Crystal Local-field Effects Research Articles

Second-Order Nonlinear Optical Responses of AlN Two-Dimensional Monolayer: A Real-Time First-Principles Study.

Two-dimensional materials have recently attracted attention due to their unique physical properties and promising applications. This work reports the electronic, linear and second-order nonlinear optical properties of aluminum nitride (AlN) monolayer by using a real-time first-principles approach based on Green's function theory. In this approach, quasi-particle corrections, crystal local field effects, and excitonic contributions are considered for investigating the linear and nonlinear responses. As a two-dimensional material with a wide direct gap of around 6.45 eV, the AlN monolayer exhibits strong resonances of absorption and second-harmonic spectra in the ultraviolet range. In the transparent spectral range from blue to deep ultraviolet (2.8-5.3 eV), strong peaks of second-order nonlinear susceptibility appear in the AlN monolayer with a large peak value of around 430 pm/V, which is one or two orders-of-magnitude larger than the nonlinear materials used in the ultraviolet range. The results presented in this work will find important applications for nonlinear imaging, spectroscopy, and nonlinear nanophotonics in the ultraviolet range.

Investigation of the Optical and Excitonic Properties of the Visible Light-Driven Photocatalytic BiVO4 Material

An investigation of the optical and excitonic properties of photocatalytic compounds based on both experimental and theoretical approaches is proposed. More specifically, this paper reports, for the first time, the local-field, optical anisotropy, and excitonic effects in BiVO4, an active photocatalytic material in the visible range. The analyses are based on electron energy-loss spectroscopy measurements, ground-state density functional theory calculations, including crystal local-field effects, and many-body corrections using the Bethe-Salpeter equation. These results are supported by a comparison with two materials, namely, TiO2 anatase and rutile, which are well-known to differ in their photocatalytic properties, those being important and negligible, respectively. The analogies found for these two categories of compounds allow the proposal of criteria that appear to be essential for producing an optimal photocatalytic material.

Electron-hole interactions in correlated electron materials: Optical properties of vanadium dioxide from first principles

Correlated materials have been studied extensively using photoemission spectroscopy. Their optical properties are instead much less explored. Here we present calculations of the optical absorption spectrum of vanadium dioxide $({\mathrm{VO}}_{2})$ in the framework of the Bethe-Salpeter equation (BSE) of many-body perturbation theory. In order to deal with localized electrons we go beyond the standard BSE implementation and extend it to correlated insulators. We show that it is not enough to describe the spectra on the basis of independent electron-hole pairs, even when the electron and hole are separately well described by state-of-the-art one-body Green's functions. Crystal local-field effects are crucial to explain the experimental findings, even qualitatively, and excitonic effects strongly modify the spectra, especially at their onset. In this context, as highighted by the analysis of the BSE results, the quasi-one-dimensional nature of the vanadium-dimer chains plays a prominent role.

High-energy collective electronic excitations in layered transition-metal dichalcogenides

We characterize experimentally and theoretically the collective electronic excitations in two prototypical layered transition-metal dichalcogenides, NbSe2 and Cu0.2NbS2. The energy- and momentum-dependent dynamical structure factor was measured by inelastic x-ray scattering (IXS) spectroscopy and simulated by time-dependent density-functional theory. We find good agreement between theory and experiment, provided that Nb semicore states are taken into account together with crystal local-field effects. Both materials have very similar spectra, characterized by two main plasmons at 9 and 23 eV, which we show to both have pi + sigma character on the basis of a detailed analysis of the band structure. Finally, we discuss the role of the layer anisotropy in the dispersion of these plasmons.

High-energy collective electronic excitations in free-standing single-layer graphene

In this joint experimental and theoretical work, we investigate collective electronic excitations (plasmons) in free-standing, single-layer graphene. The energy- and momentum-dependent electron energy-loss function was measured up to $50\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ along two independent in-plane symmetry directions ($\ensuremath{\Gamma}M$ and $\ensuremath{\Gamma}K$) over the first Brillouin zone by momentum-resolved electron energy-loss spectroscopy in a transmission electron microscope. We compare our experimental results with corresponding time-dependent density-functional theory calculations. For finite momentum transfers, good agreement with experiments is found if crystal local-field effects are taken into account. In the limit of small and vanishing momentum transfers, we discuss differences between calculations and the experimentally obtained electron energy-loss functions of graphene due to a finite momentum resolution and out-of-plane excitations.

Low-energy excitations in strongly correlated materials: A theoretical and experimental study of the dynamic structure factor in V2O3

This work contains an experimental and theoretical study of the dynamic structure factor at large momentum transfer $|Q|\ensuremath{\sim}4$ \AA{}${}^{\ensuremath{-}1}$ of the strongly correlated transition-metal oxide V${}_{2}$O${}_{3}$. We focus in particular on the transitions between $d$ states that give rise to the spectra below 6 eV. We show that the main peak in this energy range is mainly due to ${t}_{2g}\ensuremath{\rightarrow}{e}_{g}^{\ensuremath{\sigma}}$ transitions, and that it carries a signature of the phase transition between the paramagnetic insulator and the paramagnetic metal that can already be understood from the joint density of states calculated at the level of the static local density approximation. Instead, in order to obtain theoretical spectra that are overall similar to the measured ones, we have to go beyond the static approximation and include at least crystal local field effects. The latter turn out to be crucial in order to eliminate a spurious peak and hence allow a safe comparison between theory and experiment, including an analysis of the strong anisotropy of the spectra.

