Surface-plasmon dispersion and size dependence of Mie resonance: Silver versus simple metals

Multiscale modeling of surface enhanced fluorescence

The fluorescence response of a chromophore in the proximity of a plasmonic nanostructure can be enhanced by several orders of magnitude, yielding the so-called surface-enhanced fluorescence (SEF). An in-depth understanding of SEF mechanisms benefits from fully atomistic theoretical models because SEF signals can be non-trivially affected by the atomistic profile of the nanostructure's surface. This work presents the first fully atomistic multiscale approach to SEF, capable of describing realistic structures. The method is based on coupling density functional theory (DFT) with state-of-the-art atomistic electromagnetic approaches, allowing for reliable physically-based modeling of molecule-nanostructure interactions. Computed results remarkably demonstrate the key role of the NP morphology and atomistic features in quenching/enhancing the fluorescence signal.

Singular and Nonsingular Transitions in the Infrared Plasmons of Nearly Touching Nanocube Dimers

Narrow gaps between plasmon-supporting materials can confine infrared electromagnetic energy at the nanoscale, thus enabling applications in areas such as optical sensing. However, in nanoparticle dimers, the nature of the transition between touching (zero gap) and nearly nontouching (nonzero gap ≲15 nm) regimes is still a subject of debate. Here, we observe both singular and nonsingular transitions in infrared plasmons confined to dimers of fluorine-doped indium oxide nanocubes when moving from touching to nontouching configurations depending on the dimensionality of the contact region. Through spatially resolved electron energy-loss spectroscopy, we find a continuous spectral evolution of the lowest-order plasmon mode across the transition for finite touching areas, in excellent agreement with the simulations. This behavior challenges the widely accepted idea that a singular transition always emerges in the near-touching regime of plasmonic particle dimers. The apparent contradiction is resolved by theoretically examining different types of gap morphologies, revealing that the presence of a finite touching area renders the transition nonsingular, while one-dimensional and point-like contacts produce a singular behavior in which the lowest-order dipolar mode in the touching configuration, characterized by a net induced charge in each of the particles, becomes unphysical as soon as they are separated. Our results provide valuable insights into the nature of dimer plasmons in highly doped semiconductors.

Footprints of atomic-scale features in plasmonic nanoparticles as revealed by electron energy loss spectroscopy

We present a first-principles theoretical study of the atomistic footprints in the valence electron energy loss spectroscopy (EELS) of nanometer-size metallic particles. Charge density maps of excited plasmons and EEL spectra for specific electron paths through a nanoparticle (Na380 atom cluster) are modeled using ab initio calculations within time-dependent density functional theory. Our findings unveil the atomic-scale sensitivity of EELS within this low-energy spectral range. Whereas localized surface plasmons (LSPs) are particularly sensitive to the atomistic structure of the surface probed by the electron beam, confined bulk plasmons (CBPs) reveal quantum size effects within the nanoparticle's volume. Moreover, we prove that classical local dielectric theories mimicking the atomistic structure of the nanoparticles reproduce the LSP trends observed in quantum calculations, but fall short in describing the CBP behavior observed under different electron trajectories.

Intrinsic Visible Plasmonic Properties of Colloidal PtIn2 Intermetallic Nanoparticles

Materials that intrinsically exhibit localized surface plasmon resonance (LSPR) in the visible region have been predominantly researched on nanoparticles (NPs) composed of coinage metals, namely Au, Ag, and Cu. Here, as a coinage metal-free intermetallic NPs, colloidal PtIn2 NPs with a C1 (CaF2 -type) crystal structure are synthesized by the liquid phase method, which evidently exhibit LSPR at wavelengths similar to face-centered cubic (fcc)-Au NPs. Computational simulations pointed out differences in the electronic structure and photo-excited electron dynamics between C1-PtIn2 and fcc-Au NPs; reduces interband transition and stronger screening with smaller number of bound d-electrons compare with fcc-Au are unique origins of the visible plasmonic nature of C1-PtIn2 NPs. These results strongly indicate that the intermetallic NPs are expected to address the development of alternative plasmonic materials by tuning their crystal structure and composition.

Accurate prediction of the optical properties of nanoalloys with both plasmonic and magnetic elements

The alloying process plays a pivotal role in the development of advanced multifunctional plasmonic materials within the realm of modern nanotechnology. However, accurate in silico predictions are only available for metal clusters of just a few nanometers, while the support of modelling is required to navigate the broad landscape of components, structures and stoichiometry of plasmonic nanoalloys regardless of their size. Here we report on the accurate calculation and conceptual understanding of the optical properties of metastable alloys of both plasmonic (Au) and magnetic (Co) elements obtained through a tailored laser synthesis procedure. The model is based on the density functional theory calculation of the dielectric function with the Hubbard-corrected local density approximation, the correction for intrinsic size effects and use of classical electrodynamics. This approach is built to manage critical aspects in modelling of real samples, as spin polarization effects due to magnetic elements, short-range order variability, and size heterogeneity. The method provides accurate results also for other magnetic-plasmonic (Au-Fe) and typical plasmonic (Au-Ag) nanoalloys, thus being available for the investigation of several other nanomaterials waiting for assessment and exploitation in fundamental sectors such as quantum optics, magneto-optics, magneto-plasmonics, metamaterials, chiral catalysis and plasmon-enhanced catalysis.

