Kinetic Density Functional Theory for Plasmonic Nanostructures: Breaking of the Plasmon Peak in the Quantum Regime and Generation of Hot Electrons

We develop a quantum kinetic theory of the dynamic response of typical noble metals. Our approach is based on the density functional theory (DFT) and incorporates new important elements as compared to the conventional time-dependent DFT formalism. The kinetic DFT is derived starting from the master equation of motion for the density matrix, which involves both momentum and energy relaxation processes. Therefore, the quantum system is described by two relaxation parameters, unlike the conventional time-dependent DFT incorporating only one relaxation parameter. This allows us to describe both the absorption of light and the generation of hot plasmonic electrons. Using our kinetic DFT theory, we also observe the transition from the multiple peaks in small size-quantized systems to the intensive plasmonic resonance in large classical systems. Unlike the standard picture of collisional broadening of the plasmon peak in small systems, we observe a very different scenario: the formation of multiple plasmonic-like peaks in small quantized systems. These peaks are the result of a hybridization of the collective plasmon mode and the single-particle transitions in a quantized electron gas. There are a few experimental observations that seem to correlate with such a scenario of the plasmonic broadening in small systems. Our approach also incorporates the interband transitions, which are important for a qualitative description of gold and silver. Although this paper gives an application of our kinetic DFT only to the slab geometry, our theory can be applied to nanocrystals of arbitrary shape. The kinetic DFT formalism developed here can be employed to model and predict a variety of metal and hybrid nanostructures for applications in photocatalysis, sensors, photodetectors, metamaterials, etc

Optical Generation of Hot Plasmonic Carriers in Metal Nanocrystals: The Effects of Shape and Field Enhancement

We investigate theoretically photogeneration of excited carriers in plasmonic nanocrystals. The theory is based on the solution of the quantum equation of motion for the density matrix. Efficient photogeneration of plasmonic electrons and holes in small nanocrystals becomes possible due to the nonconservation of the electron momentum. The confinement and reflection of electrons in small nanocrystals allowed photon-assisted electron transitions with high excitation energies and therefore lead to a large number of energetic carriers. This process is a surface-scattering effect and efficient only for nanostructures with small sizes. Other important factors for the photogeneration effect are the field enhancement and the inhomogeneity of electromagnetic fields inside a plasmonic nanostructure. The plasmonic field effects strongly depend on the shape of the nanocrystal. For example, a plasmonic nanocube is more efficient for the electron photogeneration than a nanosphere and a nanosphere generates more energetic carriers compared to a plasmonic slab. The results obtained here can be used for designing plasmonic nanostructures for solar and photocatalytic applications

Chiral Nanocrystals: Plasmonic Spectra and Circular Dichroism

The life is inherently chiral. Consequently, chirality plays a pivotal role in biochemistry and the evolution of life itself. Optical manifestation of chirality of biomolecules, so-called circular dichroism, is a remarkable but relatively weak effect appearing typically in the UV. In contrast to the biomolecules, plasmonic nanocrystals offer an interesting opportunity to create strong circular dichroism (CD) in the visible spectral range. Here we describe plasmonic properties of single chiral nanocrystals and focus on a new mechanism of optical chirality originating from a chiral shape of a nanocrystal. After careful examination, we found that this CD mechanism is induced by the mixing between different plasmon harmonics and is qualitatively different from the previously described dipolar CD effect in chiral assemblies of spherical nanoparticles. Chiral plasmonic nanocrystals studied here offer a new approach for the creation of nanomaterials with strong chiroptical responses in the visible spectral interval

Amplified Generation of Hot Electrons and Quantum Surface Effects in Nanoparticle Dimers with Plasmonic Hot Spots