Plasmon dispersion in molecular solids: Picene and potassium-doped picene

We investigate the dynamic response of pristine and potassium-doped picene, the first example of a new family of organic molecular superconductors, by combining first-principles calculations and state-of-the-art experimental tools. We find that charge-carrier plasmons in K${}_{3}$ picene have a negative or almost negligible dispersion, which deviates from the traditional picture of metals based on the homogeneous electron gas. We show how this finding is the result of the competition between metallicity and electronic localization on the molecular units. Conduction electrons alone give rise to the negative dispersion, which is reduced by molecular polarization and crystal local-field effects. This analysis allows us to obtain a general picture of the plasmon dispersion in metallic molecular crystals.

Linear density response function in the projector augmented wave method: Applications to solids, surfaces, and interfaces

We present an implementation of the linear density response function within the projector-augmented wave (PAW) method with applications to the linear optical and dielectric properties of both solids, surfaces, and interfaces. The response function is represented in plane waves while the single-particle eigenstates can be expanded on a real space grid or in atomic orbital basis for increased efficiency. The exchange-correlation kernel is treated at the level of the adiabatic local density approximation (ALDA) and crystal local field effects are included. The calculated static and dynamical dielectric functions of Si, C, SiC, AlP and GaAs compare well with previous calculations. While optical properties of semiconductors, in particular excitonic effects, are generally not well described by ALDA, we obtain excellent agreement with experiments for the surface loss function of the Mg(0001) surface with plasmon energies deviating by less than 0.2 eV. Finally, we apply the method to study the influence of substrates on the plasmon excitations in graphene. On SiC(0001), the long wavelength $\pi$ plasmons are significantly damped although their energies remain almost unaltered. On Al(111) the $\pi$ plasmon is completely quenched due to the coupling to the metal surface plasmon.

Ab initiocalculation of many-body effects on the second-harmonic generation spectra of hexagonal SiC polytypes

We investigate the influence of crystal local fields and excitonic effects on the spectrum of the second harmonic generation of three polytypes of silicon carbide by using time-dependent density-functional theory including many-body effects, namely, quasiparticle corrections through the scissors operator, crystal local field effects, and excitonic interaction. The relation between the scalar density response and the components of the rank 3 tensor ${d}^{(2)}$ is established by calculating the response along different polarization directions. We find that local-field effects, although necessary for a rigorous description in the theory, yield only small contributions to the spectra, whereas excitonic effects have a strong influence on the second harmonic generation. We compare static values of the second harmonic coefficients to recent measurements and obtain very good agreement.

Ab initiosecond-order nonlinear optics in solids: Second-harmonic generation spectroscopy from time-dependent density-functional theory

We present in detail the formulation of the ab initio theory we have developed for the calculation of the macroscopic second-order susceptibility ${\ensuremath{\chi}}^{(2)}$. We find a general expression for ${\ensuremath{\chi}}^{(2)}$ valid for any fields, containing the ab initio relation between the microscopic and macroscopic formulation of the second-order responses. We consider the long-wavelength limit and we develop our theory in the time-dependent density-functional theory framework. This allows us to include straightforwardly many-body effects such as crystal local-field and excitonic effects. We compute the second-harmonic generation spectra for the cubic semiconductors SiC, AlAs, and GaAs and starting from the independent-particle approximation for ${\ensuremath{\chi}}^{(2)}$, we include quasiparticle effects via the scissors operator, crystal local-field, and excitonic effects. In particular, we consider two different types of kernels: the adiabatic local-density approximation and the ``long-range'' kernel. We find good agreement with other theoretical calculations and experiments presented in literature, showing the importance of very accurate description of the many-body interactions.

Dynamic structure factor and dielectric function of silicon for finite momentum transfer: Inelastic x-ray scattering experiments andab initiocalculations