Effects of Oxygen Adsorption on the Optical Properties of Ag Nanoparticles

Plasmonic metal nanoparticles are efficient light harvesters with a myriad of sensing- and energy-related applications. For such applications, the optical properties of nanoparticles of metals such as Cu, Ag, and Au can be tuned by controlling the composition, particle size, and shape, but less is known about the effects of oxidation on the plasmon resonances. In this work, we elucidate the effects of O adsorption on the optical properties of Ag particles by evaluating the thermodynamic properties of O-decorated Ag particles with calculations based on the density functional theory and subsequently computing the photoabsorption spectra with a computationally efficient time-dependent density functional theory approach. We identify stable Ag nanoparticle structures with oxidized edges and a quenching of the plasmonic character of the metal particles upon oxidation and trace back this effect to the sp orbitals (or bands) of Ag particles being involved both in the plasmonic excitation and in the hybridization to form bonds with the adsorbed O atoms. Our work has important implications for the understanding and application of plasmonic metal nanoparticles and plasmon-mediated processes under oxidizing environments.

Nonlinear Optical Response of a Plasmonic Nanoantenna to Circularly Polarized Light: Rotation of Multipolar Charge Density and Near-Field Spin Angular Momentum Inversion

The spin and orbital angular momentum carried by electromagnetic pulses open new perspectives to control nonlinear processes in light-matter interactions, with a wealth of potential applications. In this work, we use time-dependent density functional theory (TDDFT) to study the nonlinear optical response of a free-electron plasmonic nanowire to an intense, circularly polarized electromagnetic pulse. In contrast to the well-studied case of the linear polarization, we find that the nth harmonic optical response to circularly polarized light is determined by the multipole moment of order n of the induced nonlinear charge density that rotates around the nanowire axis at the fundamental frequency. As a consequence, the frequency conversion in the far field is suppressed, whereas electric near fields at all harmonic frequencies are induced in the proximity of the nanowire surface. These near fields are circularly polarized with handedness opposite to that of the incident pulse, thus producing an inversion of the spin angular momentum. An analytical approach based on general symmetry constraints nicely explains our numerical findings and allows for generalization of the TDDFT results. This work thus offers new insights into nonlinear optical processes in nanoscale plasmonic nanostructures that allow for the manipulation of the angular momentum of light at harmonic frequencies.

Strain and crystallographic identification of the helically concaved gap surfaces of chiral nanoparticles

Identifying the three-dimensional (3D) crystal plane and strain-field distributions of nanocrystals is essential for optical, catalytic, and electronic applications. However, it remains a challenge to image concave surfaces of nanoparticles. Here, we develop a methodology for visualizing the 3D information of chiral gold nanoparticles ≈ 200 nm in size with concave gap structures by Bragg coherent X-ray diffraction imaging. The distribution of the high-Miller-index planes constituting the concave chiral gap is precisely determined. The highly strained region adjacent to the chiral gaps is resolved, which was correlated to the 432-symmetric morphology of the nanoparticles and its corresponding plasmonic properties are numerically predicted from the atomically defined structures. This approach can serve as a comprehensive characterization platform for visualizing the 3D crystallographic and strain distributions of nanoparticles with a few hundred nanometers, especially for applications where structural complexity and local heterogeneity are major determinants, as exemplified in plasmonics.

Interrogating Quantum Nonlocal Effects in Nanoplasmonics through Electron-Beam Spectroscopy

A rigorous account of quantum nonlocal effects is paramount for understanding the optical response of metal nanostructures and for designing plasmonic devices at the nanoscale. Here, we present a scheme for retrieving the quantum surface response of metals, encapsulated in the Feibelman d-parameters, from electron energy-loss spectroscopy (EELS) and cathodoluminescence (CL) measurements. We theoretically demonstrate that quantum nonlocal effects have a dramatic impact on EELS and CL spectra, in the guise of spectral shifts and nonlocal damping, when either the system size or the inverse wave vector in extended structures approaches the nanometer scale. Our concept capitalizes on the unparalleled ability of free electrons to supply deeply subwavelength near-fields and, thus, probe the optical response of metals at length scales in which quantum-mechanical effects are apparent. These results pave the way for a widespread use of the d-parameter formalism, thereby facilitating a rigorous yet practical inclusion of nonclassical effects in nanoplasmonics.

Optimization of Coherent Dynamics of Localized Surface Plasmons in Gold and Silver Nanospheres; Large Size Effects

Noble metal nanoparticles have attracted attention in recent years due to a number of their exciting applications in plasmonic applications, e.g., in sensing, high-gain antennas, structural colour printing, solar energy management, nanoscale lasing, and biomedicines. The report embraces the electromagnetic description of inherent properties of spherical nanoparticles, which enable resonant excitation of Localized Surface Plasmons (defined as collective excitations of free electrons), and the complementary model in which plasmonic nanoparticles are treated as quantum quasi-particles with discrete electronic energy levels. A quantum picture including plasmon damping processes due to the irreversible coupling to the environment enables us to distinguish between the dephasing of coherent electron motion and the decay of populations of electronic states. Using the link between classical EM and the quantum picture, the explicit dependence of the population and coherence damping rates as a function of NP size is given. Contrary to the usual expectations, such dependence for Au and Ag NPs is not a monotonically growing function, which provides a new perspective for tailoring plasmonic properties in larger-sized nanoparticles, which are still hardly available experimentally. The practical tools for comparing the plasmonic performance of gold and silver nanoparticles of the same radii in an extensive range of sizes are also given.