Plasmonic excitations in optically driven nanocrystals are composed of excited single-particle electron–hole pairs in the Fermi sea. In large nanostructures, most of the excited plasmonic electrons have relatively small excitation energies due to the conservation of linear momentum. However, small optically driven nanocrystals may have large numbers of hot electrons with large energies. In this study, we develop the concept of hot electron generation further by considering the effect of a plasmonic hot spot. Plasmonic hot spots are areas in a nanostructure with highly inhomogeneous and enhanced electric fields. In our model of a nanoparticle dimer, the hot spot region appears near the gap between the nanoparticles. We then apply the quantum formalism based on the density matrix to describe this system. We show that the electromagnetic enhancement and the nonconservation of linear momentum in the hot spot of the nanoparticle dimer lead to strongly increased rates of generation of energetic (hot) electrons. The rates of hot electron generation grow faster than the absorption cross section and the electromagnetic enhancement factor with the decrease of the gap between the nanoparticles. This happens due to the breaking of the linear momentum conservation of electrons in the hot spot regions. We also show that hot electron generation effect leads to the quantum mechanism of surface-induced absorption in nanocrystals that is an intrinsic property of any confined plasmonic system. The results obtained in this study can be useful for understanding and designing plasmonic photodetectors and hybrid materials for efficient photocatalysis

Theory of Photoinjection of Hot Plasmonic Carriers from Metal Nanostructures into Semiconductors and Surface Molecules

We investigate theoretically the effects of generation and injection of plasmonic carriers from an optically excited metal nanocrystal to a semiconductor contact or to surface molecules. The energy distributions of optically excited hot carriers are dramatically different in metal nanocrystals with large and small sizes. In large nanocrystals, the majority of hot carriers has very small excitation energies, and the excited-carrier distribution resembles the case of a plasmon wave in bulk. For nanocrystal sizes smaller than 20 nm, the carrier distribution extends to larger energies and occupies the whole region <i>E</i>_F < ε < <i>E</i>_F + ℏ<i>ω</i>. The physical reason for the above behaviors is nonconservation of momentum in a nanocrystal. Because of the above properties, nanocrystals of small sizes are most suitable for designing opto-electronic and photosynthetic devices based on injection of plasmonic electrons and holes. For gold nanocrystals, the optimal sizes for efficient generation of hot carriers with overbarrier energies are in the range of 10–20 nm. Another important factor is the polarization of the exciting light. For efficient excitation of carriers with high energies, the electric-field polarization vector should be perpendicular to a prism-like nanoantenna (slab or platelet). We also show the relation between our theory for injection from plasmonic nanocrystals and the Fowler theory of injection from a bulk metal. Along with a prism geometry (or platelet geometry), we consider cubes. The results can be applied to design both purely solid-state opto-electronic devices and systems for photocatalysis and solar-energy conversion

Orientation-Sensitive Peptide-Induced Plasmonic Circular Dichroism in Silver Nanocubes

Polyproline II-based helical peptides were adsorbed to silver nanocubes through a cysteine linker and induced circular dichroism (CD) in two of their plasmon resonance modes. Inversion of the peptide’s orientation with respect to the surface led to inversion of the plasmonic CD signal. This phenomenon could not be explained by the simple molecule–plasmon dipolar interaction model and could be due to the multipolar nature of the plasmon modes. Elongation of the polyproline peptide led to a significant increase of the induced CD signal. Surprisingly, the effect did not change with sharpening of the edges of the silver nanocubes. The change to a polyproline I helix caused nulling of the induced plasmonic CD

Optical Properties of Chiral Plasmonic Tetramers: Circular Dichroism and Multipole Effects

Chiral metal nanoparticle assemblies exhibit plasmonic circular dichroism (CD) in the visible spectral interval. It was found previously that the circular dichroism signals can be induced by dipolar interactions between nanoparticles in a chiral assembly. In order to enhance plasmonic circular dichroism response, one can take advantage of multipole effects and anisotropy of nanostructures. We calculate the plasmonic circular dichroism of several nanoparticle (NP) assemblies using the interacting point-dipole approach and the purely numerical method based on the discrete dipole approximation (DDA). We found that the multipole effects revealed by the DDA calculations are crucial to describe and understand CD responses of tightly packed assemblies. The chiral equilateral tetrahedral 4-NP complexes are especially interesting because they do not have the dipolar contribution to the CD signal. Therefore, CD signals of equilateral tetrahedral 4-NP complexes originate solely from the multipole interactions. The strength of CD signals rapidly decreases with the particle–particle distance as 1/<i>R</i>^9.7 for the helices and as 1/<i>R</i>^18.1 for the equilateral tetrahedral 4-NP complexes, where <i>R</i> is a particle–particle distance. We show that the CD spectra are much more sensitive to the geometry of a plasmonic complex compared to the extinction spectra. Small variations in geometry can result in large changes in CD responses. This study can be used to design nanostructures with strong CD for optical and sensor applications

