Plasmon Dispersion Relation Research Articles

Guiding infrared electromagnetic waves through TI nanowires with extremely large wavenumber and azimuthal index.

In this paper, the dispersion relations of the surface plasmon polaritons (SPPs) in TI nanowires have been investigated. For simplicity, TI nanowire has been modeled as a dielectric cylinder with a conductive surface, the conductivity of which is an anti-symmetric tensor. The off-diagonal terms of the conductivity tensor only slightly change the dispersion relations. Due to small conductivities, these SPPs have extremely large wavenumbers and azimuthal indices; the electric fields are tightly confined near the conductive surface. For high-order modes, cut-off phenomena have been observed. In the end, the effects of losses and much larger bulk permittivities on the dispersion relations of surface plasmons have been discussed. The simple model proposed in this paper can be directly applied to other materials with arbitrary surface conductivity. Our investigations show that TI nanostructures are promising platforms for nanophotonic applications in the future.

Nonlocal dispersion relation of gap plasmons in asymmetric-MIM waveguides

In this paper, we combine the classical electrodynamics theory with the generalized nonlocal optical response (GNOR) model to theoretically investigate the propagation behaviors of gap plasmons (GPs) in an asymmetric metal-insulator-metal (A-MIM) waveguide. The nonlocal dispersion relation of GPs is derived, and the computational analysis is conducted for three different types of A-MIM waveguides. The results show that, compared with the local response, the introduction of the nonlocal effects induces not only frequency blueshift and loss increment, but also changes in field distribution, electron density distribution, and propagation length of GPs.

Transport signatures of plasmon fluctuations in electron hydrodynamics

In two-dimensional electron systems, plasmons are gapless and long-lived collective excitations of propagating charge density oscillations. We study the fluctuation mechanism of plasmon-assisted transport in the regime of electron hydrodynamics. We consider pristine electron liquids where charge fluctuations are thermally induced by viscous stresses and intrinsic currents, while attenuation of plasmons is determined by the Maxwell mechanism of charge relaxation. It is shown that, while the contribution of plasmons to the shear viscosity and thermal conductivity of a Fermi liquid is small, plasmon resonances in the bilayer devices enhance the drag resistance. In systems without Galilean invariance, fluctuation-driven contributions to dissipative coefficients can be described only in terms of hydrodynamic quantities: intrinsic conductivity, viscosity, and plasmon dispersion relation.

Plasmon Thermal Conductance and Thermal Conductivity of Metallic Nanofilms

The thermal conductance and thermal conductivity of surface plasmon polaritons propagating along a metallic nanofilm deposited on a substrate are quantified and analyzed, as functions of the film thickness, length, and temperature. This is done by analytically solving the dispersion relation of plasmons for their wave vectors and propagation length. It is shown that the plasmon energy transport along the film interfaces is driven by two modes characterized by symmetric and antisymmetric spatial distributions of the magnetic field. For a gold nanofilm deposited on a silicon substrate, both modes have comparable contributions of the plasmon thermal conductance, which takes higher values for hotter and/or longer nanofilms and saturates for films thicker than 50 nm. This saturation arises from the decoupling of the plasmon modes, the transition of which to a coupled state for thinner films maximizes the plasmon thermal conductivity. For a 1-cm-long gold nanofilm at 300 K, the maximum thermal conductivity appears for a thickness of 10 nm and takes the value of $15\phantom{\rule{0.2em}{0ex}}\mathrm{W}\phantom{\rule{0.1em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.1em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$, which is about 25% of its electron counterpart. As a result of the huge propagation distance ($>1\phantom{\rule{0.2em}{0ex}}\mathrm{cm}$) of plasmons, this plasmon thermal conductivity increases significantly with the film length and temperature and it could therefore be useful to improve the heat dissipation along metallic nanofilms.

Plasmon Damping Rates in Coulomb-Coupled 2D Layers in a Heterostructure.

The Coulomb excitations of charge density oscillation are calculated for a double-layer heterostructure. Specifically, we consider two-dimensional (2D) layers of silicene and graphene on a substrate. From the obtained surface response function, we calculated the plasmon dispersion relations, which demonstrate how the Coulomb interaction renormalizes the plasmon frequencies. Most importantly, we have conducted a thorough investigation of how the decay rates of the plasmons in these heterostructures are affected by the Coulomb coupling between different types of two-dimensional materials whose separations could be varied. A novel effect of nullification of the silicene band gap is noticed when graphene is introduced into the system. To utilize these effects for experimental and industrial purposes, graphical results for the different parameters are presented.

