Plasmonics is a rapid growing field, which has enabled both fundamental science and inventions of various quantum optoelectronic devices. An accurate and efficient method to calculate the optical response of metallic structures with feature size in the nanoscale plays an important role. Quantum hydrodynamic theory (QHT) provides an efficient description of the free-electron gas, where quantum effects of nonlocality and spill-out are taken into account. In this work, we introduce a general QHT that includes diffusion to account for the broadening, which is a key problem in practical applications of surface plasmon. We will introduce a density-dependent diffusion coefficient to give very accurate linewidth. It is a self-consistent method, in which both the ground and excited states are solved by using the same energy functional, with the kinetic energy described by the Thomas-Fermi and von Weizsäcker (vW) formalisms. In addition, our QHT method is stable by introduction of an electron density-dependent damping rate. For sodium nanosphere of various sizes, the plasmon energy and broadening by our QHT method are in excellent agreement with those by density functional theory and Kreibig formula. By applying our QHT method to sodium jellium nanorods, we clearly show that our method enables a parameter-free simulation, i.e. without resorting to any empirical parameter, such as size-dependent damping rate and diffusing coefficient. It is found that there exists a perfect linear relation between the resonance wavelength and aspect radio. The width decreases with increasing aspect ratio and height. The calculations show that our QHT method provides an explicit and unified way to account for size-dependent frequency shifts and broadening of arbitrarily shaped geometries. It is reliable and robust with great predicability, and hence provides a general and efficient platform to study plasmonics.
We experimentally investigate the decoherence of single surface plasmon polaritons in metal stripe waveguides. In our study we use a Mach-Zehnder configuration previously considered for measuring decoherence in atomic, electronic and photonic systems. By placing waveguides of different length in one arm we are able to measure the amplitude damping time T_1 = 1.90 +/- 0.01 x 10^-14 s, pure phase damping time T_2^* = 11.19 +/- 4.89 x 10^-14 s and total phase damping time T_2 = 2.83 +/- 0.32 x 10^-14 s. We find that decoherence is mainly due to amplitude damping and thus loss arising from inelast…
We launch surface plasmons from one end of a silver nanowire by asymmetric illumination with white light and use plasmon-to-light scattering at the nanowire ends to probe spectroscopically the plasmonic Fabry-Perot wire modes. The spectral positions of the maxima and minima in the scattered intensity from both nanowire ends are found to be either in phase or out-of phase, depending on the nanowire length and the spectral range. This behavior can be explained by a generalized Fabry-Perot model. The turnover-point between the two regimes is sensitive to the surface plasmon round trip losses and …
We develop a general quantum theory of the coupled plasmonic modes resulting from the near-field interaction between localized surface plasmons in a heterogeneous metallic nanoparticle dimer. In particular, we provide analytical expressions for the frequencies and decay rates of the bright and dark plasmonic modes. We show that, for sufficiently small nanoparticles, the main decay channel for the dark plasmonic mode, which is weakly coupled to light and, hence, immune to radiation damping, is of nonradiative origin and corresponds to Landau damping, i.e., decay into electron-hole pairs.
The recent generalised nonlocal optical response (GNOR) theory for plasmonics is analysed, and its main input parameter, namely the complex hydrodynamic convection-diffusion constant, is quantified in terms of enhanced Landau damping due to diffusive surface scattering of electrons at the surface of the metal. GNOR has been successful in describing plasmon damping effects, in addition to the frequency shifts originating from induced-charge screening, through a phenomenological electron diffusion term implemented into the traditional hydrodynamic Drude model of nonlocal plasmonics. Nevertheless…
We propose and illustrate a quantum hydrodynamic (QHD) model for the description of plasmonic oscillations in the $\rm C_{60}$ molecule. Although simpler than competing approaches such as time-dependent density functional theory (TDDFT), the model contains the key ingredients to characterize plasmonic modes, namely the Hartree, exchange and correlation potentials, as well as nonlocal, nonlinear and quantum effects to the lowest order. A variational technique is used to solve analytically the QHD model for the case of breathing (monopolar) plasmonic oscillations, revealing a bulk mode near the …
