We analyze theoretically the effects of electron-phonon interaction in the dynamics of an electron that can be trapped to a localized state and detrapped to an extended band state of a small quantum dot (QD) using a simple model system. It consists of a one-dimensional tight-binding linear chain of a few sites, having a discrete set of energy levels mimicking the discrete levels of the conduction band of the QD that is connected at its end to another site, the trap, having a single energy level well below the conduction band, where the electron is allowed to interact with a local phonon of a single frequency. In spite of its simplicity, the time-dependent model has no analytical solution but a numerically exact one can be found, producing a rich dynamics. The electronic motion is quasiperiodic in time, with oscillations around a mean value that are basic characteristics of the weak and strong coupling regimes of electron-phonon interaction and set the timescales of the system. Using values of the parameters appropriate for defects in semiconductor QDs, we find these timescales to range typically from tenths of picoseconds to a few picoseconds. The values of the time-averaged trap occupancy strongly depend on the the strength of the electron-phonon interaction and can be as large as 40% when the coupling is most efficient, independently of other parameters. An interesting result of the present paper is the formation of resonances at specific values of the electron-phonon coupling parameter that only exist when several levels are allowed to coherently cooperate in the filling of the trap. They are characterized by a trap occupancy that is a periodic function of time with large amplitude and period picturing an electron that is periodically trapped and detrapped. We conclude that the formation of these resonances is a robust consequence of electron-phonon interaction in small systems. Electron-phonon interaction is an efficient mechanism that can provide ca. 50% filling of a deep trap state on a subpicosecond to picosecond timescale, much faster than radiative decay occurring in timescales of tens of picoseconds to nanoseconds, while the occupancy of this state will be smaller than ca. 1% in the absence of electron-phonon coupling.

Self-heating thermionic hollow cathodes are essential components in modern plasma thrusters. To fully understand their operation, three interdependent physical domains must be considered: plasma discharge physics, thermal response of the cathode structure, and chemical evolution of plasma exposed surfaces. In this work, we develop the first self-consistently coupled plasma–thermal–chemical simulation platform for hollow cathode operation using lanthanum hexaboride (LaB6) and Xe and study its performance against our experimentally determined temperature measurements. Results show that the customary assumptions of single-step resonant neutralization and full energy accommodation in ion-surface collisions fail to reproduce our empirical observations. We propose a two-step neutralization mechanism that consists of resonant neutralization to the first excited state of xenon followed by Auger de-excitation to the ground state, along with system specific accommodation factors. In this way, the agreement between the results of the simulations and experiments was achieved. These fundamental processes could govern neutralization in other cathode technologies where low work function emitters are employed and should therefore be accounted for in physical models. In addition, the new simulation platform allows us to better estimate the equilibrium work function of LaB6 hollow cathode emitters. In the cathode studied here, we found that the effective work function is 2.25 eV, which is significantly lower than previous estimates, and leads to better than expected cathode material performance with important implications for space missions.

ZnO has been known for a long time to be a highly efficient luminescent material. In the last few years, the experimental investigation of the luminescent properties of colloidal ZnO nanocrystals in the nanometer range of sizes has attracted a lot of interest for their potential applications in light-emitting diodes and other optical devices and in this work we approach the problem from a theoretical perspective. Here, we develop a simple theory for the green photoluminescence of ZnO quantum dots (QDs) that allows us to understand and rationalize several experimental findings on fundamental grounds. We study the spectrum of light emitted in the radiative recombination of a conduction band electron with a deeply trapped hole and find that the experimental behavior of this emission band with particle size can be understood in terms of quantum size effects of the electronic states and their overlap with the deep hole. We focus the comparison of our results on detailed experiments performed for colloidal ZnO nanoparticles in ethanol and find that the experimental evolution of the luminescent signal with particle size at room temperature can be better reproduced by assuming the deep hole to be localized near the surface of the nanoparticles. However, the experimental behavior of the intensity and the decay time of the signal with temperature can be rationalized in terms of holes predominantly trapped near the center of the nanoparticles at low temperatures being transferred to surface defects at room temperature. Furthermore, the calculated values of the radiative lifetimes are comparable to the experimental values of the decay time of the visible emission signal. We also study the visible emission band as a function of the number of electrons in the conduction band of the nanoparticle, finding a pronounced dependence of the radiative lifetime but a weak dependence of the energetic position of the maximum intensity.