Visualizing screening in noble-metal clusters: static vs. dynamic

The localized surface-plasmon resonance of metal nanoparticles and clusters corresponds to a collective charge oscillation of the quasi-free metal electrons. The polarization of the more localized d electrons opposes the overall polarization of the electron cloud and thus screens the surface plasmon. By contrast, a static electric external field is well screened, as even very small noble-metal clusters are highly metallic: the field inside is practically zero except for the effect of the Friedel-oscillation-like modulations which lead to small values of the polarization of the d electrons. In the present article, we present and compare representations of the induced densities (i) connected to the surface-plasmon resonance and (ii) resulting from an external static electric field. The two cases allow for an intuitive understanding of the differences between the dynamic and the static screening.

Plasmonic Au-Cu nanostructures: Synthesis and applications

Plasmonic Au-Cu nanostructures composed of Au and Cu metals, have demonstrated advantages over their monolithic counterparts, which have recently attracted considerable attention. Au-Cu nanostructures are currently used in various research fields, including catalysis, light harvesting, optoelectronics, and biotechnologies. Herein, recent developments in Au-Cu nanostructures are summarized. The development of three types of Au-Cu nanostructures is reviewed, including alloys, core-shell structures, and Janus structures. Afterwards, we discuss the peculiar plasmonic properties of Au-Cu nanostructures as well as their potential applications. The excellent properties of Au-Cu nanostructures enable applications in catalysis, plasmon-enhanced spectroscopy, photothermal conversion and therapy. Lastly, we present our thoughts on the current status and future prospects of the Au-Cu nanostructures research field. This review is intended to contribute to the development of fabrication strategies and applications relating to Au-Cu nanostructures.

Do We Really Need Quantum Mechanics to Describe Plasmonic Properties of Metal Nanostructures?

Optical properties of metal nanostructures are the basis of several scientific and technological applications. When the nanostructure characteristic size is of the order of few nm or less, it is generally accepted that only a description that explicitly describes electrons by quantum mechanics can reproduce faithfully its optical response. For example, the plasmon resonance shift upon shrinking the nanostructure size (red-shift for simple metals, blue-shift for d-metals such as gold and silver) is universally accepted to originate from the quantum nature of the system. Here we show instead that an atomistic approach based on classical physics, ωFQFμ (frequency dependent fluctuating charges and fluctuating dipoles), is able to reproduce all the typical "quantum" size effects, such as the sign and the magnitude of the plasmon shift, the progressive loss of the plasmon resonance for gold, the atomistically detailed features in the induced electron density, and the non local effects in the nanoparticle response. To support our findings, we compare the ωFQFμ results for Ag and Au with literature time-dependent DFT simulations, showing the capability of fully classical physics to reproduce these TDDFT results. Only electron tunneling between nanostructures emerges as a genuine quantum mechanical effect, that we had to include in the model by an ad hoc term.

Unique interface reflection phenomena tailored by nanoscale electromagnetic boundary conditions

Local interface response effects are neglected based on the traditional electromagnetic boundary conditions (EMBCs) in an abrupt interface model. In this study, generalized nanoscale EMBCs are derived with interface response functions (IRFs) representing field inhomogeneity across the interface based on integral Maxwell's equations. They are rewritten in two different forms that correspond to the equivalent abrupt interface models with interface-induced dipoles or charges and currents. Interesting behaviors of Brewster angle shifting, non-extinction at Brewster angle, and unique absorption or gain effects are revealed based on the advanced Fresnel formula. IRFs-controlled GH-shift and angular GH-shift of a Gaussian beam near the Brewster angles are generated by the gradient interface. These unique phenomena provide some guidance for measuring the IRFs and expanding interface photonics at the nanoscale.

Orbital-Free Methods for Plasmonics: Linear Response

Plasmonic systems, such as metal nanoparticles, are widely used in different application areas, going from biology to photovoltaics.The modeling of the optical response of such systems is of fundamental importance to analyze their behavior and to design new systems with required properties.When the characteristic sizes/distances reach a few nanometers, non-local and spill-out effects become relevant and conventional classical electrodynamics models are no more appropriate. Methods based on the Time-Dependent Density-Functional Theory (TD-DFT) represent the current reference for the description of quantum effects. However, TD-DFT is based on knowledge of all occupied orbitals whose calculation is computationally prohibitive to model large plasmonic systems of interest for applications.On the other hand, methods based on the Orbital-Free (OF) formulation of TD-DFT, can scale linearly with the system size.In this Review, OF methods ranging from semiclassical models to the quantum hydrodynamic theory, will be derived from the linear response TD-DFT, so that the key approximations and properties of each method can be clearly highlighted. The accuracy of the various approximations will be then validated for the linear optical properties of jellium nanoparticles, the most relevant model system in plasmonics. OF methods can describe the collective excitations in plasmonic systems with great accuracy andwithout system-tuned parameters. The accuracy on these methods depends only on the accuracy on the (universal) kinetic energy functional of the ground-state electronic density. Current approximations and future development directions will be indicated.

