Bulk Plasmon Modes Research Articles

Intrinsic nonreciprocal bulk plasmons in noncentrosymmetric magnetic systems

Nonreciprocal plasmonics plays a crucial role in enabling one-way light propagation at the nanoscale and is a fundamental building block for photonic applications. Here, we investigate intrinsic nonreciprocity in bulk plasmon dispersion in systems that break both parity and time-reversal symmetry. We demonstrate that both interband and intraband bulk plasmon modes exhibit intrinsically asymmetric dispersion depending on the sign of the wave vector. Our study reveals that the intrinsic nonreciprocity in interband plasmon dispersion is governed by quantum metric connection. The nonreciprocity in the intraband plasmon dispersion is dictated by the quantum metric dipole and a higher-order ``Drude''-weight-like term. We corroborate our findings via explicit numerical calculations for the two-dimensional Qi-Wu-Zhang model, and we demonstrate the existence of intrinsic nonreciprocal intraband and interband plasmon modes in moir\'e systems such as twisted bilayer graphene. Our findings offer insights into the underlying physics of nonreciprocal plasmonics and pave the way for designing novel photonic devices.

Excitation of tunable plasmons in silicon using microwave transmission through a metallic aperture

Plasmon resonances in semiconductors at microwave frequencies offer the possibility for many functionalities and integration schemes. Semiconductor materials, such as germanium, gallium arsenide, and silicon, have the further advantage of being able to be integrated with standard electronics technology. Here, we probe the bulk plasmon modes in silicon in the vicinity of a copper plate perforated by a single aperture at frequencies between 10 and 60 GHz. Sharp transmission minima are observed at discrete frequencies. The observed frequencies depend on the size of the aperture and the carrier concentration in the silicon; they are well reproduced by the dispersion relation for bulk plasmons. Our results show that one can excite plasmons in silicon in the millimeter-wave region, opening a route to microwave plasmonics for large-scale applications, using low-cost technology.

Topological characteristic of Weyl degeneracies in a reciprocal chiral metamaterials system

Being a research hotspot in the field of topological semimetals, Weyl points (WPs) are monopoles of Berry curvature in momentum space. In this paper, we report the existence of photonic Weyl degeneracies in a reciprocal chiral metamaterials system. Due to the flat dispersion relation of the bulk plasmon modes, Weyl degeneracies here lie right on the critical transition between the type-I and type-II WPs. The photonic ‘Fermi arc’ connects the projection of pairs of WPs at the interface between the metamaterials and vacuum. Despite the bulk equi-frequency surfaces have changed dramatically, the ‘Fermi arc’ always exists. In addition, numerical simulations of topologically protected ‘Fermi arc’ surface states show that the surface waves are not scattered or reflected by the presence of sharp corners. Notably, such metamaterials host either type-I, type-II WPs or triple degenerate points (TDPs) depending on the nonlocal response. Our work provides an ideal photonic platform for studying the closely relation between WPs and other exotic states.

Photonic Transmittance in Metallic and Left Handed Superlattices

We study the transmission of electromagnetic waves through layered structures of metallic and left-handed media. Resonant band structures of transmission coefficients are obtained as functions of the incidence angle, the geometric parameters, and the number of unit cells of the superlattices. The theory of finite periodic systems that we use is free of assumptions, the finiteness of the periodic system being an essential condition. We rederive the correct recurrence relation of the Chebyshev polynomials that carry the physical information of the coherent coupling of plasmon modes and interface plasmons and surface plasmons, responsible for the photonic bands and the resonant structure of the surface plasmon polaritons. Unlike the dispersion relations of infinite periodic systems, which at best predict the bandwidths, we show that the dispersion relation of this theory predicts not only the bands, but also the resonant plasmons’ frequencies, above and below the plasma frequency. We show that, besides the strong influence of the incidence angle and the characteristic low transmission of a single conductor slab for frequencies ω below the plasma frequency ω p , the coherent coupling of the bulk plasmon modes and the interface surface plasmon polaritons lead to oscillating transmission coefficients and, depending on the parity of the number of unit cells n of the superlattice, the transmission coefficient vanishes or amplifies as the conductor width increases. Similarly, the well-established transmission coefficient of a single left-handed slab, which exhibits optical antimatter effects, becomes highly resonant with superluminal effects in superlattices. We determine the space-time evolution of a wave packet through the λ / 4 photonic superlattice whose bandwidth becomes negligible, and the transmission coefficient becomes a sequence of isolated and equidistant peaks with negative phase times. We show that the space-time evolution of a Gaussian wave packet, with the centroid at any of these peaks, agrees with the theoretical predictions, and no violation of the causality principle occurs.