Doped semiconductor quantum dots are a new class of plasmonic systems exhibiting infrared resonances. At ultralow concentrations of charge carriers that can be achieved by controlled doping, only few carriers occupy each quantum dot; therefore, a spectrum with well-defined atomic-like peaks is expected. Here we investigate theoretically how surface imperfections and inhomogeneities in shape and morphology (surface "roughness") always present in these nanocrystals, randomize their energy levels, and blur the atomic-like features. We assume a Gaussian distribution of each energy level and use their standard deviation σ as a measure of the nanocrystals' roughness. For nearly perfect nanospheres with small roughness (σ), the spectrum exhibits well-defined peaks. However, increasing roughness effectively randomizes the energy level distribution, and when σ approaches 15% of the nanoparticle's Fermi energy, any trace of an atomic-like structure is lost in the spectrum, and a continuous yet few-conduction-electron localized surface plasmon resonance emerges.

The study of time-dependent current fluctuations in nanoscale conductors is of great importance as it can provide informations on the interactions and quantum correlations between electrons [1]. While these studies have been traditionally restricted to the stationary regime, the advent of single-electron sources [2], has triggered a renewed interest in investigating the short-time behavior as well [3].

The detailed understanding of the physical parameters that determine Localized Surface Plasmon Resonances (LSPRs) is essential to develop new applications for plasmonics. A relatively new area of research has been opened by the identification of LSPRs in low carrier density systems obtained by doping semiconductor quantum dots. We investigate theoretically how diffuse surface scattering of electrons in combination with the effect of quantization due to size (QSE) impact the evolution of the LSPRs with the size of these nanosystems. Two key parameters are the length $R_0$ giving the strength of the QSE and the velocity $\beta_T$ of the electronic excitations entering in the length scale for diffuse surface scattering. While the QSE itself only produces a blueshift in energy of the LSPRs, the diffuse surface scattering mechanism gives to both energy and linewidth an oscillatory-damped behavior as a function of size, with characteristic lengths that depend on material parameters. Thus, the evolution of the LSPRs with size at the nanometer scale is very dependent on the relation of size to these lengths, which we illustrate with several examples. The variety of behaviors we find could be useful for designing plasmonic devices based on doped semiconductor nano structures having desired properties.

Localized surface plasmon resonances (LSPRs) have recently been identified in extremely diluted electron systems obtained by doping semiconductor quantum dots. Here, we investigate the role that different surface effects, namely, electronic spill-out and diffuse surface scattering, play in the optical properties of these ultralow electron density nanosystems. Diffuse scattering originates from imperfections or roughness at a microscopic scale on the surface. Using an electromagnetic theory that describes this mechanism in conjunction with a dielectric function including the quantum size effect, we find that the LSPRs show an oscillatory behavior in both position and width for large particles and a strong blue shift in energy and an increased width for smaller radii, consistent with recent experimental results for photodoped ZnO nanocrystals. We thus show that the commonly ignored process of diffuse surface scattering is a more important mechanism affecting the plasmonic properties of ultralow electron density nanoparticles than the spill-out effect.

We develop a theoretical approach to study the transient dynamics and the time-dependent statistics for the Anderson-Holstein model in the regime of strong electron-phonon coupling. For this purpose we adapt a recently introduced diagrammatic approach to the time domain. The generating function for the time-dependent charge transfer probabilities is evaluated numerically by discretizing the Keldysh contour. The method allows us to analyze the system evolution to the steady state after a sudden connection of the dot to the leads, starting from different initial conditions. Simple analytical results are obtained in the regime of very short times. We study in particular the apparent bistable behavior occurring for strong electron-phonon coupling, small bias voltages, and a detuned dot level. The results obtained are in remarkably good agreement with numerically exact results obtained by quantum Monte Carlo methods. We analyze the waiting time distribution and charge transfer probabilities, showing that only a single electron transfer is responsible for the rich structure found in the short-time regime. A universal scaling (independent of the model parameters) is found for the relative amplitude of the higher order current cumulants in the short-time regime, starting from an initially empty dot. We finally analyze the convergence to the steady state of the differential conductance and of the differential Fano factor at the inelastic threshold, which exhibits a peculiar oscillatory behavior.

