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.

Atomic-Scale Defects Might Determine the Second Harmonic Generation from Plasmonic Graphene Nanostructures.

In this work, we theoretically investigate the impact of the atomic scale lattice imperfections of graphene nanoflakes on their nonlinear response enhanced by the resonance between an incident electromagnetic field and localized plasmon. As a case study, we address the second harmonic generation from graphene plasmonic nanoantennas of different symmetries with missing carbon atom vacancy defects in the honeycomb lattice. Using the many-body time-dependent density matrix approach, we find that one defect in the nanoflake comprising over five thousand carbon atoms can strongly impact the nonlinear hyperpolarizability and override the symmetry constraints. The effect reported here cannot be captured using the relaxation time approximation within the quantum or classical framework. Results obtained in this work have thus important implications for the design of nonlinear graphene devices.

Tip-Induced and Electrical Control of the Photoluminescence Yield of Monolayer WS2.

The photoluminescence (PL) of monolayer tungsten disulfide (WS2) is locally and electrically controlled using the nonplasmonic tip and tunneling current of a scanning tunneling microscope (STM). The spatial and spectral distribution of the emitted light is determined using an optical microscope. When the STM tip is engaged, short-range PL quenching due to near-field electromagnetic effects is present, independent of the sign and value of the bias voltage applied to the tip-sample tunneling junction. In addition, a bias-voltage-dependent long-range PL quenching is measured when the sample is positively biased. We explain these observations by considering the native n-doping of monolayer WS2 and the charge carrier density gradients induced by electron tunneling in micrometer-scale areas around the tip position. The combination of wide-field PL microscopy and charge carrier injection using an STM opens up new ways to explore the interplay between excitons and charge carriers in two-dimensional semiconductors.

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.

Time-dependent density functional theory calculations of electronic friction in non-homogeneous media.

The excitation of low-energy electron-hole pairs is one of the most relevant processes in the gas-surface interaction. An efficient tool to account for these excitations in simulations of atomic and molecular dynamics at surfaces is the so-called local density friction approximation (LDFA). The LDFA is based on a strong approximation that simplifies the dynamics of the electronic system: a local friction coefficient is defined using the value of the electronic density for the unperturbed system at each point of the dynamics. In this work, we apply real-time time-dependent density functional theory to the problem of the electronic friction of a negative point charge colliding with spherical jellium metal clusters. Our non-adiabatic, parameter-free results provide a benchmark for the widely used LDFA approximation and allow the discussion of various processes relevant to the electronic response of the system in the presence of the projectile.

Electronic Exciton-Plasmon Coupling in a Nanocavity Beyond the Electromagnetic Interaction Picture.

The optical response of a system formed by a quantum emitter and a plasmonic gap nanoantenna is theoretically addressed within the frameworks of classical electrodynamics and the time-dependent density functional theory (TDDFT). A fully quantum many-body description of the electron dynamics within TDDFT allows for analyzing the effect of electronic coupling between the emitter and the nanoantenna, usually ignored in classical descriptions of the optical response. We show that the hybridization between the electronic states of the quantum emitter and those of the metallic nanoparticles strongly modifies the energy, the width, and the very existence of the optical resonances of the coupled system. We thus conclude that the application of a quantum many-body treatment that correctly addresses charge-transfer processes between the emitter and the nanoantenna is crucial to address complex electronic processes involving plasmon-exciton interactions directly impacting optoelectronic applications.

Attosecond Dynamics of sp-Band Photoexcitation.

We report measurements of the temporal dynamics of the valence band photoemission from the magnesium (0001) surface across the resonance of the Γ[over ¯] surface state at 134 eV and link them to observations of high-resolution synchrotron photoemission and numerical calculations of the time-dependent Schrödinger equation using an effective single-electron model potential. We observe a decrease in the time delay between photoemission from delocalized valence states and the localized core orbitals on resonance. Our approach to rigorously link excitation energy-resolved conventional steady-state photoemission with attosecond streaking spectroscopy reveals the connection between energy-space properties of bound electronic states and the temporal dynamics of the fundamental electronic excitations underlying the photoelectric effect.

Ultrafast electronic response of graphene to a strong and localized electric field.

The way conduction electrons respond to ultrafast external perturbations in low dimensional materials is at the core of the design of future devices for (opto)electronics, photodetection and spintronics. Highly charged ions provide a tool for probing the electronic response of solids to extremely strong electric fields localized down to nanometre-sized areas. With ion transmission times in the order of femtoseconds, we can directly probe the local electronic dynamics of an ultrathin foil on this timescale. Here we report on the ability of freestanding single layer graphene to provide tens of electrons for charge neutralization of a slow highly charged ion within a few femtoseconds. With values higher than 1012 A cm-2, the resulting local current density in graphene exceeds previously measured breakdown currents by three orders of magnitude. Surprisingly, the passing ion does not tear nanometre-sized holes into the single layer graphene. We use time-dependent density functional theory to gain insight into the multielectron dynamics.