Energy loss spectrum and surface modes of two-dimensional black phosphorus

The structural features and the electron energy loss spectrum of black phosphorus (BP) have been experimentally analyzed and they are discussed based on a theoretical calculation. The low-energy loss spectra of typical samples reveal that the emerging high-mobility two-dimensional material BP often exhibits both bulk and surface plasmon modes. The surface modes of BP are strongly thickness dependent. Electrodynamic analysis indicates that the Fuchs–Kliewer-like surface plasmon modes consist of two branches with different charge symmetry: the upper side and lower side have the same charge polarity as the lower branch and the opposite charge polarity to the upper branch. This study provides fundamental insight into the characteristic nature of BP plasmonics.

Probing plasmon resonances of individual aluminum nanoparticles

The plasmon resonances of individual aluminum nanoparticles are investigated by electron energy-loss spectroscopy (EELS) in scanning transmission electron microscope (STEM). Surface plasmon mode and bulk plasmon mode of Al nanoparticles are clearly characterized in the EEL spectra. Discrete dipole approximation (DDA) calculations show that as the particle diameter increases from 20 nm to 100 nm, the plasmon resonance shifts to lower energy and higher mode of surface plasmon arises when the diameter reaches 60 nm and larger.

Plasmon Excitations of Multi-layer Graphene on a Conducting Substrate.

We predict the existence of low-frequency nonlocal plasmons at the vacuum-surface interface of a superlattice of N graphene layers interacting with conducting substrate. We derive a dispersion function that incorporates the polarization function of both the graphene monolayers and the semi-infinite electron liquid at whose surface the electrons scatter specularly. We find a surface plasmon-polariton that is not damped by particle-hole excitations or the bulk modes and which separates below the continuum mini-band of bulk plasmon modes. The surface plasmon frequency of the hybrid structure always lies below , the surface plasmon frequency of the conducting substrate. The intensity of this mode depends on the distance of the graphene layers from the conductor’s surface, the energy band gap between valence and conduction bands of graphene monolayer and, most importantly, on the number of two-dimensional layers. For a sufficiently large number of layers the hybrid structure has no surface plasmon. The existence of plasmons with different dispersion relations indicates that quasiparticles with different group velocity may coexist for various ranges of wavelengths determined by the number of layers in the superlattice.

Second Harmonic Generation from Metal Nano-Particle Resonators: Numerical Analysis On the Basis of the Hydrodynamic Drude Model

A detailed computational study of the wavelength-dependent efficiency of optical second-harmonic generation in plasmonic nanostructures is presented. The computations are based on a discontinuous Galerkin Maxwell solver that utilizes a hydrodynamic material model to calculate the free-electron dynamics in metals without any further approximations. Besides wave-mixing effects, the material model thus contains the full nonlocal characteristics of the electromagnetic response, as well as intensity-dependent phenomena such as the Kerr effect. To be specific, two prototypical nanostructures are studied in depth with the help of two independent computer codes. For an infinitely long metal cylinder, it is found that the spectral position of linear particle plasmon modes (dipolar modes, higher-order modes, and, for frequencies above the plasma frequency also bulk plasmon modes) and their associated relative strengths for scattering and absorption both at the fundamental and second-harmonic wavelengths largely con...