Quantum surface effects in the electromagnetic coupling between a quantum emitter and a plasmonic nanoantenna: time-dependent density functional theory vs. semiclassical Feibelman approach

We use time-dependent density functional theory (TDDFT) within the jellium model to study the impact of quantum-mechanical effects on the self-interaction Green's function that governs the electromagnetic interaction between quantum emitters and plasmonic metallic nanoantennas. A semiclassical model based on the Feibelman parameters, which incorporates quantum surface-response corrections into an otherwise classical description, confirms surface-enabled Landau damping and the spill out of the induced charges as the dominant quantum mechanisms strongly affecting the nanoantenna-emitter interaction. These quantum effects produce a redshift and broadening of plasmonic resonances not present in classical theories that consider a local dielectric response of the metals. We show that the Feibelman approach correctly reproduces the nonlocal surface response obtained by full quantum TDDFT calculations for most nanoantenna-emitter configurations. However, when the emitter is located in very close proximity to the nanoantenna surface, we show that the standard Feibelman approach fails, requiring an implementation that explicitly accounts for the nonlocality of the surface response in the direction parallel to the surface. Our study thus provides a fundamental description of the electromagnetic coupling between plasmonic nanoantennas and quantum emitters at the nanoscale.

Fabrication of Metal-Insulator-Metal Nanostructures Composed of Au-MgF2-Au and Its Potential in Responding to Two Different Factors in Sample Solutions Using Individual Plasmon Modes

In this paper, metal–insulator–metal (MIM) nanostructures, which were designed to exhibit two absorption peaks within 500–1100 nm wavelength range, were fabricated using magnesium difluoride (MgF₂) as the insulator layer. Since the MIM nanostructures have two plasmon modes corresponding to the absorption peaks, they independently responded to the changes in two phases: the surrounding medium and the inside insulator layer, the structure is expected to obtain multiple information from sample solution: refractive index (RI) and molecular interaction between solution components and the insulator layer. The fabricated MIM nanostructure had a diameter of 139.6 ± 2.8 nm and a slope of 70°, and exhibited absorption peaks derived from individual plasmon modes at the 719 and 907 nm wavelengths. The evaluation of the response to surrounding solution component of the MIM nanostructures revealed a linear response of one plasmon mode toward the RI of the surrounding medium and a large blue shift of the other plasmon mode under conditions where glycerol was present at high concentration. From optical simulation and the evaluation of the MgF₂ fabricated by deposition, the blue shift was expected to be due to the swelling of MgF₂ interacting with the hydroxyl groups abundantly included in the glycerol molecules. The results indicated the individual responses of two plasmon modes in MIM nanostructures toward medium components, and brought the prospect for the simultaneous measurement of multiple elements using two or more plasmon modes.

Plasmonic metal nanostructures with extremely small features: new effects, fabrication and applications

Surface plasmons in metals promise many fascinating properties and applications in optics, sensing, photonics and nonlinear fields. Plasmonic nanostructures with extremely small features especially demonstrate amazing new effects as the feature sizes scale down to the sub-nanometer scale, such as quantum size effects, quantum tunneling, spill-out of electrons and nonlocal states etc. The unusual physical, optical and photo-electronic properties observed in metallic structures with extreme feature sizes enable their unique applications in electromagnetic field focusing, spectra enhancing, imaging, quantum photonics, etc. In this review, we focus on the new effects, fabrication and applications of plasmonic metal nanostructures with extremely small features. For simplicity and consistency, we will focus our topic on the plasmonic metal nanostructures with feature sizes of sub-nanometers. Subsequently, we discussed four main and typical plasmonic metal nanostructures with extremely small features, including: (1) ultra-sharp plasmonic metal nanotips; (2) ultra-thin plasmonic metal films; (3) ultra-small plasmonic metal particles and (4) ultra-small plasmonic metal nanogaps. Additionally, the corresponding fascinating new effects (quantum nonlinear, non-locality, quantum size effect and quantum tunneling), applications (spectral enhancement, high-order harmonic wave generation, sensing and terahertz wave detection) and reliable fabrication methods will also be discussed. We end the discussion with a brief summary and outlook of the main challenges and possible breakthroughs in the field. We hope our discussion can inspire the broader design, fabrication and application of plasmonic metal nanostructures with extremely small feature sizes in the future.

Quantum surface-response of metals revealed by acoustic graphene plasmons

A quantitative understanding of the electromagnetic response of materials is essential for the precise engineering of maximal, versatile, and controllable light-matter interactions. Material surfaces, in particular, are prominent platforms for enhancing electromagnetic interactions and for tailoring chemical processes. However, at the deep nanoscale, the electromagnetic response of electron systems is significantly impacted by quantum surface-response at material interfaces, which is challenging to probe using standard optical techniques. Here, we show how ultraconfined acoustic graphene plasmons in graphene-dielectric-metal structures can be used to probe the quantum surface-response functions of nearby metals, here encoded through the so-called Feibelman d-parameters. Based on our theoretical formalism, we introduce a concrete proposal for experimentally inferring the low-frequency quantum response of metals from quantum shifts of the acoustic graphene plasmons dispersion, and demonstrate that the high field confinement of acoustic graphene plasmons can resolve intrinsically quantum mechanical electronic length-scales with subnanometer resolution. Our findings reveal a promising scheme to probe the quantum response of metals, and further suggest the utilization of acoustic graphene plasmons as plasmon rulers with ångström-scale accuracy.