Plasmonic Metamaterials and Nanocomposites with the Narrow Transparency Window Effect in Broad Extinction Spectra

We propose and describe plasmonic nanomaterials with unique optical properties. These nanostructured materials strongly attenuate light across a broad wavelength interval ranged from 400 nm to 5 μm but exhibit a narrow transparency window centered at a given wavelength. The main elements used in our systems are nanorods and nanocrosses of variable sizes. The nanomaterial can be designed as a solution, nanocomposite film or metastructure. The principle of the formation of the transparency window in the broad extinction spectrum is based on the narrow lines of longitudinal plasmons of single nanorods and nanorod complexes. To realize the spectrum with a transmission window, we design a nanocomposite material as a mixture of nanorods of different sizes. Simultaneously, we exclude nanorods of certain lengths from the nanorod ensemble. The width of the plasmonic transparency window is determined by the intrinsic and radiative broadenings of the nanocrystal plasmons. Nanocrystals can be randomly dispersed in a solution or arranged in metastructures. We show that interactions between nanocrystals in a dense ensemble can destroy the window effect and, simultaneously, we design the metastructure geometries with weak destructive interactions. We also describe the effect of narrowing of the transparency window with increasing the concentration of nanocrystals. Two well-established technologies can be used to fabricate such nano- and metamaterials, the colloidal synthesis, and lithography. Nanocomposites proposed here can be used as optical materials and smart coatings for shielding of electromagnetic radiation in a wide spectral interval with a simultaneous possibility of communication using a narrow transparency window

Fractal Nanoparticle Plasmonics: The Cayley Tree

There has been strong, ongoing interest over the past decade in developing strategies to design and engineer materials with tailored optical properties. Fractal-like nanoparticles and films have long been known to possess a remarkably broad-band optical response and are potential nanoscale components for realizing spectrum-spanning optical effects. Here we examine the role of self-similarity in a fractal geometry for the design of plasmon line shapes. By computing and fabricating simple Cayley tree nanostructures of increasing fractal order <i>N</i>, we are able to identify the principle behind how the multimodal plasmon spectrum of this system develops as the fractal order is increased. With increasing <i>N</i>, the fractal structure acquires an increasing number of modes with certain degeneracies: these modes correspond to plasmon oscillations on the different length scales inside a fractal. As a result, fractals with large <i>N</i> exhibit broad, multipeaked spectra from plasmons with large degeneracy numbers. The Cayley tree serves as an example of a more general, fractal-based route for the design of structures and media with highly complex optical line shapes

Mie Sensing with Neural Networks: Recognition of Nano-Object Parameters, the Invisibility Point, and Restricted Models

In this work, we use artificial neural networks (ANNs) to recognize the material composition, sizes of nanoparticles and their concentrations in different media with high accuracy, solely from the absorbance spectrum of a macroscopic sample. We construct ANNs operating in the following two schemes. The first scheme is designed to recognize the dimensions and refractive indices of dielectric scatterers in mixed ensembles. The second ANN model simultaneously recognizes the dimensions of gold nanospheres in a mixture and the refractive index of a matrix. A challenge in the first scheme arises at and near the invisibility point, i.e., when the refractive index of nanoparticles is close to that of the medium. Of course, particle recognition in this regime faces fundamental physical limitations. However, such recognition near the invisibility point is possible, and our study reveals its unique properties. Interestingly, the recognition process for the refractive index in the vicinity of the invisibility point shows very small errors. In contrast, the errors for the recognition of the radius grow strongly near this point. Another regime with limited recognition occurs when the extinction spectra are not unique and can correspond to different realizations of nanoparticle mixtures. Regarding multi-particle or polydisperse solutions, the ML-based models should in such cases be rationally restricted to maintain the feasibility of the recognition process. Overall, the recognition schemes proposed and investigated by us can find their applications in the field of sensing