Electron and energy transfer processes between an atom or molecule and a surface are extremely important for many applications in physics and chemistry. Therefore a profound understanding of these processes is essential in order to analyze a large variety of physical systems. The microscopic description of the two-electron Auger processes, leading to neutralization/ionization of an ion/neutral atom in front of a solid surface, has been a long-standing problem. It can be dated back to the 1950s when H.D. Hagstrum proposed to use the information contained in the spectrum of the electrons emitted during the neutralization of slow noble gas ions as a surface analytical tool complementing photoelectron spectroscopy. However, only recently a comprehensive description of the Auger neutralization mechanism has been achieved by the combined efforts of theoretical and experimental methods. In this article we review the theoretical models for this problem, stressing how their outcome compare with experimental results. We also analyze the inverse problem of Auger ionization. We emphasize the understanding of the key quantities governing the processes and outline the challenges remaining. This opens new perspectives for future developments of theoretical and experimental work in this field.

A theoretical approach for the non-equilibrium transport properties of nanoscale systems coupled to metallic electrodes with strong electron-phonon interactions is presented. It consists in a resummation of the dominant Feynman diagrams from the perturbative expansion in the coupling to the leads. We show that this scheme eliminates the main pathologies found in previous simple analytical approaches for the polaronic regime. The results for the spectral and transport properties are compared with those from several other approaches for a wide range of parameters. The method can be formulated in a simple way to obtain the full counting statistics. Results for the shot and thermal noise are presented.

Nanometer-sized metal particles exhibit broadening of the localized surface plasmon resonance (LSPR) in comparison to its value predicted by the classical Mie theory. Using our model for the LSPR dependence on non-local surface screening and size quantization, we quantitatively relate the observed plasmon width to the nanoparticle radius R and the permittivity of the surrounding medium ε(m). For Ag nanospheres larger than 8 nm only the non-local dynamical effects occurring at the surface are important and, up to a diameter of 25 nm, dominate over the bulk scattering mechanism. Qualitatively, the LSPR width is inversely proportional to the particle size and has a nonmonotonic dependence on the permittivity of the host medium, exhibiting for Ag a maximum at ε(m) ≈ 2.5. Our calculated LSPR width is compared with recent experimental data.

Charge exchange by Auger neutralization (AN) plays an important role in surface analysis techniques such as low energy ion scattering (LEIS). Recent advances in the theoretical description of AN have included a model based on a linear combination of atomic orbitals (LCAO) approach, which is able to calculate accurate neutralization probabilities of He+ due to AN in LEIS. Previous investigations have shown that the neutralization probability is strongly influenced by the distance dependent shift of the He 1s level. In this study simulations of He+ scattered from Cu(100) and Cu(110) surfaces at fixed azimuth angles are presented. Additionally, the azimuth dependence of ion- and neutral-yield for He+ scattered from Cu(100) is simulated and compared to experimental data. Calculations were performed using the LCAO model in combination with molecular dynamics simulations. The excellent agreement between simulation and experiment provides evidence that the obtained values for the level shift are a characteristic property of the surface.

We present a theoretical model for analyzing the size dependence of the surface plasmon resonance of metallic nanospheres in a range of sizes down to a single nanometer. Within this model, we explicitly show how different microscopic mechanisms, namely quantization due to size (quantum size effect (QSE)) and dynamical surface screening, affect the energy of the surface plasmon. We demonstrate that the latter mechanism, which can move the surface plasma energy both toward the red or the blue, can be comparable to or even stronger than QSE. Thus, depending on material parameters, QSE may only be observed for ultra-small metal nanoparticles much closer to 1 nm in size than to 10 nm. Results presented herein are in quantitative agreement with recent published experimental results for Ag and Au.