Tunable Size Dependence of Quantum Plasmon of Charged Gold Nanoparticles

The quantum behavior of surface plasmons has received extensive attention, benefiting from the development of exquisite nanotechnology and the diverse applications. Blueshift, redshift, and nonshift of localized surface plasmon resonances (LSPRs) have all been reported as the particle size decreases and enters the quantum size regime, but the underlying physical mechanism to induce these controversial size dependences is not clear. Herein, we propose an improved semiclassical model for modifying the dielectric function of metal nanospheres by combining the intrinsic quantized electron transitions and surface electron injection or extraction to investigate the plasmon shift and LSPR size dependence of the charged Au nanoparticles. We experimentally observe that the nonmonotonic blueshift of LSPRs with size for Au nanoparticles is turned into an approximately monotonic blueshift by increasing the electron donor concentration in the reduction solution, and it can also be transformed to an approximately monotonic redshift after surface passivation by ligand molecules. Moreover, we demonstrate controlled blueshift and redshift for the electron and hole plasmons in Cu_{2-x}S@Au core-shell nanoparticles by injecting electrons. The experimental observations and the theoretical calculations clarify the controversial size dependences of LSPR reported in the literature, reveal the critical role of surface electron injection or extraction in the transformation between the different size dependences of LSPRs, and are helpful for understanding the nature of surface plasmons in the quantum size regime.

Plasmonic Resonances of Metal Nanoparticles: Atomistic vs. Continuum Approaches

The fully atomistic model, ωFQ, based on textbook concepts (Drude theory, electrostatics, quantum tunneling) and recently developed by some of the present authors in Nanoscale, 11, 6004-6015 is applied to the calculation of the optical properties of complex Na, Ag, and Au nanostructures. In ωFQ, each atom of the nanostructures is endowed with an electric charge that can vary according to the external electric field. The electric conductivity between nearest atoms is modeled by adopting the Drude model, which is reformulated in terms of electric charges. Quantum tunneling effects are considered by letting the dielectric response of the system arise from atom-atom conductivity. ωFQ is challenged to reproduce the optical response of metal nanoparticles of different sizes and shapes, and its performance is compared with continuum Boundary Element Method (BEM) calculations.

Efficient Plasmon-Mediated Energy Funneling to the Surface of Au@Pt Core-Shell Nanocrystals

The structure and ultrafast photodynamics of ∼8 nm Au@Pt core-shell nanocrystals with ultrathin (<3 atomic layers) Pt-Au alloy shells are investigated to show that they meet the design principles for efficient bimetallic plasmonic photocatalysis. Photoelectron spectra recorded at two different photon energies are used to determine the radial concentration profile of the Pt-Au shell and the electron density near the Fermi energy, which play a key role in plasmon damping and electronic and thermal conductivity. Transient absorption measurements track the flow of energy from the plasmonic core to the electronic manifold of the Pt shell and back to the lattice of the core in the form of heat. We show that strong coupling to the high density of Pt(d) electrons at the Fermi level leads to accelerated dephasing of the Au plasmon on the femtosecond time scale, electron-electron energy transfer from Au(sp) core electrons to Pt(d) shell electrons on the sub-picosecond time scale, and enhanced thermal resistance on the 50 ps time scale. Electron-electron scattering efficiently funnels hot carriers into the ultrathin catalytically active shell at the nanocrystal surface, making them available to drive chemical reactions before losing energy to the lattice via electron-phonon scattering on the 2 ps time scale. The combination of strong broadband light absorption, enhanced electromagnetic fields at the catalytic metal sites, and efficient delivery of hot carriers to the catalyst surface makes core-shell nanocrystals with plasmonic metal cores and ultrathin catalytic metal shells promising nanostructures for the realization of high-efficiency plasmonic catalysts.

Nonequilibrium Thermodynamics of Colloidal Gold Nanocrystals Monitored by Ultrafast Electron Diffraction and Optical Scattering Microscopy

Metal nanocrystals exhibit important optoelectronic and photocatalytic functionalities in response to light. These dynamic energy conversion processes have been commonly studied by transient optical probes to date, but an understanding of the atomistic response following photoexcitation has remained elusive. Here, we use femtosecond resolution electron diffraction to investigate transient lattice responses in optically excited colloidal gold nanocrystals, revealing the effects of nanocrystal size and surface ligands on the electron-phonon coupling and thermal relaxation dynamics. First, we uncover a strong size effect on the electron-phonon coupling, which arises from reduced dielectric screening at the nanocrystal surfaces and prevails independent of the optical excitation mechanism (i.e., inter- and intraband). Second, we find that surface ligands act as a tuning parameter for hot carrier cooling. Particularly, gold nanocrystals with thiol-based ligands show significantly slower carrier cooling as compared to amine-based ligands under intraband optical excitation due to electronic coupling at the nanocrystal/ligand interfaces. Finally, we spatiotemporally resolve thermal transport and heat dissipation in photoexcited nanocrystal films by combining electron diffraction with stroboscopic elastic scattering microscopy. Taken together, we resolve the distinct thermal relaxation time scales ranging from 1 ps to 100 ns associated with the multiple interfaces through which heat flows at the nanoscale. Our findings provide insights into optimization of gold nanocrystals and their thin films for photocatalysis and thermoelectric applications.