Plasmon modes of spherical nanoparticles: The effects of quantum nonlocality

Abstract We develop a new method for calculating the electrostatic surface and bulk plasmon modes of a spherical metal nanoparticle, by taking into account the quantum nonlocal effects. To describe these phenomena, we develop analytical theory based on the quantum hydrodynamical model of plasmon excitation. We derive new dispersion relation for the system and investigate its differences with previous treatments based on the standard nonlocal model.

Plasmon modes of metallic nanowires including quantum nonlocal effects

The properties of electrostatic surface and bulk plasmon modes of cylindrical metallic nanowires are investigated, using the quantum hydrodynamic theory of plasmon excitation which allows an analytical study of quantum tunneling effects through the Bohm potential term. New dispersion relations are obtained for each type of mode and their differences with previous treatments based on the standard hydrodynamic model are analyzed in detail. Numerical results show by considering the quantum effects, as the value of wave number increases, the surface modes are slightly red-shifted first and then blue-shifted while the bulk modes are blue-shifted.

Negative refraction in graphene-based hyperbolic metamaterials

Here, we numerically investigate the existence of negative group refraction in graphene-based hyperbolic metamaterials (HMM) at THz frequencies. The hyperbolic dispersion of the graphene-based HMM can be tuned by varying the chemical potential and surrounding dielectric layer thickness. The negative group and positive phase indices of refraction are observed for oblique incidence at far below the critical frequency, which permits negative energy refraction and forward wavefront propagation. The highly confined bulk plasmon modes are also observed in the negative group index region that further evidence the negative refraction behaviour of the graphene-based hyperbolic metamaterials.

Visualizing hybridized quantum plasmons in coupled nanowires: From classical to tunneling regime

We present full quantum mechanical calculations of the hybridized plasmon modes of two nanowires at small separation, providing real space visualization of the modes in the transition from the classical to the quantum tunneling regime. The plasmon modes are obtained as certain eigenfunctions of the dynamical dielectric function which is computed using time dependent density functional theory (TDDFT). For freestanding wires, the energy of both surface and bulk plasmon modes deviate from the classical result for low wire radii and high momentum transfer due to effects of electron spill-out, non-local response, and coupling to single-particle transitions. For the wire dimer the shape of the hybridized plasmon modes are continuously altered with decreasing separation, and below 6 {\AA} the energy dispersion of the modes deviate from classical results due to the onset of weak tunneling. Below 2-3 {\AA} separation this mode is replaced by a charge-transfer plasmon which blue shifts with decreasing separation in agreement with experiment, and marks the onset of the strong tunneling regime.

Plasmon-polariton signature in the transmission and reflection spectra of one-dimensional metamaterial heterostructures

ABSTRACTThe transmission and reflection properties of a meta-stack composed of a periodic AB arrangement of an air(A)/metamaterial(B) bilayer is presented, with the multi layered system embedded between two semi-infinite layers of the A material. For oblique incidence, a finite projection along the growth direction of the electric or magnetic field of the incident wave associated with the TM or TE modes, respectively, leads to a coupling of the photon modes with the bulk electric or magnetic metamaterial plasmons, in each layer of the meta-stack. This field-matter coupling gives rise to plasmon-polariton modes and signatures of electric or magnetic longitudinal bulk-plasmon polariton modes in the transmission, as well as in the reflection properties of the meta-stack, by means of a plasmon-polariton gap. Such features survive even in the case of a single bilayer and experimental observation should be, therefore, easily achieved.

Infrared Spectroscopy of Tunable Dirac Terahertz Magneto-Plasmons in Graphene

We present infrared spectroscopy study of plasmon excitations in graphene in high magnetic fields. The plasmon resonance in patterned graphene disks splits into edge and bulk plasmon modes in magnetic fields. Remarkably, the edge plasmons develop increasingly longer lifetimes in high fields due to the suppression of backscattering. Moreover, due to the linear band structure of graphene, the splitting of the edge and bulk plasmon modes develops a strong doping dependence, which differs from the behavior of conventional semiconductor two-dimensional electron gas (2DEG) systems. We also observe the appearance of a higher order mode indicating an anharmonic confinement potential even in these well-defined circular disks. Our work not only opens an avenue for the investigation of the properties of Dirac magnetoplasmons but also supports the great potential of graphene for tunable terahertz magneto-optical devices.

