Plasmon Dispersion Research Articles

Tilt-induced kink in the plasmon dispersion of two-dimensional Dirac electrons

The list of two dimensional Dirac systems with a tilt in their Dirac cone spectrum is expanding, and now in addition to organic system $\alpha$(BEDT-TTF)$_2$I$_3$ includes the two dimensional $8Pmmn$-borophene sheet, which allows for controlled doping by the gate voltage. We analytically calculate the polarization function of tilted Dirac cone for arbitrary tilt parameter, $0\le \eta <1$, and arbitrary doping. This enables us to find two interesting plasmonic effects solely caused by the tilt: (i) In addition to the standard plasmon oscillations, strong enough tilt, induces an additional linearly dispersing overdamped branch of plasmons, which is strongly Landau damped due to overlap with a large density of intra-band free particle-hole (PH) excitations. (ii) There appears a kink in the plasmon dispersion for any non-zero tilt parameter. The kink appears when the plasmon branch enters the inter-band continuum of PH excitations. This kink becomes most manifest for wave vectors perpendicular to the tilt direction and fades away by approaching the tilt direction. Experimental measurement of the wave vector and energy of the plasmonic kink, when combined with our analytic formula for the kink energy scale, allows for a direct experimental measurement of the tilt parameter.

Magnetic Hyperbolic Metasurface: Concept, Design, and Applications.

A fundamental cornerstone in nanophotonics is the ability to achieve hyperbolic dispersion of surface plasmons, which shows excellent potentials in many unique applications, such as near‐field heat transport, planar hyperlens, strongly enhanced spontaneous emission, and so forth. The hyperbolic metasurfaces with such an ability, however, are currently restricted to electric hyperbolic metasurface paradigm, and realization of magnetic hyperbolic metasurfaces remains elusive despite the importance of manipulating magnetic surface plasmons (MSPs) at subwavelength scale. Here, magnetic hyperbolic metasurfaces are proposed and designed, on which diffraction‐free propagation, anomalous diffraction, negative refraction, and frequency‐dependent strong spatial distributions of the MSPs in the hyperbolic regime are experimentally observed at microwave frequencies. The findings can be applied to manipulate MSPs and design planarized devices for near‐field focusing, imaging, and spatial multiplexers. This concept is also generalizable to terahertz and optical frequencies and inspires novel quantum optical apparatuses with strong magnetic light–matter interactions.

Finite-temperature correlations in a two-dimensional electron gas within a dynamical self-consistent mean-field approximation

Abstract We have studied the effect of temperature on density-density correlations in a two-dimensional quantum electron gas by using the dynamical Singwi-Tosi-Land-Sjolander (STLS) theory. Static correlation functions viz. structure factor S(q; T), pair-correlation function g(r; T), and static density susceptibility χ(q, 0; T) are calculated over a wide range of temperature and electron density. The inclusion of the dynamics of correlations is found to cause a strong peak in S(q; T) at q ∼ 2.5kF for low densities. Correspondingly, there develops a sharp peak in χ(q, 0; T) that diverges below a critical density. This divergence is interpreted as a precursor of transition to finite-temperature Wigner crystal state. Rise in temperature tends to oppose the crystallization, with critical transition density decreasing with temperature. It is rather found that the dynamical correction to the conventional (static) STLS theory becomes small at a sufficiently high temperature. We have also calculated the plasmon dispersion for the GaAs quantum well based electron system and found that, except at ultra-low densities, agreement with the experimental data of Hirjibehedin et al. is reasonably good. Our results show a red shift in plasmon frequency over the predictions of the STLS and dynamical Hubbard approaches.

Closed-Form Approximations to Solutions of Plasmon Dispersion at a Dielectric/Conductor Interface

The dispersion equation for surface plasmons (SPs) at a dielectric/conductor interface has been studied extensively with respect to the design of plasmonic devices. A key design requirement is the reduction of damping in the propagating SP polariton wave. Satisfaction of this constraint requires that an “electron gas” in a conducting medium, such as a doped semiconductor, move along the interface at speeds that approximate the polariton wave speed. At these low relative speeds, the efficient exchange of energy between the drifting electrons and a traveling SP polariton may be enabled. The ill-conditioned, eighth-order, complex coefficients dispersion equation derived earlier is dependent upon six parameters that vary over many orders of magnitude. The dispersion equation is also found to be singular in regions of practical interest, and, taken together, these properties have hampered the success of numerical investigations. Therefore, the dispersion equation is analytically investigated here, and closed-form results are found for the parametric dependence of the surface polariton’s propagation constant on five dimensionless groups. These new solutions show how compensation of propagation losses without the use of structures can be achieved and provide avenues that guide device design. The closed-form results are used to initialize numerical optimization by providing sufficiently accurate starting points within the parameter space that avoid numerical ill-conditioning.