How metallic are noble-metal clusters? Static screening and polarizability in quantum-sized silver and gold nanoparticles

Metallicity of nanoparticles can be defined in different ways. One possibility is to look at the degree to which external fields are screened inside the object. This screening would be complete in a classical perfect metal where surface charges arrange on the classical -i.e., abrupt - surface such that no internal fields exist. However, it is obvious that this situation is modified for very small clusters: the surface charges are "smeared out" at the surface, and the screening might be less complete. In the present work we ask the question as to how close small noble-metal clusters are to a classical metal. We show that, indeed, the screening is almost complete (≈96%) already for as little as one atomic layer of the coinage metals, silver and gold alike. At the same time, we show that quantum effects, viz., electronic shell closings and the Friedel-like oscillations of the density, play a role, meaning that the clusters cannot be described solely using the concept of screening in a classical metal.

Plasmon-emitter interactions at the nanoscale

Plasmon-emitter interactions are of central importance in modern nanoplasmonics and are generally maximal at short emitter-surface separations. However, when the separation falls below 10-20 nm, the classical theory deteriorates progressively due to its neglect of quantum effects such as nonlocality, electronic spill-out, and Landau damping. Here we show how this neglect can be remedied in a unified theoretical treatment of mesoscopic electrodynamics incorporating Feibelman [Formula: see text]-parameters. Our approach incorporates nonclassical resonance shifts and surface-enabled Landau damping-a nonlocal damping effect-which have a dramatic impact on the amplitude and spectral distribution of plasmon-emitter interactions. We consider a broad array of plasmon-emitter interactions ranging from dipolar and multipolar spontaneous emission enhancement, to plasmon-assisted energy transfer and enhancement of two-photon transitions. The formalism gives a complete account of both plasmons and plasmon-emitter interactions at the nanoscale, constituting a simple yet rigorous platform to include nonclassical effects in plasmon-enabled nanophotonic phenomena.

A general theoretical and experimental framework for nanoscale electromagnetism

The macroscopic electromagnetic boundary conditions, which have been established for over a century¹, are essential for the understanding of photonics at macroscopic length scales. Even state-of-the-art nanoplasmonic studies^2-4, exemplars of extremely interface-localized fields, rely on their validity. This classical description, however, neglects the intrinsic electronic length scales (of the order of ångström) associated with interfaces, leading to considerable discrepancies between classical predictions and experimental observations in systems with deeply nanoscale feature sizes, which are typically evident below about 10 to 20 nanometres^5-10. The onset of these discrepancies has a mesoscopic character: it lies between the granular microscopic (electronic-scale) and continuous macroscopic (wavelength-scale) domains. Existing top-down phenomenological approaches deal only with individual aspects of these omissions, such as nonlocality^11-13 and local-response spill-out^14,15. Alternatively, bottom-up first-principles approaches-for example, time-dependent density functional theory^16,17-are severely constrained by computational demands and thus become impractical for multiscale problems. Consequently, a general and unified framework for nanoscale electromagnetism remains absent. Here we introduce and experimentally demonstrate such a framework-amenable to both analytics and numerics, and applicable to multiscale problems-that reintroduces the electronic length scale via surface-response functions known as Feibelman d parameters^18,19. We establish an experimental procedure to measure these complex dispersive surface-response functions, using quasi-normal-mode perturbation theory and observations of pronounced nonclassical effects. We observe nonclassical spectral shifts in excess of 30 per cent and the breakdown of Kreibig-like broadening in a quintessential multiscale architecture: film-coupled nanoresonators, with feature sizes comparable to both the wavelength and the electronic length scale. Our results provide a general framework for modelling and understanding nanoscale (that is, all relevant length scales above about 1 nanometre) electromagnetic phenomena.

Quantum Effects In Imaging Nano-Structures Using Photon-Induced Near-Field Electron Microscopy

In this paper, we introduce the quantum mechanical approach as a more physically-realistic model to accurately quantify the electron-photon interaction in Photon-induced near-field electron microscopy (PINEM). Further, we compare the maximum coupling speed between the electrons and the photons in the quantum and classical regime. For a nanosphere of radius 2.13 nm, full quantum calculations show that the maximum coupling between photon and electron occurs at a slower speed than classical calculations report. In addition, a significant reduction in PINEM field intensity is observed for the full quantum model. Furthermore, we discuss the size limitation for particles imaged using the PIMEN technique and the role of the background material in improving the PINEM intensity. We further report a significant reduction in PINEM intensity in nearly touching plasmonic particles (0.3 nm gap) due to tunneling effect.