Theory of strong coupling between molecules and surface plasmons on a grating.

The strong coupling of molecules with surface plasmons results in hybrid states which are part molecule, part surface-bound light. Since molecular resonances may acquire the spatial coherence of plasmons, which have mm-scale propagation lengths, strong-coupling with molecular resonances potentially enables long-range molecular energy transfer. Gratings are often used to couple incident light to surface plasmons, by scattering the otherwise non-radiative surface plasmon inside the light-line. We calculate the dispersion relation for surface plasmons strongly coupled to molecular resonances when grating scattering is involved. By treating the molecules as independent oscillators rather than the more typically considered single collective dipole, we find the full multi-band dispersion relation. This approach offers a natural way to include the dark states in the dispersion. We demonstrate that for a molecular resonance tuned near the crossing point of forward and backward grating-scattered plasmon modes, the interaction between plasmons and molecules gives a five-band dispersion relation, including a bright state not captured in calculations using a single collective dipole. We also show that the role of the grating in breaking the translational invariance of the system appears in the position-dependent coupling between the molecules and the surface plasmon. The presence of the grating is thus not only important for the experimental observation of molecule-surface-plasmon coupling, but also provides an additional design parameter that tunes the system.

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.

Ultralight Dark Photon and Casimir Effect

We investigate the influence of a dark photon on the Casimir effect and calculate the corresponding leading contribution to the Casimir energy. For expected magnitudes of the photon - dark photon mixing parameter, the influence turns out to be negligible. The plasmon dispersion relation is also not noticeably modified by the presence of a dark photon.

Weyl–Wigner description of massless Dirac plasmas: ab initio quantum plasmonics for monolayer graphene

We derive, from first principles and using the Weyl–Wigner formalism, a fully quantum kinetic model describing the dynamics in phase space of Dirac electrons in single-layer graphene. In the limit ℏ → 0, we recover the well-known semiclassical Boltzmann equation, widely used in graphene plasmonics. The polarizability function is calculated and, as a benchmark, we retrieve the result based on the random-phase approximation. By keeping all orders in ℏ, we use the newly derived kinetic equation to construct a fluid model for macroscopic variables written in the pseudospin space. As we show, the novel ℏ-dependent terms can be written as corrections to the average current and pressure tensor. Upon linearization of the fluid equations, we obtain a quantum correction to the plasmon dispersion relation, of order ℏ 2, akin to the Bohm term of quantum plasmas. In addition, the average variables provide a way to examine the value of the effective hydrodynamic mass of the carriers. For the latter, we find a relation in which Drude’s mass is multiplied by the square of a velocity-dependent, Lorentz-like factor, with the speed of light replaced by the Fermi velocity, a feature stemming from the quasi-relativistic nature of the Dirac fermions.

Exact dispersion relations for the hybrid plasmon-phonon modes in graphene on dielectric substrates with polar optical phonons.

Intrinsic optical phonons and extrinsic polar optical phonons (POPs) strongly affect the graphene surface plasmons. Specifically, extraneous POPs present on the surface of an underlying substrate change the behavior of the graphene's surface plasmons sharply due to the plasmon-phonon hybridization. Here, we report modeling of exact dispersion relations for graphene's surface plasmons affected by intrinsic optical phonons and extrinsic POPs of the surface of polar dielectric substrates with one or more vibrational frequencies. In doing so, we have employed random phase approximation with modified two-dimensional polarizability (2D-Π0). The adapted Π0 addresses limitations of the previously derived plasmons dispersion, obtained using classical two-dimensional polarizability. We show the new model overcomes the unsatisfying behavior of the plasmonic dispersion relation obtained by the classical 2D-Π0 at high-wavenumbers and its inability to indicate the starting point of the mode damping. Our new simple model eliminates the complexity of the other presented models in describing the surface plasmons' behavior, specifically at high wavenumbers. Besides, we use our dispersion model to learn about the plasmon content of the hybrid modes, which is a vital value to compute output current in plasmonic graphene-based devices. The coupled-mode lifetime due to the hybrid nature depends on both plasmon and phonon lifetimes. We capture this value here. There is an excellent agreement between our theoretical results and the experimental data reported earlier. They pave the way for the exact modeling of graphene plasmons on common polar substrates and bring in the closeness of the theoretical approaches and experimental results.

Anomalous behavior of plasma response functions at strong coupling.

