edge and surface plasmons is discussed in the presence of electric field based on the evolution of the dielectric function. Confined edge and surface plasmon modes change under electric field makes graphene nanoribbons a suitable candidate for new terahertz plasmonic applications.

Chiral surface and edge plasmons in ferromagnetic conductors

The recently introduced concept of "surface Berry plasmons" is studied in the concrete instance of a ferromagnetic conductor in which the Berry curvature, generated by spin-orbit (SO) interaction, has opposite signs for carriers parallel or antiparallel to the magnetization. By using collisionless hy- drodynamic equations with appropriate boundary conditions, we study both the surface plasmons of a three-dimensional ferromagnetic conductor and the edge plasmons of a two-dimensional one. The anomalous velocity and the broken inversion symmetry at the surface or the edge of the conductor create a "handedness", whereby the plasmon frequency depends not only on the angle between the wave vector and the magnetization, but also on the direction of propagation along a given line. In particular, we find that the frequency of the edge plasmon depends on the direction of propagation along the edge. These Berry curvature effects are compared and contrasted with similar effects induced in the plasmon dispersion by an external magnetic field in the absence of Berry curvature. We argue that Berry curvature effects may be used to control the direction of propagation of the surface plasmons via coupling with the magnetization of ferromagnetic conductors, and thus create a link between plasmonics and spintronics.

Ultrahigh refractive index sensitivity via lattice-induced meta-dipole modes in flat metallic nanoantenna arrays

We investigate control of plasmonic-photonic coupling in flat metallic nanoantenna arrays. We demonstrate that when the nanoantennas are packed together along their short axis (transverse lattice constant) and the incident light polarization is along their long axis, they can support lattice-induced plasmonic resonance coupled to a super-photonic mode that densely fills the superstrate volume. Our results show that at a certain wavelength, this resonance joins the plasmonic tip modes of the nanoantennas, forming meta-dipole modes. These modes have field profiles similar to those of the natural plasmonic dipole modes of individual nanoantennas, but they occur at much shorter wavelengths and offer a very high bulk refractive index sensitivity (925 ± 12 nm/RIU). We show that with an increase in the transverse lattice constant, such a sensitivity decreases as the meta-dipole modes disappear. Under this condition, the refractive index sensitivity supported by natural modes of the nanoantennas increases, as the plasmonic edge mode suppression caused by charge rearrangement decreases.

Nonsymmorphic symmetry-protected topological modes in plasmonic nanoribbon lattices

Using a dynamic eigenresponse theory, we study the topological edge plasmon modes in dispersive plasmonic lattices constructed by unit cells of multiple nanoribbons. In dipole approximation, the bulk-edge correspondence in the lattices made of dimerized unit cell and one of its square-root daughter with nonsymmorphic symmetry are demonstrated. Calculations with consideration of dynamic long-range effects and retardation are compared to those given by nearest-neighbor approximations. It is shown that nonsymmorphic symmetry opens up two symmetric gaps where versatile topological edge plasmon modes are found. Unprecedented spectral shifts of the edge states with respect to the zero modes due to long-range coupling are found. The proposed ribbon structure is favorable to electrical gating and thus could serve as an on-chip platform for electrically controllable subwavelength edge states at optical wavelengths. Our eigenresponse approach provides a powerful tool for the radiative topological mode analysis in strongly coupled plasmonic lattices.

Valley-polarized edge pseudomagnetoplasmons in graphene: A two-component hydrodynamic model

By means of a nonlinear two-component hydrodynamic model, we study the valley-polarized collective motion of electrons in a strained graphene sheet. The self-consistent numerical solution in real space indicates the existence of valley-polarized edge plasmons due to a strain-induced pseudomagnetic field. The valley polarization of the edge pseudomagnetoplasmon can occur in a specific valley, depending on the pseudomagnetic field and the electron density in equilibrium. A full valley polarization is achieved at the edge of the graphene sheet for a pseudomagnetic field of tens of Tesla, which is a realistic value in current experimental technologies.

Observation and Manipulation of Visible Edge Plasmons in Bi2Te3 Nanoplates.

Noble metals, like Ag and Au, are the most intensively studied plasmonic materials in the visible range. Plasmons in semiconductors, however, are usually believed to be in the infrared wavelength region due to the intrinsic low carrier concentrations. Herein, we observe the edge plasmon modes of Bi2Te3, a narrow-band gap semiconductor, in the visible spectral range using photoemission electron microscopy (PEEM). The Bi2Te3 nanoplates excited by 400 nm femtosecond laser pulses exhibit strong photoemission intensities along the edges, which follow a cos4 dependence on the polarization state of incident beam. Because of the phase retardation effect, plasmonic response along different edges can be selectively exited. The thickness-dependent photoemission intensities exclude the spin-orbit induced surface states as the origin of these plasmonic modes. Instead, we propose that the interband transition-induced nonequilibrium carriers might play a key role. Our results not only experimentally demonstrate the possibility of visible plasmons in semiconducting materials but also open up a new avenue for exploring the optical properties of topological insulator materials using PEEM.