Identifying Electronic Modes by Fourier Transform from δ-Kick Time-Evolution TDDFT Calculations

Time-dependent density-functional theory (TDDFT) is widely used for calculating electron excitations in clusters and large molecules. For optical excitations, TDDFT is customarily applied in two distinct approaches: transition-based linear-response TDDFT (LR-TDDFT) and the real-time formalism (RT-TDDFT). The former directly provides the energies and transition densities of the excitations, but it requires the calculation of a large number of empty electron states, which makes it cumbersome for large systems. By contrast, RT-TDDFT circumvents the evaluation of empty orbitals, which is especially advantageous when dealing with large systems. A drawback of the procedure is that information about the nature of individual spectral features is not automatically obtained, although it is of course contained in the time-dependent induced density. Fourier transform of the induced density has been used in some simple cases, but the method is, surprisingly, not widely used to complement the RT-TDDFT calculations; although the reliability of RT-TDDFT spectra is now widely accepted, a critical assessment for the corresponding transition densities and a demonstration of the technical feasibility of the Fourier-transform evaluation for general cases is still lacking. In the present work, we show that the transition densities of the optically allowed excitations can be efficiently extracted from a single δ-kick time-evolution calculation even in complex systems like noble metals. We assess the results by comparison with the corresponding LR-TDDFT ones and also with the induced densities arising from RT-TDDFT simulations of the excitation process.

Microscopic Electron Dynamics in Metal Nanoparticles for Photovoltaic Systems

Nanoparticles&mdash;regularly patterned or randomly dispersed&mdash;are a key ingredient for emerging technologies in photonics. Of particular interest are scattering and field enhancement effects of metal nanoparticles for energy harvesting and converting systems. An often neglected aspect in the modeling of nanoparticles are light interaction effects at the ultimate nanoscale beyond classical electrodynamics. Those arise from microscopic electron dynamics in confined systems, the accelerated motion in the plasmon oscillation and the quantum nature of the free electron gas in metals, such as Coulomb repulsion and electron diffusion. We give a detailed account on free electron phenomena in metal nanoparticles and discuss analytic expressions stemming from microscopic (Random Phase Approximation&mdash;RPA) and semi-classical (hydrodynamic) theories. These can be incorporated into standard computational schemes to produce more reliable results on the optical properties of metal nanoparticles. We combine these solutions into a single framework and study systematically their joint impact on isolated Au, Ag, and Al nanoparticles as well as dimer structures. The spectral position of the plasmon resonance and its broadening as well as local field enhancement show an intriguing dependence on the particle size due to the relevance of additional damping channels.

Study of volume and surface plasmons in small silicon–hydrogen nanoclusters using the GW method

Numerical calculations of surface and volume plasma excitations in silicon–hydrogen nanoclusters in the range Si₁₀–Si₆₀ and Si₃H₈–Si₆₄H₅₆ (size range 4–13.5 Å) are performed within the GW approximation.

Quantum Corrections in Nanoplasmonics: Shape, Scale, and Material

The classical treatment of plasmonics is insufficient at the nanometer-scale due to quantum mechanical surface phenomena. Here, an extension of the classical paradigm is reported which rigorously remedies this deficiency through the incorporation of first-principles surface response functions-the Feibelman d parameters-in general geometries. Several analytical results for the leading-order plasmonic quantum corrections are obtained in a first-principles setting; particularly, a clear separation of the roles of shape, scale, and material is established. The utility of the formalism is illustrated by the derivation of a modified sum rule for complementary structures, a rigorous reformulation of Kreibig's phenomenological damping prescription, and an account of the small-scale resonance shifting of simple and noble metal nanostructures.

Plasmon Response and Electron Dynamics in Charged Metallic Nanoparticles

Using the time-dependent density functional theory, we perform quantum calculations of the electron dynamics in small charged metallic nanoparticles (clusters) of spherical geometry. We show that the excess charge is accumulated at the surface of the nanoparticle within a narrow layer given by the typical screening distance of the electronic system. As a consequence, for nanoparticles in vacuum, the dipolar plasmon mode displays only a small frequency shift upon charging. We obtain a blue shift for positively charged clusters and a red shift for negatively charged clusters, consistent with the change of the electron spill-out from the nanoparticle boundaries. For negatively charged clusters, the Fermi level is eventually promoted above the vacuum level leading to the decay of the excess charge via resonant electron transfer into the continuum. We show that, depending on the charge, the process of electron loss can be very fast, on the femtosecond time scale. Our results are of great relevance to correctly interpret the optical response of the nanoparticles obtained in electrochemistry, and demonstrate that the measured shift of the plasmon resonances upon charging of nanoparticles cannot be explained without account for the surface chemistry and the dielectric environment.

Atomistic electrodynamics simulations of bare and ligand-coated nanoparticles in the quantum size regime

The optical properties of metallic nanoparticles with nanometre dimensions exhibit features that cannot be described by classical electrodynamics. In this quantum size regime, the near-field properties are significantly modified and depend strongly on the geometric arrangements. However, simulating realistically sized systems while retaining the atomistic description remains computationally intractable for fully quantum mechanical approaches. Here we introduce an atomistic electrodynamics model where the traditional description of nanoparticles in terms of a macroscopic homogenous dielectric constant is replaced by an atomic representation with dielectric properties that depend on the local chemical environment. This model provides a unified description of bare and ligand-coated nanoparticles, as well as strongly interacting nanoparticle dimer systems. The non-local screening owing to an inhomogeneous ligand layer is shown to drastically modify the near-field properties. This will be important to consider in optimization of plasmonic nanostructures for near-field spectroscopy and sensing applications.