Plasmon-assisted electron-electron collisions at metallic surfaces

We present a theoretical treatment for the ejection of a secondary electron from a clean metallic surface induced by the impact of a fast primary electron. Assuming a direct scattering between the incident, primary electron and the electron in a metal, we calculate the electron-pair energy distributions at the surfaces of Al and Be. Different models for the screening of the electron-electron interaction are examined, and the footprints of the surface- and the bulk-plasmon modes are determined and analyzed. The formulated theoretical approach is compared with the available experimental data on the electron-pair emission from Al.

Collective excitations on silver surfaces studied by photoyield

The surface electronic structure of Ag has been studied using angle and energy resolved photoyield (AERPY) using low photon energies (2.7–18 eV). The adlayer standing-wave-like bulk plasmon mode is clearly observed in Ag(1 1 1) and Ag(1 0 0) thin films. A feature at 3.7 eV, observed both on Ag adlayers and bulk crystal surface, is assigned to the multipole plasmon mode. No signature of the multipole plasmon is observed around 6.7 eV, which is in disagreement with the prediction of the s–d polarization model.

Electronic excitations on silver surfaces

The surface electronic structure and optical response of Ag has been studied using angle- and energy-resolved photoyield (AERPY) and angle-resolved photoemission spectroscopy (ARPES) using low energy photons (2.7-18 eV). ARPES data for Ag(100) exhibit an unexpected dispersing feature which cannot be assigned to a direct transition peak in the ΓX direction of the bulk Brillouin zone. The origin of this feature is found in the surface mediated indirect transitions related to the direct transition in the ΓL direction. From the AERPY experiments, the adlayer standing-wave-like bulk plasmon mode is clearly observed in Ag(100) and Ag(111) thin films. The silver multipole plasmon is observed both on Ag adlayers and bulk single crystal surfaces at 3.7 eV. No signature of the multipole plasmon is observed around 6.7 eV, in disagreement with the prediction of the s-d polarization model.

Scanning probe energy loss spectroscopy: Angular resolved measurements on silicon and graphite surfaces

We report angle resolved “scanning probe energy loss spectroscopy” measurements from Si(111)-7×7 and graphite surfaces. Electrons incident on the surface after field emission from a scanning tunneling microscope tip are backscattered and detected with an energy and angle resolved hemispherical analyzer. We find that the reflected signal is sharply peaked in the direction parallel to the surface plane. Characteristic energy loss peaks corresponding to bulk and surface plasmon modes of the different surfaces are observed.

Inelastic x-ray scattering in single-crystal C60.

We have measured energy-loss spectra of electrons in a single crystal of ${\mathrm{C}}_{60}$ for several momentum transfers (0.65\ensuremath{\le}q\ensuremath{\le}1.15 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}1}$) with energy resolution of 1.5 eV by the inelastic scattering of synchrotron x rays. Two features dominate the spectra; an interband transition near 5 eV due to the carbon 2${\mathit{p}}_{\mathit{z}}$ electrons, and a bulk plasmon mode peaked near 30 eV, which arises from all four of the carbon valence electrons. The spectra are isotropic.

Acoustic plasmon exchange in multilayered systems. I. The effective interaction potential

Using a plasmon exchange model, analytic expressions for the effective interaction between charge carriers in a multilayered system containing one, two, three and four conducting layers per unit cell has been calculated. The interaction is mediated by one pseudo-optical plasmon band and L-1 proper narrow acoustic plasmon bands where L is the number of layers per cell. It is found that the pseudo-optical plasmon band has a proper optical (high energy) limit, equivalent to bulk plasmon modes, as well as an acoustic (low energy) limit. In part II (ibid. vol.4, p.1814, 1992) the authors show that this interaction can lead to superconductivity in the high-Tc superconductors.