Using data from equilibrium molecular dynamics computer simulations we have built up a catalog of response functions for the Coulomb one-component plasma over a wide range of Γ coupling values, including the strongly coupled Γ>1 liquid regime. We focus on the domain of negative compressibility (Γ>3), where the proper response displays an acausal behavior, implying a modification of the relation between its real and imaginary parts in the Kramers-Kronig relations. We give a description of the details of this acausal feature, in both the frequency and time domains. We show that the viscoelastic pole of the density response function morphs into an imaginary pole in the upper ω half-plane that is responsible for the anomalous behavior of the response in this coupling range. By examining the plasmon dispersion relation through the dielectric response function, rather than via the peaks of the dynamical structure function, we obtain a more reliable representation for the dispersion. We demonstrate that there is an intimate link between the formation of the roton minimum in the dispersion and the negative compressibility of the system. The feasibility of the extension of our analysis to systems with a short-range interaction is explored.

Plasmon Resonances of Graphene-Dielectric-Metal Structures Calculated by the Method of Recurrence Relations

Graphene supports surface plasmons in the terahertz range, and compared with noble-metal plasmons, they show an extreme level of field confinement and relatively long propagation distances, with the advantage of being highly tunable via electrostatic field. Nevertheless, its interaction with light is normally rather weak. To obtain a more powerful capability of excite plasmons, a combination of graphene and artificial structures (metamaterials) present a powerful tunability for enhancing light-matter interaction. These features make graphene metamaterials a promising candidate for plasmonics and surface plasmon resonance for biological sensors. In this work, we study the plasmon spectra in a finite number of graphene layers on a metallic-dielectric substrate surrounded by materials with different dielectric constants. It is shown that using standard electromagnetic boundary conditions and solving the recurrence relation (a suitable alternative to transfer matrix method) for the coefficients of the electric potential between graphene layers, an explicit effective dielectric function of the metamaterial can be obtained giving the plasmon dispersion relations. It is found that the metal-dielectric-layered graphene structure supports both high-energy optical plasmon oscillations and out-of-phase low-energy acoustic charge density excitations. Experimentally, the Kretschmann configuration can be used to excite the surface plasmon resonances. It is based on the observation of a sharp minimum in the reflection coefficient versus angle (or wavelength) curve.

Topological Graphene Plasmons in a Plasmonic Realization of the Su–Schrieffer–Heeger Model

Graphene hybrids, made of thin insulators, graphene, and metals can support propagating acoustic plasmons (AGPs). The metal screening modifies the dispersion relation of usual graphene plasmons leading to slowly propagating plasmons, with record confinement of electromagnetic radiation. Here, we show that a graphene monolayer, covered by a thin dielectric material and an array of metallic nanorods can be used as a robust platform to emulate the Su-Schrieffer-Heeger model. We calculate the Zak's phase of the different plasmonic bands to characterise their topology. The system shows bulk-edge correspondence: strongly localized interface states are generated in the domain walls separating arrays in different topological phases. We find signatures of the nontrivial phase which can directly be probed by far-field mid-IR radiation, hence allowing a direct experimental confirmation of graphene topological plasmons. The robust field enhancement, highly localized nature of the interface states, and their gate-tuned frequencies expand the capabilities of AGP-based devices.

Electron-phonon hydrodynamics

We develop the theory of hydrodynamics of an isotropic Fermi liquid of electrons coupled to isotropic acoustic phonons, assuming that umklapp processes may be neglected. At low temperatures, the fluid is approximately Galilean invariant; at high temperatures, the fluid is nearly relativistic; at intermediate temperatures, there are seven additional temperature regimes with unconventional thermodynamic properties and hydrodynamic transport coefficients in a three-dimensional system. We predict qualitative signatures of electron-phonon fluids in incoherent transport coefficients, shear and Hall viscosity, and plasmon dispersion relations. Our theory may be relevant for numerous quantum materials where strong electron-phonon scattering has been proposed to underlie a hydrodynamic regime, including $\mathrm{WTe}_2$, $\mathrm{WP}_2$, and $\mathrm{PtSn}_4$.

Acoustic Plasmons in Graphene Sandwiched between Two Metallic Slabs

We study the effect of two metallic slabs on the collective dynamics of electrons in graphene positioned between the two slabs. We show that if the slabs are perfect conductors, the plasmons of graphene display a linear dispersion relation. The velocity of these acoustic plasmons crucially depends on the distance between the two metal gates and the graphene sheet. In the case of generic slabs, the dispersion relation of graphene plasmons is much more complicated, but we find that acoustic plasmons can still be obtained under specific conditions.