Investigating the properties of metallic nanoparticles in the 2–10 nm range is a computational challenge. Here, the authors introduce an atomistic electrodynamics model to describe bare and coated particles and dimers, and show that the ligand layer modifies the near-field properties of the particles.

Multipole plasmons and their disappearance in few-nanometre silver nanoparticles

Electron energy-loss spectroscopy can be used for detailed spatial and spectral characterization of optical excitations in metal nanoparticles. In previous electron energy-loss experiments on silver nanoparticles with radii smaller than 20 nm, only the dipolar surface plasmon resonance was assumed to play a role. Here, applying electron energy-loss spectroscopy to individual silver nanoparticles encapsulated in silicon nitride, we observe besides the usual dipole resonance an additional surface plasmon resonance corresponding to higher angular momenta for nanoparticle radii as small as 4 nm. We study the radius and electron beam impact position dependence of both resonances separately. For particles smaller than 4 nm in radius the higher-order surface plasmon mode disappears, in agreement with generalized non-local optical response theory, while the dipole resonance blueshift exceeds our theoretical predictions. Unlike in optical spectra, multipole surface plasmons are important in electron energy-loss spectra even of ultrasmall metallic nanoparticles.

Plane wave scattering from a plasmonic nanowire-film system with the inclusion of non-local effects

In this paper we present a theoretical analysis of the electromagnetic response of a plasmonic nanowire-film system. The analytical solution accounts for both the dispersive as well as non-local nature of the plasmonic media. The physical structure comprises of a plasmonic nanowire made of a plasmonic metal such as gold or silver placed over a plasmonic film of the same material. Such a nanostructure exhibits a spectrum that is extremely sensitive to various geometric parameters such as spacer thickness and nanowire radius, which makes it favorable for various sensing applications. The non-locality of the plasmonic medium, which can be captured using the hydrodynamic model, significantly affects the resonant wavelength of this system for structures of small dimensions (~ less than 5 nm gap between the nanowire and the film). We present an analytical method that can be used to predict the effect of non-locality on the resonances of the system. To validate the analytical method, we also report a comparison of our analytical solution with a numerical Finite Difference Time Domain analysis (FDTD) of the same structure with the plasmonic medium being treated as local in nature.

Projected Dipole Model for Quantum Plasmonics

Quantum effects of plasmonic phenomena have been explored through ab initio studies, but only for exceedingly small metallic nanostructures, leaving most experimentally relevant structures too large to handle. We propose instead an effective description with the computationally appealing features of classical electrodynamics, while quantum properties are described accurately through an infinitely thin layer of dipoles oriented normally to the metal surface. The nonlocal polarizability of the dipole layer-the only introduced parameter-is mapped from the free-electron distribution near the metal surface as obtained with 1D quantum calculations, such as time-dependent density-functional theory (TDDFT), and is determined once and for all. The model can be applied in two and three dimensions to any system size that is tractable within classical electrodynamics, while capturing quantum plasmonic aspects of nonlocal response and a finite work function with TDDFT-level accuracy. Applying the theory to dimers, we find quantum corrections to the hybridization even in mesoscopic dimers, as long as the gap itself is subnanometric.

Hot electron plasmon-protected solar cell

A solar cell based on a hot electron plasmon protection effect is proposed and made plausible by simulations, non-local modeling of the response, and quantum mechanical calculations. In this cell, a thin-film, plasmonic metamaterial structure acts as both an efficient photon absorber in the visible frequency range and a plasmonic resonator in the IR range, the latter of which absorbs and protects against phonon emission the free energy of the hot electrons in an adjacent semiconductor junction. We show that in this structure, electron-plasmon scattering is much more efficient than electron-phonon scattering in cooling-off hot electrons, and the plasmon-stored energy is recoverable as an additional cell voltage. The proposed structure could become a prototype of a new generation of high efficiency solar cells.

Plasmons in supported size-selected silver nanoclusters

The plasmonic behavior of size-selected supported silver clusters is studied by surface second harmonic generation spectroscopy for the first time. A blue shift of ∼0.2 eV in the plasmon resonance is observed with decreasing cluster size from Ag55 to Ag9. In addition to the general blue shift, a nonscalable size-dependence is also observed in plasmonic behavior of Ag nanoclusters, which is attributed to varying structural properties of the clusters. The results are in quantitative agreement with a hybrid theoretical model based on Mie theory and the existing DFT calculations.

Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics

The standard hydrodynamic Drude model with hard-wall boundary conditions can give accurate quantitative predictions for the optical response of noble-metal nanoparticles. However, it is less accurate for other metallic nanosystems, where surface effects due to electron density spill-out in free space cannot be neglected. Here we address the fundamental question whether the description of surface effects in plasmonics necessarily requires a fully quantum-mechanical ab initio approach. We present a self-consistent hydrodynamic model (SC-HDM), where both the ground state and the excited state properties of an inhomogeneous electron gas can be determined. With this method we are able to explain the size-dependent surface resonance shifts of Na and Ag nanowires and nanospheres. The results we obtain are in good agreement with experiments and more advanced quantum methods. The SC-HDM gives accurate results with modest computational effort, and can be applied to arbitrary nanoplasmonic systems of much larger sizes than accessible with ab initio methods.