Quantum effects in the plasmon response of bimetallic core-shell nanostructures.

We report a quantum mechanical study of the plasmonic response of bimetallic spherical core/shell nanoparticles. The systems comprise up to 104 electrons and their optical response is addressed with Time Dependent Density Functional Theory calculations. These quantum results are compared with classical electromagnetic calculations for core/shell systems formed by Al/Na, Al/Au and Ag/Na, as representative examples of bimetallic systems. We show that for shell widths in the nanometer range, the system cannot be described as a simple stack of two metals. The finite size effect and the transition layer formed between the core and the shell strongly modify the optical properties of the compound nanoparticle. In particular this configuration leads to a frequency shift of the plasmon resonance with shell character and an increased plasmon decay into electron-hole pairs which eventually quenches this resonance for very thin shells. This effect is difficult to capture with a classical theory even upon adjustment of the parameters of a combination of metallic dielectric functions.

Quantum mechanical effects in plasmonic structures with subnanometre gaps.

Metallic structures with nanogap features have proven highly effective as building blocks for plasmonic systems, as they can provide a wide tuning range of operating frequencies and large near-field enhancements. Recent work has shown that quantum mechanical effects such as electron tunnelling and nonlocal screening become important as the gap distances approach the subnanometre length-scale. Such quantum effects challenge the classical picture of nanogap plasmons and have stimulated a number of theoretical and experimental studies. This review outlines the findings of many groups into quantum mechanical effects in nanogap plasmons, and discusses outstanding challenges and future directions.

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.

Nanooptics of Plasmonic Nanomatryoshkas: Shrinking the Size of a Core-Shell Junction to Subnanometer.

Quantum effects in plasmonic systems play an important role in defining the optical response of structures with subnanometer gaps. Electron tunneling across the gaps can occur, altering both the far-field optical response and the near-field confinement and enhancement. In this study, we experimentally and theoretically investigate plasmon coupling in gold "nanomatryoshka" (NM) nanoparticles with different core-shell separations. Plasmon coupling effects between the core and the shell become significant when their separation decreases to 15 nm. When their separation decreases to below 1 nm, the near- and far-field properties can no longer be described by classical approaches but require the inclusion of quantum mechanical effects such as electron transport through the self-assembled monolayer of molecular junction. In addition, surface-enhanced Raman scattering measurements indicate strong electron-transport induced charge transfer across the molecular junction. Our quantum modeling provides an estimate for the AC conductances of molecules in the junction. The insights acquired from this work pave the way for the development of novel quantum plasmonic devices and substrates for surface-enhanced Raman scattering.

Quantum effects in the optical response of extended plasmonic gaps: validation of the quantum corrected model in core-shell nanomatryushkas.

Electron tunneling through narrow gaps between metal nanoparticles can strongly affect the plasmonic response of the hybrid nanostructure. Although quantum mechanical in nature, this effect can be properly taken into account within a classical framework of Maxwell equations using the so-called Quantum Corrected Model (QCM). We extend previous studies on spherical cluster and cylindrical nanowire dimers where the tunneling current occurs in the extremely localized gap regions, and perform quantum mechanical time dependent density functional theory (TDDFT) calculations of the plasmonic response of cylindrical core-shell nanoparticles (nanomatryushkas). In this axially symmetric situation, the tunneling region extends over the entire gap between the metal core and the metallic shell. For core-shell separations below 0.5 nm, the standard classical calculations fail to describe the plasmonic response of the cylindrical nanomatryushka, while the QCM can reproduce the quantum results. Using the QCM we also retrieve the quantum results for the absorption cross section of the spherical nanomatryushka calculated by V. Kulkarni et al. [Nano Lett. 13, 5873 (2013)]. The comparison between the model and the full quantum calculations establishes the applicability of the QCM for a wider range of geometries that hold tunneling gaps.

A classical treatment of optical tunneling in plasmonic gaps: extending the quantum corrected model to practical situations.

The optical response of plasmonic nanogaps is challenging to address when the separation between the two nanoparticles forming the gap is reduced to a few nanometers or even subnanometer distances. We have compared results of the plasmon response within different levels of approximation, and identified a classical local regime, a nonlocal regime and a quantum regime of interaction. For separations of a few Ångstroms, in the quantum regime, optical tunneling can occur, strongly modifying the optics of the nanogap. We have considered a classical effective model, so called Quantum Corrected Model (QCM), that has been introduced to correctly describe the main features of optical transport in plasmonic nanogaps. The basics of this model are explained in detail, and its implementation is extended to include nonlocal effects and address practical situations involving different materials and temperatures of operation.