Polariton topological transition effects on radiative heat transfer

Twisted two-dimensional bilayer materials exhibit many exotic physical phenomena. Manipulating the twist angle between the two layers enables fine control of the physical structure, resulting in development of many novel physics, such as the magic-angle flat-band superconductivity, the formation of moire exciton and interlayer magnetism. Here, combined with analogous principles, we study theoretically the near-field radiative heat transfer (NFRHT) between two twisted hyperbolic systems. This two twisted hyperbolic systems are mirror images of each other. Each twisted hyperbolic system is composed of two graphene gratings, where there is an angle {\phi} between this two graphene gratings. By analyzing the photonic transmission coefficient as well as the plasmon dispersion relation of twisted hyperbolic system, we prove that the topological transitions of the surface state at a special angle (from open (hyperbolic) to closed (elliptical) contours) can modulate efficiently the radiative heat transfer. Meanwhile the role of the thickness of dielectric spacer and vacuum gap on the manipulating the topological transitions of the surface state and the NFRHT are also discussed. We predict the hysteresis effect of topological transitions at a larger vacuum gap, and demonstrate that as thickness of dielectric spacer increase, the transition from the enhancement effect of heat transfer caused by the twisted hyperbolic system to a suppression. This technology could novel mechanism and control method for NFRHT, and may open a promising pathway for highly efficient thermal management, energy harvesting, and subwavelength thermal imaging.

RETRACTED: Ultrahigh resolution two-dimensional atomic localization via tunable surface plasmon polaritons

This article has been retracted: please see Elsevier Policy on Article Withdrawal ( https://www.elsevier.com/about/our-business/policies/article-withdrawal ). This article has been retracted at the request of Authors We are retracting this Article because the result is wrong for the following two crucial reasons. This article considered a nanohybrid system consisted of a core of atomic medium with dielectric constant e1 and an outer Ag metallic nanoparticle (MNP) shell with dielectric constant e2. Such nano-structures make the light fields inside the nanohybrid system highly inhomogeneous. It is impossible for the controlling fields to form the strong standing waves in such spherical shell nanostructures. Thus the Equation (1) of the modelling for the driving laser field with Rabi frequency Wc(x,y) inside the NMP shell is not valid. Furthermore, the modes inside such spherical structures are usually the well-known whispering gallery modes. The surface plasmonic dispersion relation given in (12), which is usually used for a plane interface, is not applicable in the spherical nanohybrid system. Since these two equations (1) and (12) are fundamentally wrong, we think that all results based on them are incorrect. Therefore all authors wish to retract this Article. We deeply regret for the inconvenience caused to Optics and Laser Technology and apologize to the scientific community.

First-principles modeling of plasmons in aluminum under ambient and extreme conditions

The theoretical understanding of plasmon behavior is crucial for an accurate interpretation of inelastic scattering diagnostics in many experiments. We highlight the utility of linear response time-dependent density functional theory (LR-TDDFT) as a first-principles framework for consistently modeling plasmon properties. We provide a comprehensive analysis of plasmons in aluminum from ambient to warm dense matter conditions and assess typical properties such as the dynamical structure factor, the plasmon dispersion, and the plasmon lifetime. We compare our results with scattering measurements and with other TDDFT results as well as models such as the random phase approximation, the Mermin approach, and the dielectric function obtained using static local field corrections of the uniform electron gas parametrized from path-integral Monte Carlo simulations. We conclude that results for the plasmon dispersion and lifetime are inconsistent between experiment and theories and that the common practice of extracting and studying plasmon dispersion relations is an insufficient procedure to capture the complicated physics contained in the dynamic structure factor in its full breadth.

Особенности затухания и усиления терагерцовых плазмонных мод в графене с учетом пространственной дисперсии

In this paper, we consider the effect of charge carrier drift on plasmon modes (plasmons) in electron Dirac liquid in graphene with a shifted Fermi level. Dispersion relations for plasmons were obtained using an electromagnetic approach and a hydrodynamic description of an electron liquid. Damped and amplified plasmon eigenmodes are studied numerically depending on the relationship of the magnitudes and directions of the direct electric current and the phase velocity of the plasmon.

Negative refraction and rotons in the relativistic Bose gas

We investigate the dispersion of a classical electromagnetic field in a relativistic ideal gas of charged bosons using scalar quantum electrodynamics at finite temperature and charge density. We derive the effective electromagnetic responses and the electromagnetic propagation modes that characterize the gas as a left-handed material with negative effective index of refraction neff=−1 below the transverse plasmon frequency. In the condensed phase, we show that the longitudinal plasmon dispersion relation exhibits a roton-type local minimum that disappears at the transition temperature.