Quantization of surface charge density on hyperboloidal and paraboloidal domains with application to plasmon decay rate on nanoprobes

Field quantization in high curvature geometries help understanding the elastic and inelastic scattering of photons and electrons in nanostructures and probelike metallic domains. The results find important applications in high-resolution photonic and electronic modalities of scanning probe microscopy, nano-optics, plasmonics, and quantum sensing. We present a calculation of relevant photon interactions in both hyperboloidal and paraboloidal material domains. The two morphologies are compared for their plasmon dispersion properties, field distributions, and radiative decay rates, which are shown to be consistent with the corresponding quantities for the finite prolate spheroidal domains. The results are relevant to other material domains that model a nanostructure such as a probe tip, quantum dot, or nanoantenna.

Electric current-driven spectral tunability of surface plasmon polaritons in gold coated tapered fibers

Here we introduce the concept of electrically tuning surface plasmon polaritons using current-driven heat dissipation, allowing controlling plasmonic properties via a straightforward-to-access quantity. The key idea is based on an electrical current flowing through the plasmonic layer, changing plasmon dispersion and phase-matching condition via a temperature-imposed modification of the refractive index of one of the dielectric media involved. This scheme was experimentally demonstrated on the example of an electrically connected plasmonic fiber taper that has sensitivities &amp;gt;50000 nm/RIU. By applying a current, dissipative heat generated inside metal film heats the surrounding liquid, reducing its refractive index correspondingly and thus modifying the phase-matching condition to the fundamental taper mode. We observed spectral shifts of the plasmonic resonance up to 300 nm towards shorter wavelength by an electrical power of ≤ 80 mW, clearly showing that our concept is important for applications that demand precise real-time and external control on plasmonic dispersion and resonance wavelengths.

Effect of high-frequency electromagnetic radiation on the plasmon dispersion in biased graphene bilayer

Abstract The Floquet spectrum of electron in biased graphene bilayer subjected to the high-frequency electromagnetic radiation has been derived. The magnitude of gap in electron spectrum renormalized by radiation has been calculated. The quasienergy gap has been shown to increase with electromagnetic wave intensity. The possibility of controlling of curvature of dispersion curve for plasmon by changing of both bias voltage and high-frequency field intensity has been shown. The dependence of this curvature on both bias voltage and electromagnetic field amplitude has been predicted to have the nonmonotonous character. Intensity of electromagnetic radiation causing the suppression of the plasma oscillations has been found.

Plasmon modes in bilayer-graphene–GaAs heterostructures including layer-thickness and exchange-correlation effects

We investigate the dispersion relation and decay rate of plasmon modes in a double-layer system made of bilayer graphene (BLG) and infinite GaAs quantum well at zero-temperature within the generalized random-phase-approximation and taking into account the 2DEG layer-thickness and inhomogeneity of the background dielectric. We illustrate that the acoustic plasmon dispersion curve of the considered system differs significantly from that of monolayer graphene (MLG)–GaAs heterostructure and BLG–GaAs without layer-thickness. Calculations also demonstrate that meanwhile the optical plasmon curve is affected slightly by spacer width and exchange-correlation, the acoustic one depends remarkably on the interlayer distance, inhomogeneity of the background dielectric, carrier densities, spacer dielectric constant, quantum well width and exchange-correlations.

Energy-loss function for monolayer phosphorene

We calculate the energy-loss function for monolayer phosphorene in the framework of time-dependent density functional theory. The calculations are performed in the adiabatic local density approximation with local field effects. We study the origin of the features in the absorption spectra and the energy dispersion of the features in the excitation spectra. The energy dispersions show a strong directional dependence. At vanishing momentum transfer, the excitation spectra are dominated by a plasmon peak at 10.5 eV. At finite momentum transfer, the plasmon dispersion can be described by the layer electron gas model.