We develop a theoretical model of the surface plasmon resonance of metallic nanospheres in the size range down to the single nanometer size. Within this model we explicitly show how different microscopic mechanisms, namely quantization due to size (QSE) and electron spill-out, affect the energy of the surface plasmon. We demonstrate, that electron spill-out effects, which can move the surface plasma energy both toward the red or the blue, can be comparable to or even stronger than QSE. Thus, depending on circumstances, QSE may only be observed for ultrasmall metal nanoparticles much closer to 1 nm in size than to 10 nm. Results presented herein are in quantitative agreement with recent published experimental results for Ag and Au.

In this work we compare characteristics of Auger neutralization of [Formula: see text] ions at noble metal and free-electron metal surfaces. For noble metals, we find that the position of the energy level of He with respect to the Fermi level has a non-negligible influence on the values of the calculated Auger rates through the evaluation of the surface dielectric susceptibility. We conclude that even though our calculated rates are accurate, further theoretical effort is needed to obtain realistic values of the energy level of He in front of these surfaces.

In this work, a new theoretical approach to study the non-equilibrium transport properties of nanoscale systems coupled to metallic electrodes with strong electron-phonon interactions is presented. The proposed approach consists in a resummation of the dominant Feynman diagrams from the exact preturbative expansion. This scheme is compared with methods that can be found in the literature. It shows a good agreement with these methods in the range where they are known to provide good results, for a wide range of parameters. Also, it is compared with path-integral Monte Carlo calculations giving a relatively good agreement for polaronic and non polaronic regimes. Some preliminary results for the current noise obtained with our method are presented.

When low-energy He ions are scattered from a Ge surface, the fraction of positive ions exhibits characteristic oscillations as a function of ion energy. These oscillations are caused by quasi-resonant neutralization (qRN), a process which is active for materials with a narrow band nearly resonant with the unperturbed He 1s-level. In this paper we measure the fraction of He+ backscattered from Ge(100). In conjunction with recently developed theoretical methods, we extract quantitative information on the efficiency of qRN. Our evaluation reveals that qRN is a highly efficient process leading to ion fractions two orders of magnitude lower than in systems for which neutralization is only due to Auger processes.

We calculate the time-dependent nonequilibrium current through a single-level quantum dot strongly coupled to a vibrational mode. The nonequilibrium real-time dynamics caused by an instantaneous coupling of the leads to the quantum dot is discussed using an approximate method. The approach, which is specially designed for the strong polaronic regime, is based on the so-called polaron tunneling approximation. Considering different initial dot occupations, we show that a common steady state is reached after times much larger than the typical electron tunneling times due to a polaron blocking effect in the dot charge. A direct comparison is made with numerically exact data, showing good agreement for the time scales accessible by the diagrammatic Monte Carlo simulation method.

We report on the absorption of electromagnetic radiation by metallic nanoparticles in the radio and far infrared frequency range, and subsequent heating of nanoparticle solutions. A recent series of papers has measured considerable radio frequency (RF) heating of gold nanoparticle solutions. In this work, we show that claims of RF heating by metallic nanoparticles are not supported by theory. We analyze several mechanisms by which nonmagnetic metallic nanoparticles can absorb low frequency radiation, including both classical and quantum effects. We conclude that none of these absorption mechanisms, nor any combination of them, can increase temperatures at the rates recently reported. A recent experiment supports this finding.

In Low Energy Ion Scattering (LEIS), Auger-neutralization is an omnipresent charge exchange mechanism, especially when noble gas ions are used as projectiles, with a primary energy below the threshold energy, Eth, for collision induced charge exchange processes (neutralization and reionization). Recent experiments revealed a significant dependence of the ion survival probability, P+, on the crystal plane, when He+ ions are scattered from a metal surface. This is in contrast to the fact, that the neutralization probability in LEIS is usually assumed to be independent of the chemical environment of the collision partner (absence of matrix effects). In order to investigate this crystal effect, an existent theory on Auger-neutralization (based on a Linear Combination of Atomic Orbitals) is adapted to the LEIS geometry. With this model, Auger-neutralization rates are calculated for a Ag(1 1 0) surface. Trajectories for He particles scattered from this surface into different azimuth directions are obtained by means of Molecular Dynamics simulations. Subsequently, the ion survival probability is calculated and compared to measurements. Good agreement is obtained which gives confidence in the applicability of this model in the LEIS regime. Moreover, it was possible to obtain detailed information on the properties of the neutralization process.