Active quantum plasmonics.

The ability of localized surface plasmons to squeeze light and engineer nanoscale electromagnetic fields through electron-photon coupling at dimensions below the wavelength has turned plasmonics into a driving tool in a variety of technological applications, targeting novel and more efficient optoelectronic processes. In this context, the development of active control of plasmon excitations is a major fundamental and practical challenge. We propose a mechanism for fast and active control of the optical response of metallic nanostructures based on exploiting quantum effects in subnanometric plasmonic gaps. By applying an external dc bias across a narrow gap, a substantial change in the tunneling conductance across the junction can be induced at optical frequencies, which modifies the plasmonic resonances of the system in a reversible manner. We demonstrate the feasibility of the concept using time-dependent density functional theory calculations. Thus, along with two-dimensional structures, metal nanoparticle plasmonics can benefit from the reversibility, fast response time, and versatility of an active control strategy based on applied bias. The proposed electrical manipulation of light using quantum plasmonics establishes a new platform for many practical applications in optoelectronics.

Quantum effects and nonlocality in strongly coupled plasmonic nanowire dimers.

Using a fully quantum mechanical approach we study the optical response of a strongly coupled metallic nanowire dimer for variable separation widths of the junction between the nanowires. The translational invariance of the system allows to apply the time-dependent density functional theory (TDDFT) for nanowires of diameters up to 10 nm which is the largest size considered so far in quantum modeling of plasmonic dimers. By performing a detailed analysis of the optical extinction, induced charge densities, and near fields, we reveal the major nonlocal quantum effects determining the plasmonic modes and field enhancement in the system. These effects consist mainly of electron tunneling between the nanowires at small junction widths and dynamical screening. The TDDFT results are compared with results from classical electromagnetic calculations based on the local Drude and non-local hydrodynamic descriptions of the nanowire permittivity, as well as with results from a recently developed quantum corrected model. The latter provides a way to include quantum mechanical effects such as electron tunneling in standard classical electromagnetic simulations. We show that the TDDFT results can be thus retrieved semi-quantitatively within a classical framework. We also discuss the shortcomings of classical non-local hydrodynamic approaches. Finally, the implications of the actual position of the screening charge density at the gap interfaces are discussed in connection with plasmon ruler applications at subnanometric distances.

Revealing the quantum regime in tunnelling plasmonics.

When two metal nanostructures are placed nanometres apart, their optically driven free electrons couple electrically across the gap. The resulting plasmons have enhanced optical fields of a specific colour tightly confined inside the gap. Many emerging nanophotonic technologies depend on the careful control of this plasmonic coupling, including optical nanoantennas for high-sensitivity chemical and biological sensors, nanoscale control of active devices, and improved photovoltaic devices. But for subnanometre gaps, coherent quantum tunnelling becomes possible and the system enters a regime of extreme non-locality in which previous classical treatments fail. Electron correlations across the gap that are driven by quantum tunnelling require a new description of non-local transport, which is crucial in nanoscale optoelectronics and single-molecule electronics. Here, by simultaneously measuring both the electrical and optical properties of two gold nanostructures with controllable subnanometre separation, we reveal the quantum regime of tunnelling plasmonics in unprecedented detail. All observed phenomena are in good agreement with recent quantum-based models of plasmonic systems, which eliminate the singularities predicted by classical theories. These findings imply that tunnelling establishes a quantum limit for plasmonic field confinement of about 10(-8)λ(3) for visible light (of wavelength λ). Our work thus prompts new theoretical and experimental investigations into quantum-domain plasmonic systems, and will affect the future of nanoplasmonic device engineering and nanoscale photochemistry.

Bridging quantum and classical plasmonics with a quantum-corrected model.

Electromagnetic coupling between plasmonic resonances in metallic nanoparticles allows for engineering of the optical response and generation of strong localized near-fields. Classical electrodynamics fails to describe this coupling across sub-nanometer gaps, where quantum effects become important owing to non-local screening and the spill-out of electrons. However, full quantum simulations are not presently feasible for realistically sized systems. Here we present a novel approach, the quantum-corrected model (QCM), that incorporates quantum-mechanical effects within a classical electrodynamic framework. The QCM approach models the junction between adjacent nanoparticles by means of a local dielectric response that includes electron tunnelling and tunnelling resistivity at the gap and can be integrated within a classical electrodynamical description of large and complex structures. The QCM predicts optical properties in excellent agreement with fully quantum mechanical calculations for small interacting systems, opening a new venue for addressing quantum effects in realistic plasmonic systems.