Effect of strain on plasmons, screening, and energy loss in graphene/substrate contacts

The combined effect due to mechanical strain, coupling to the plasmons in a doped conducting substrate, the plasmon-phonon scattering in conjunction with the role played by encapsulation of a secondary two-dimensional (2D) layer is investigated both theoretically and numerically. The calculations are based on the random-phase approximation (RPA) for the surface response function which yields the plasmon dispersion equation that is applicable in the presence or absence of an applied uniaxial strain. We present results showing the dependence of the frequency of the charge density oscillations on the strain modulus and direction of the wave vector in the Brillouin zone. The shielding of a dilute distribution of charges as well as the rate of loss of energy for impinging charges is investigated for this hybrid layered structure.

Confining graphene plasmons to the ultimate limit

Graphene plasmons have recently attracted a great deal of attention because of their tunability, long lifetime, and high degree of field confinement in the vertical direction. Nearby metal gates have been shown to modify the graphene plasmon dispersion and further confine their electric field. We study the plasmons of a graphene sheet deposited on a metal, in the regime in which metal bands do not hybridize with massless Dirac fermion bands. We derive exact results for the dispersion and lifetime of the plasmons of such hybrid system, taking into account metal nonlocalities. The graphene plasmon dispersion is found to be acoustic and pushed down in energy towards the upper boundary of the intraband graphene particle-hole continuum, thereby strongly enhancing the vertical confinement of these excitations. Landau damping of such acoustic plasmons due to particle-hole excitations in the metal gate is found to be surprisingly weak, with quality factors exceeding $Q = 10^{2}$.

On the Theory of Plasmon Dispersion in Electron-Doped Cuprates

An explicit expression for the dynamic charge susceptibility for electron-doped cuprates has been derived. This expression accurately reproduces the wave vector dependence of the plasmon frequency observed in inelastic X-ray scattering experiments for Nd2 – xCexCuO4. The imaginary part of the charge susceptibility along the triangular path in the Brillouin zone is plotted. It is demonstrated that the spectral weight of the plasmon mode near q = 0 is negligibly low. The calculated frequencies of the plasmon mode for all wave vectors in the Brillouin zone turn out to lie outside the range of damping related to electron−hole excitations. A formula for the charge susceptibility is derived within the t−t′−t″−J model supplemented by the Coulomb interaction operator and three-site terms. The derivation is performed by the Green’s function technique employing the formalism of composite Hubbard operators and the Mori projection method, which have proved themselves in the analysis of collective spin excitations. The used Fourier transform of the Coulomb interaction corresponds to the monolayer model with a spatially periodic structure, which is embedded in a three-dimensional crystal lattice.

Real-time waveform modulator based on dispersion engineering of magnetic surface plasmons

With the aim to further reduce insertion loss, we propose the design of a real-time waveform modulator by engineering the dispersion of magnetic surface plasmons (MSPs). The magnetic fields of MSPs are strongly localized, which is different from conventional electric surface plasmons (ESPs). Since there are no magnetic media in the design, the transmission loss of MSPs resulting from dielectric loss is lower than that of ESPs. Therefore, a waveform modulator with lower insertion loss can be realized. As an example, we demonstrate a real-time waveform modulator operating in the X band. Both the simulation and experiment prove that the waveform modulator is broadband and high-efficiency. The design method can also be applied to the design of a true-time delayer, a real-time Fourier transformer, a true-time compressor, and so on.

Plasmon spectroscopy: Robust metallicity of Au wires on Si(557) upon oxidation

We investigated initial steps of oxidation of the Si(557)-Au system by plasmon spectroscopy and first-principles calculations. The measurements, performed using an electron energy loss instrument with simultaneous high resolution in energy and momentum, reveal that metallicity is preserved under all oxidation conditions that are experimentally accessible in UHV. Corresponding simulations, performed within density functional theory, confirm this finding: Only the oxidation of the Si environment of the Au chains turned out to be strongly exothermic, with similar binding energy for adsorption on different structural elements. While large and site specific changes of the band structure were observed, the upper edge of the excitation spectrum of electron-hole pairs, to which plasmon dispersion is most sensitive, remains almost unchanged during the various steps of oxidation, due to the opposite and largely compensating contributions of different adsorption configurations. This investigation not only proves the robustness of metallicity of the gold chains upon oxidation of the surrounding environment of Si atoms, but also demonstrates the usefulness of plasmon spectroscopy in characterizing the electronic excitation spectrum of quasi-one-dimensional systems and unoccupied band structure.