Plasmonics has attracted much attention not only because it has useful properties such as strong field enhancement, but also because it reveals the quantum nature of matter. To handle quantum plasmonics effects, ab initio packages or empirical Feibelman d-parameters have been used to explore the quantum correction of plasmonic resonances. However, most of these methods are formulated within the quasi-static framework. The self-consistent hydrodynamics model offers a reliable approach to study quantum plasmonics because it can incorporate the quantum effect of the electron gas into classical el…
Multiscale plasmonic systems e.g. extended metallic nanostructures with sub-nanometer inter-distances) play a key role in the development of next-generation nano-photonic devices. An accurate modeling of the optical interactions in these systems requires an accurate description of both quantum effects and far-field properties. Classical electromagnetism can only describe the latter, while Time-Dependent Density Functional Theory (TD-DFT) can provide a full first-principles quantum treatment. However, TD-DFT becomes computationally prohibitive for sizes that exceed few nanometers, which are irr…
Using the hydrodynamic model in the electrostatic approximation, we describe the formation of graphene surface plasmons when a charge is in motion either perpendicular or parallel to a graphene sheet. In the first case, the electron-energy loss (EEL) spectrum of the electron is computed, showing that the resonances in the spectrum are linked to the frequency of the graphene surface plasmons. In the second case, we discuss the formation of plasmonic wakes due to the dragging of the surface plasmons induced by the motion of the charge. This effect is similar to Coulomb drag between two electron …
We study a one-dimensional plasmonic system with non-trivial topology: a chain of metallic nanoparticles with alternating spacing, which is the plasmonic analogue to the Su-Schreiffer-Heeger model. We extend previous efforts by including long range hopping with retardation and radiative damping, which leads to a non-Hermitian Hamiltonian with frequency dependence. We calculate band structures numerically and show that topological features such as quantised Zak phase persist due to chiral symmetry. This predicts parameters leading to topologically protected edge modes, which allows for position…
We show that a small conducting object, such as a nanosphere or a nanoring, embedded into or placed in the vicinity of the two-dimensional electron liquid (2DEL) and subjected to a circularly polarized electromagnetic radiation induces ``twisted'' plasmonic oscillations in the adjacent 2DEL. The oscillations are rectified due to the hydrodynamic nonlinearities leading to the helicity sensitive circular dc current and to a magnetic moment. This hydrodynamic inverse Faraday effect (HIFE) can be observed at room temperature in different materials. The HIFE is dramatically enhanced in a periodic a…
Plasmonic resonances of nanoparticles have drawn lots of attentions due to their interesting and useful properties such as strong field enhancements. These systems are typically studied using either classical electrodynamics or fully quantum theory. Each approach can handle some aspects of plasmonic systems accurately and efficiently, while having its own limitation. The self-consistent hydrodynamics model has the advantage that it can incorporate the quantum effect of the electron gas into classical electrodynamics in a consistent way. We use the method to study the plasmonic response of poly…
The ultraconfined light of plasmonic modes put their effective wavelength close to the mean free path of electrons inside the metal electron gas. The Drude model, which can not take the repulsive interactions of electrons into account, then clearly begins to show its limits. In an intermediate length scale where a full quantum treatment is computationally prohibitive, the semiclassical hydrodynamic model, instrinsically non-local, has proven successful. Here we generalize the expression for the absorption volume density and the reciprocity theorem in the framework of this hydrodynamic model. W…
We propose a new current-driven mechanism for achieving significant plasmon dispersion nonreciprocity in systems with narrow, strongly hybridized electron bands. The magnitude of the effect is controlled by the strength of electron-electron interactions $α$, which leads to its particular prominence in moiré materials, characterized by $α\gg 1$. Moreover, this phenomenon is most evident in the regime where Landau damping is quenched and plasmon lifetime is increased. The synergy of these two effects holds a great promise for novel optoelectronic applications of moiré materials.