Tuning Infrared Plasmon Resonance of Black Phosphorene Nanoribbon with a Dielectric Interface

We report on the tunable edge-plasmon-enhanced absorption of phosphorene nanoribbons supported on a dielectric substrate. Monolayer anisotropic black phosphorous (phosphorene) nanoribbons are explored for light trapping and absorption enhancement on different dielectric substrates. We show that these phosphorene ribbons support infrared surface plasmons with high spatial confinement. The peak position and bandwidth of the calculated phosphorene absorption spectra are tunable with low loss over a wide wavelength range via the surrounding dielectric environment of the periodic nanoribbons. Simulation results show strong edge plasmon modes and enhanced absorption as well as a red-shift of the peak resonance wavelength. The periodic Fabry-Perot grating model was used to analytically evaluate the absorption resonance arising from the edge of the ribbons for comparison with the simulation. The results show promise for the promotion of phosphorene plasmons for both fundamental studies and potential applications in the infrared spectral range.

Zero-field edge plasmons in a magnetic topological insulator

Incorporating ferromagnetic dopants into three-dimensional topological insulator thin films has recently led to the realisation of the quantum anomalous Hall effect. These materials are of great interest since they may support electrical currents that flow without resistance, even at zero magnetic field. To date, the quantum anomalous Hall effect has been investigated using low-frequency transport measurements. However, transport results can be difficult to interpret due to the presence of parallel conductive paths, or because additional non-chiral edge channels may exist. Here we move beyond transport measurements by probing the microwave response of a magnetised disk of Cr-(Bi,Sb)2Te3. We identify features associated with chiral edge plasmons, a signature that robust edge channels are intrinsic to this material system. Our results provide a measure of the velocity of edge excitations without contacting the sample, and pave the way for an on-chip circuit element of practical importance: the zero-field microwave circulator.

Self-Similarity of Plasmon Edge Modes on Koch Fractal Antennas.

We investigate the plasmonic behavior of Koch snowflake fractal geometries and their possible application as broadband optical antennas. Lithographically defined planar silver Koch fractal antennas were fabricated and characterized with high spatial and spectral resolution using electron energy loss spectroscopy. The experimental data are supported by numerical calculations carried out with a surface integral equation method. Multiple surface plasmon edge modes supported by the fractal structures have been imaged and analyzed. Furthermore, by isolating and reproducing self-similar features in long silver strip antennas, the edge modes present in the Koch snowflake fractals are identified. We demonstrate that the fractal response can be obtained by the sum of basic self-similar segments called characteristic edge units. Interestingly, the plasmon edge modes follow a fractal-scaling rule that depends on these self-similar segments formed in the structure after a fractal iteration. As the size of a fractal structure is reduced, coupling of the modes in the characteristic edge units becomes relevant, and the symmetry of the fractal affects the formation of hybrid modes. This analysis can be utilized not only to understand the edge modes in other planar structures but also in the design and fabrication of fractal structures for nanophotonic applications.

Effect of edge plasmons on the optical properties of MoS2 monolayer flakes

The electronic edge states of MoS${}_{2}$ nanoparticles are important for the catalytic activity of the particles and could also have potential for photocatalysis. Here, the authors explore computationally optical properties of MoS${}_{2}$ monolayer nanoflakes. These nanostructures show a rich size-dependent optical response below the absorption onset of the infinite monolayer. The authors present a detailed analysis of the emerging optical absorption resonances revealing their edge-state origins. In particular, metallic edge states support localized edge plasmons, and overall, resonances are sensitive to changes in the edge-atom configuration.

Hybridized Plasmons in 2D Nanoslits: From Graphene to Anisotropic 2D Materials

Plasmon coupling and hybridization in complex nanostructures constitutes a fertile playground for controlling light at the nanoscale. Here, we present a semi-analytical model to describe the emergence of hybrid plasmon modes guided along 2D nano-slits. In particular, we find two new coupled plasmonic resonances arising from symmetric and antisymmetric hybridizations of the edge plasmons of the constituent half-sheets. These give rise to an antibonding and a bonding mode, lying above and below the energy of the bare edge plasmon. Our treatment is notably generic, being able to account for slits of arbitrary width, and remains valid irrespective of the 2D conductive material (e.g., doped graphene, 2D transition metal dichalcogenides, or phosphorene). We derive the dispersion relation of the hybrid modes of a 2D nano-slit along with the corresponding induced potential and electric field distributions. We also discuss the plasmonic spectrum of a 2D slit together with the one from its complementarity structure, that is, a ribbon. Finally, the case of a nano-slit made from an anisotropic 2D material is considered. Focusing on black phosphorus (which is highly anisotropic), we investigate the features of its plasmonic spectrum along the two main crystal axes. Our results offer insights into the interaction of plasmons in complex 2D nanostructures, thereby expanding the current toolkit of plasmonic resonances in 2D materials, and paving the way for the emergence of future compact devices based on atomically thin plasmonics.

Infrared Topological Plasmons in Graphene.

We propose a two-dimensional plasmonic platform-periodically patterned monolayer graphene-which hosts topological one-way edge states operable up to infrared frequencies. We classify the band topology of this plasmonic system under time-reversal-symmetry breaking induced by a static magnetic field. At finite doping, the system supports topologically nontrivial band gaps with mid-gap frequencies up to tens of terahertz. By the bulk-edge correspondence, these band gaps host topologically protected one-way edge plasmons, which are immune to backscattering from structural defects and subject only to intrinsic material and radiation loss. Our findings reveal a promising approach to engineer topologically robust chiral plasmonic devices and demonstrate a realistic example of high-frequency topological edge states.