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.

Strong confinement of unconventional plasmons and optical properties of graphene-transition metal dichalcogenide heterostructures

In an earlier work, it was shown that the dispersion of the Van der Waals heterostructures (vdWHs) of graphene monolayer on 2D transition metal dichalcogenide (GrTMD) substrate comprises of the spin-split, gapped bands. Using these it was also shown that the intra-band plasmon dispersion for the finite doping and the long wavelength limit involves the q2/3 (unconventional) behavior and not the well known q1/2 behavior. In this paper the optical conductivity and the optical properties of this vdWH are reported. We find that there are no (inter-band) plasmons for electron doping as long as the Gr-TMD hetero-structure is surrounded by the positive dielectric constant materials above and below. However, if the heterostructure is surrounded by negative dielectric constant (NDC) materials, one finds that there would be acoustic plasmons. For the hole doping case NDC material is not required. We find that the gate voltage tunable intra-band acoustic plasmons also emerge when the carrier density is greater than a moderately critical value. The stronger incarceration capability of GrTMD plasmon compared to that of doped graphene is another notable outcome of the present work. One finds that the intra-band absorbance is decreases with the frequency at a given gate voltage and increases with the gate voltage at a given frequency; the inter-band transmittance, however, is a decreasing function of frequency and the gate voltage.

Plasmon modes in Dirac–Schrödinger hybrid electron systems including layer-thickness and exchange-correlation effects

We calculate the plasmon dispersion relation and damping rate of collective excitations in a double-layer system consisting of monolayer graphene and GaAs quantum well at zero temperature including layer-thickness and exchange-correlation effects. We use the generalized random-phase-approximation dielectric function and take into account the nonhomogeneity of the dielectric background of the system. We show that the effects of layer thickness, electron densities, and exchange-correlations are more pronounced for acoustic modes, while the optical branch depends remarkably on dielectric constants of the contacting media.

Spatially resolved measurement of plasmon dispersion using Fourier-plane spectral imaging

We show that Fourier-plane imaging in conjunction with the Kretschmann-Raether configuration can be used for measuring polariton dispersion with spatial discrimination of the sample, over the whole visible spectral range. We demonstrate the functionality of our design on several architectures, including plasmonic waveguides, and show that our new design enables the measurement of plasmonic dispersion curves of spatially-inhomogeneous structures with features as small as 3{\mu}m, in a single shot.

Controlling Surface Plasmon Optical Transmission by Stretching a Silver-Coated Elastomeric Grating Substrate

In this study, transmission surface plasmon resonance (TSPR) of a silver-coated elastomeric grating substrate was tuned via mechanical stretching. The wavelengths of TSPR excitation peaks, corresponding to surface plasmon dispersion modes of + 1 and − 1, were simultaneously observed. The TSPR excitation wavelength was dramatically shifted up to 80 nm when the strain of the substrate reached 13.3%. The fine control of TSPR properties of the silver-coated elastomeric grating substrate has potential applications in mechanically tunable band pass filters, optical sensors, etc.

Phonon-assisted damping of plasmons in three- and two-dimensional metals

We investigate the effects of crystal lattice vibrations on the dispersion of plasmons. The loss function of the homogeneous electron gas (HEG) in two and three dimensions is evaluated numerically in presence of electronic coupling to an optical phonon mode. Our calculations are based on many-body perturbation theory for the dielectric function as formulated by the Hedin-Baym equations in the Fan-Migdal approximation. The coupling to phonons broadens the spectral signatures of plasmons in the electron-energy loss spectrum (EELS) and it induces the decay of plasmons on timescales shorter than 1 ps. Our results further reveal the formation of a kink in the plasmon dispersion of the 2D HEG, which marks the onset of plasmon-phonon scattering. Overall, these features constitute a fingerprint of plasmon-phonon coupling in the EELS of simple metals. It is shown that these effects may be accounted for by resorting to a simplified treatment of the electron-phonon interaction which is amenable to first-principles calculations.