The field of plasmonics seeks to find materials with an intensive plasmon (large plasmon pole weight) with low Landau, phonon and other losses (small decay width). In this paper we propose a new class of materials that show exceptionally good plasmonic properties. These materials consist of van der Waals stacked 'plasmon active' layers (atomically thin metallic layers) and 'supporting' layers (atomically thin wide band gap insulating layers). One such material that can be experimentally realized - lithium intercalated hexagonal boron-nitride is studied in detail. We show that its 2D plasmon in…
An accurate description of the optical response of subwavelength metallic particles and nanogap structures is a key problem of plasmonics. Quantum hydrodynamic theory (QHT) has emerged as a powerful method to calculate the optical response of metallic nanoparticles (NPs) since it takes into account nonlocality and spill-out effects. Nevertheless, the absorption spectra of metallic NPs obtained with conventional QHT, i.e., incorporating Thomas-Fermi (TF) and von Weizsäcker (vW) kinetic energy (KE) contributions, can be affected by several spurious resonances at energies higher than the main loc…
We study the strong coupling between the molecular excited state and the plasmonic modes of silver hole arrays with a resonant frequency very close to the asymptotic line of the plasmonic dispersion relation, at the nonlinear regime. We demonstrate that the strong coupling regime can be achieved between the two sub-systems at low molecular densities with negligible damping of the electromagnetic field. Our results are supported by rigorous numerical simulations showing that the strong coupling is observed when the molecular transition lies within the nonlinear regime of the dispersion relation…
The optical response of a coupled nanowire dimer is studied using a fully quantum mechanical approach. The translational invariance of the system allows to apply the time--dependent density functional theory for the plasmonic dimer with the largest size considered so far in quantum calculations. Detailed comparisons with results from classical electromagnetic calculations based on local and non local hydrodynamic response, as well as with results of the recently developed quantum corrected model is performed. We show that electron tunneling and dynamical screening are the major nonlocal quantu…
Plasmonic nanoparticles provide an ideal environment for the enhancement of fluorescent emission. On the one hand, they locally amplify the electromagnetic fields, increasing the emitter excitation rate, and on the other hand, they provide a high local density of states that accelerates spontaneous emission. However, when the emitter is placed in close proximity to a single metal nanoparticle, the number of nonradiative states increases dramatically, causing the fluorescence to quench. It has been predicted theoretically that, through a judicious placing of the emitter, fluorescence in plasmon…
The hydrodynamic Drude model known from metal plasmonics also applies to semiconductor structures of sizes in between single-particle quantum confinement and bulk. But contrary to metals, for semiconductors two or more types of plasma may have to be taken into account in order to properly describe their plasmonic properties. In this combined analytical and computational study, we explore predictions of the recently proposed two-fluid hydrodynamic Drude model for the optical properties of plasmonic semiconductor nanowires, in particular for thermally excited InSb nanowires. We focus on the low-…
Plasmonics takes advantage of the collective response of electrons to electromagnetic waves, enabling dramatic scaling of optical devices beyond the diffraction limit. Here, we demonstrate the mid-infrared (4 to 15 microns) plasmons in deeply scaled graphene nanostructures down to 50 nm, more than 100 times smaller than the on-resonance light wavelength in free space. We reveal, for the first time, the crucial damping channels of graphene plasmons via its intrinsic optical phonons and scattering from the edges. A plasmon lifetime of 20 femto-seconds and smaller is observed, when damping throug…
We identify a possible mechanism of the plasmon instabilities in periodically gated two-dimensional electron systems with a modulated electron density (plasmonic crystals) under direct current. The instability occurs due to the amplified reflection of the small density perturbations from the gated/ungated boundaries under the proper phase matching conditions between the crystal unit cells. Based on the transfer-matrix formalism, we derive the generic dispersion equation for the travelling plasmons in these structures. Its solution in the hydrodynamic limit shows that the threshold drift veloci…
We demonstrate the coupling of bright and dark Surface Lattice Resonances (SLRs), which are collective Fano resonances in 2D plasmonic crystals. As a result of this coupling, a frequency stop-gap in the dispersion relation of SLRs is observed. The different field symmetries of the low and high frequency SLR bands lead to pronounced differences in their coupling to free space radiation. Standing waves of very narrow spectral width compared to localized surface plasmon resonances are formed at the high frequency band edge, while subradiant damping onsets at the low frequency band edge leading th…
We present a quantum-mechanical model for surface-assisted carrier excitation by optical fields in plasmonic nanostructures of arbitrary shape. We derive an explicit expression, in terms of local fields inside the metal structure, for surface absorbed power and surface scattering rate that determine the enhancement of carrier excitation efficiency near the metal-dielectric interface. We show that surface scattering is highly sensitive to the local field polarization, and can be incorporated into metal dielectric function along with phonon and impurity scattering. We also show that the obtained…
The nonlocal response of plasmonic materials and nanostructures is usually described within a hydrodynamic approach which is based on the Euler-Drude equation. In this work, we reconsider this approach within linear response theory and employ Halevi's extension to this standard hydrodynamic model. After discussing the impact of this improved model, which we term the Halevi model, on the propagation of longitudinal volume modes, we accordingly extend the Mie-Ruppin theory. Specifically, we derive the dispersion relation of cylindrical surface plasmons. This reveals a nonlocal, collisional dampi…
We develop an exactly solvable classical kinetic model of transport in Dirac materials accounting for strong electron-electron (e-e) and electron-hole (e-h) collisions. We use this model to track the evolution of graphene conductivity and properties of its collective excitations across the hydrodynamic-to-ballistic crossover. We find the relaxation rate of electric current by e-e collisions that is possible due to the lack of Galilean invariance, and introduce a universal numerical measure of this non-invariance in arbitrary dimension. We find the two branches of collective excitations in the …
The nonclassical modification of plasmon-assisted fluorescence enhancement is theoretically explored by placing two-level dipole emitters at the narrow gaps encountered in canonical plasmonic architectures, namely dimers and trimers of different metallic nanoparticles. Through detailed simulations, in comparison with appropriate analytical modelling, it is shown that within classical electrodynamics, and for the reduced separations explored here, fluorescence enhancement factors of the order of $10^{5}$ can be achieved, with a divergent behaviour as the particle touching regime is approached. …
Contrary to classical predictions, the optical response of few-nm plasmonic particles depends on particle size due to effects such as nonlocality and electron spill-out. Ensembles of such nanoparticles (NPs) are therefore expected to exhibit a nonclassical inhomogeneous spectral broadening due to size distribution. For a normal distribution of free-electron NPs, and within the simple nonlocal Hydrodynamic Drude Model (HDM), both the nonlocal blueshift and the plasmon linewidth are shown to be considerably affected by ensemble averaging. Size-variance effects tend however to conceal nonlocality…
We investigate the statistics of photons emitted by tunneling electrons in a single electronic level plasmonic nanojunction. We compute the waiting-time distribution of successive emitted photons $w(τ)$. When the cavity damping rate $κ$ is larger than the electronic tunneling rate $Γ$, we show that in the photon-antibunching regime, $w(τ)$ indicates that the average delay-time between two successive photon emission events is given by $1/Γ$. This is in contrast with the usually considered second-order correlation function of emitted photons, $g^{(2)}(τ)$, which displays the single time scale $1…
Quantum effects play a significant role in nanometric plasmonic devices, such as small metal clusters and metallic nanoshells. For structures containing a large number of electrons, ab-initio methods such as the time-dependent density functional theory (TD-DFT) are often impractical because of severe computational constraints. Quantum hydrodynamics (QHD) offers a valuable alternative by representing the electron population as a continuous fluid medium evolving under the action of the self-consistent and external fields. Although relatively simple, QHD can incorporate quantum and nonlinear effe…
Nonlocal compensation of magnetic damping by spin injection has been theoretically shown to establish dynamic, noncollinear magnetization states that carry spin currents over micrometer distances. Such states can be generically referred to as dissipative exchange flows (DEFs) because spatially diffusing spin currents are established by the mutual exchange torque exerted by neighboring spins. Analytical studies to date have been limited to the weak spin injection assumption whereby the equation of motion for the magnetization is mapped to hydrodynamic equations describing spin flow and then lin…
The lifetime of localized surface plasmon plays an important role in many aspects of plasmonics and its applications. In small metal nanostructures, the dominant mechanism restricting plasmon lifetime is size-dependent Landau damping. We performed quantum-mechanical calculations of Landau damping for the bright surface plasmon mode in a metal nanoshell. In contrast to the conventional model based on the electron surface scattering, we found that the damping rate decreases as the nanoshell thickness is reduced. The origin of this behavior is traced to the spatial distribution of plasmon local f…
Heavily doped semiconductors have emerged as tunable low-loss plasmonic materials at mid-infrared frequencies. In this article we investigate nonlinear optical phenomena associated with high concentration of free electrons. We use a hydrodynamic description to study free electron dynamics in heavily doped semiconductors up to third-order terms, which are usually negligible for noble metals. We find that cascaded third-harmonic generation due to second-harmonic signals can be as strong as direct third-harmonic generation contributions even when the second-harmonic generation efficiency is zero.…
We present a comprehensive theory of the one-dimensional plasmonic crystal formed in the grating gated two-dimensional electron gas (2DEG) in semiconductor heterostructures. To describe collective plasma excitations in the 2DEG, we develop a generalized transmission line theoretical formalism consistent with the plasma hydrodynamic model. We then apply this formalism to analyze the plasmonic spectra of 2DEG systems with step-like periodic changes of electron density and/or gate screening. We show that in a periodically modulated 2DEG, a plasmonic crystal is formed and derive closed-form analyt…
We study the spectra and damping of surface plasmon-polaritons in double graphene layer structures. It is shown that application of bias voltage between layers shifts the edge of plasmon absorption associated with the interband transitions. This effect could be used in efficient plasmonic modulators. We reveal the influence of spatial dispersion of conductivity on plasmonic spectra and show that it results in the shift of cutoff frequency to the higher values.
Plasmon-exciton polaritons provide exciting possibilities to control light-matter interactions at the nanoscale by enabling closer investigation of quantum optical effects and facilitating novel technologies based, for instance, on Bose-Einstein condensation and polaritonic lasing. Nevertheless, observing and visualising polaritons is challenging, and traditional optical microscopy techniques often lead to ambiguities regarding the emergence and strength of the plasmon-exciton coupling. Electron microscopy offers a more robust means to study and verify the nature of plexcitons, but is still hi…
Edge states are ubiquitous for many condensed matter systems with multicomponent wave functions. For example, edge states play a crucial role in transport in zigzag graphene nanoribbons. Here, we report microscopic calculations of quantum plasmonics in doped graphene nanodisks with zigzag edges. We express the nanodisk conductivity $σ(ω)$ as a sum of the conventional bulk conductivity $σ_{\scriptscriptstyle\text{B}}(ω)$, and a novel term $σ_{\scriptscriptstyle\text{E}}(ω)$, corresponding to a coupling between the edge and bulk states. We show that the edge states give rise to a red-shift and b…
Localized surface plasmons (LSP) in semiconductor particles are expected to exhibit spatial nonlocal response effects as the geometry enters the nanometer scale. To investigate these nonlocal effects, we apply the hydrodynamic model to nanospheres of two different semiconductor materials: intrinsic InSb and $n$-doped GaAs. Our results show that the semiconductors indeed display nonlocal effects, and that these effects are even more pronounced than in metals. In a $150\mathrm{\,nm}$ InSb particle at $300\mathrm{\,K}$, the LSP frequency is blueshifted 35%, which is orders of magnitude larger tha…
Recent scanning tunnelling microscopy (STM) experiments reported single-molecule fluorescence induced by tunneling currents in the nanoplasmonic cavity formed by the STM tip and the substrate.The electric field of the cavity mode couples with the current-induced charge fluctuations of the molecule, allowing the excitation of the mode. We investigate theoretically this system for the experimentally relevant limit of large damping rate $κ$ for the cavity mode and arbitrary coupling strength to a single-electronic level. We find that for bias voltages close to the first inelastic threshold of pho…
We calculate the quantum state of the plasmon field excited by an ensemble of molecular emitters, which are driven by exchange of electrons with metallic nano-particle electrodes. Assuming identical emitters that are coupled collectively to the plasmon mode but are otherwise subject to independent relaxation channels, we show that symmetry constraints on the total system density matrix imply a drastic reduction in the numerical complexity. For $N_{\text{m}}$ three-level molecules we may thus represent the density matrix by a number of terms scaling as $(N_{\rm m}+8)!/(8!N_{\rm m}!)$ instead of…
As characteristic lengths in plasmonics rapidly approach the sub-nm regime, quantum-informed models that can capture those aspects of the quantum nature of the electron gas that are not accessible by the standard approximations of classical electrodynamics, or even go beyond the free-electron description, become increasingly more important. Here we propose a template for comparing and validating the predictions of such models, through the circular dichroism signal of a metallic nanoparticle helix. For illustration purposes, we compare three widely used models, each dominant at different nanopa…
We investigate an interplay between quantum geometrical effects and surface plasmons through surface plasmonic structures, based on an electron hydrodynamic theory. First we demonstrate that the quantum nonlinear Hall effect can be dramatically enhanced over a very broad range of frequency by utilizing plasmonic resonances and near-field effects of grating gates. Under the resonant condition, the enhancement becomes several orders of magnitude larger than the case without the nanostructures, while the peaks of high-harmonic plasmons expand broadly and emerge under the off-resonant condition, l…
We theoretically investigate the creation of a magnetic moment in gold nanoparticles by circularly polarized laser light. To this end, we describe the collective electron dynamics in gold nanoparticles using a semiclassical approach based on a quantum hydrodynamic model that incorporates the prin- cipal quantum many-body and nonlocal effects, such as the electron spill-out, the Hartree potential, and the exchange and correlation effects. We use a variational approach to investigate the breathing and the dipole dynamics induced by an external electric field. We show that gold nanoparticles can …
Recent advances in nanotechnology have created tremendous excitement across different disciplines but in order to fully control and manipulate nano-scale objects, we must understand the forces at work at the nano-scale, which can be very different from those that dominate the macro-scale. We show that there is a new kind of curvature-induced force that acts between nano-corrugated electrically neutral plasmonic surfaces. Absent in flat surfaces, such a force owes its existence entirely to geometric curvature, and originates from the kinetic energy associated with the electron density which ten…
We study the damping of plasma waves in linear Josephson junction chains as well as in two capacitively coupled chains. In the parameter regime where the ground capacitance can be neglected, the theory of the antisymmetric mode in the double chain can be mapped onto the theory of a single chain. We consider two sources of relaxation: the scattering from quantum phase slips (QPS) and the interaction among plasmons related to the nonlinearity of the Josephson potential. The contribution to the relaxation rate $1/τ$ from the nonlinearity scales with the fourth power of frequency $ω$, while the ph…