We present a detailed investigation of the dynamic structure factor $S(\mathbf{Q},\ensuremath{\omega})$ as well as of the dielectric function ${\ensuremath{\epsilon}}_{\text{M}}(\mathbf{Q},\ensuremath{\omega})$ of the prototypical semiconductor silicon for finite momentum transfer, combining inelastic x-ray scattering measurements and ab initio calculations. We show that, in contrast to optical spectra, for finite momentum transfer, time-dependent density-functional theory in adiabatic local-density approximation (TDLDA) together with the inclusion of lifetime effects in a modified independent-particle polarizability ${\ensuremath{\chi}}^{0,\text{LT}}$ describes the physics of valence excitations with high precision. This applies to the dynamic structure factor as well as to the dielectric function, which demonstrates that TDLDA contains the short-range many-body effects that are crucial for a correct description of ${\ensuremath{\epsilon}}_{\text{M}}(\mathbf{Q},\ensuremath{\omega})$ in silicon at finite momentum transfer. The form of a nonlocal and energy-dependent exchange-correlation kernel is presented which provides the inclusion of the lifetime effects using the true independent-particle polarizability ${\ensuremath{\chi}}^{0}$. The description of the silicon ${L}_{2,3}$ absorption edge has been possible by including the outer core electrons $2s$ and $2p$ in the valence electrons of the pseudopotential. The energy of the edge is underestimated but a scissor shift of the respective states by the self-energy correction for these states yields good agreement with experiment. Short-range crystal local-field effects and exchange-correlation effects become important with increasing momentum transfer. The inclusion of crystal local-field effects in the random-phase approximation is able to describe the anisotropy of the response well. Our results demonstrate the quantitative predictive power of the first-principles description.

Inelastic X-ray scattering and first-principles study of electron excitations in MgB 2

An experimental and theoretical study of electronic excitations in MgB 2 covering the domain of large energy and momentum transfers is reported. Energy-loss spectra for several values of momentum transfers were measured in a polycrystalline sample by means of inelastic X-ray scattering spectroscopy. Ab initio calculations of the dielectric function as well as the energy-loss function were performed in the frame of the time-dependent local density approximation with inclusion of crystal local-field effects. We obtained very good agreement between the experimental and the theoretical energy dispersion of the peak maximum of the loss function. We found that crystal local-field effects are responsible for this agreement at large momenta. Fine structure observed in the measured spectra was interpreted in terms of strong interband transitions predicted by the calculations in the Γ A and Γ K directions. The theoretical dispersion of these features is in good accordance with the experimental data. Further spectral features in the measured spectra due to Mg 2s and 2p core electron excitations are also discussed.

Anomalous Angular Dependence of the Dynamic Structure Factor near Bragg Reflections: Graphite

The electron energy-loss function of graphite is studied for momentum transfers q beyond the first Brillouin zone. We find that near Bragg reflections the spectra can change drastically for very small variations in q. The effect is investigated by means of first principle calculations in the random phase approximation and confirmed by inelastic x-ray scattering measurements of the dynamic structure factor S(q, omega). We demonstrate that this effect is governed by crystal local field effects and the stacking of graphite. It is traced back to a strong coupling between excitations at small and large momentum transfers.

Energy loss spectra of lithium under pressure

According to the nearly free-electron-like approximation, electrons in alkaline metals are expected to be delocalized under pressure. However, recent theoretical and experimental results strikingly indicate the opposite behavior. For example, under pressure electronic band structure flattens anisotropically and increases the covalent character of alkaline metals, which induces the observed complexities in these systems. Specially considering that even at ambient pressure the observed anomalous features in the loss spectra of lithium cannot be explained within the nearly free-electron-like model, these additional anomalies under pressure are also expected to strongly modify its dynamic electronic response function. In this paper, we present ab initio calculations of the energy-loss spectra of lithium up to 40 GPa. Besides analyzing the dispersion of the new type of plasmons arising in lithium under pressure, the role of band structure versus crystal local field effects and exchange correlation has also been investigated.

Signatures of Short-Range Many-Body Effects in the Dielectric Function of Silicon for Finite Momentum Transfer

We present an investigation of the dynamic structure factor and of the dielectric function epsilonM(Q,omega) of the prototypical semiconductor silicon for finite momentum transfer, combining inelastic x-ray scattering experiments and ab initio calculations. In contrast with optical spectra, for finite momentum transfer time-dependent density-functional theory in the adiabatic local-density approximation together with lifetime broadening describes the physics of valence excitations correctly. Major structures in the spectra, governed by short-range crystal and exchange-correlation local-field effects, are strongly influenced by a mixing of transitions of positive and negative energies, in striking difference to spectra for vanishing momentum transfer. This mixing gives rise to a pronounced Fano asymmetry.

Low-Energy Charge-Density Excitations inMgB2: Striking Interplay between Single-Particle and Collective Behavior for Large Momenta

A sharp feature in the charge-density excitation spectra of single-crystal MgB2, displaying a remarkable cosinelike, periodic energy dispersion with momentum transfer (q) along the c* axis, has been observed for the first time by high-resolution nonresonant inelastic x-ray scattering (NIXS). Time-dependent density-functional theory calculations show that the physics underlying the NIXS data is strong coupling between single-particle and collective degrees of freedom, mediated by large crystal local-field effects. As a result, the small-q collective mode residing in the single-particle excitation gap of the B pi bands reappears periodically in higher Brillouin zones. The NIXS data thus embody a novel signature of the layered electronic structure of MgB2.

Large crystal local-field effects in the dynamical structure factor of rutileTiO2

We present ab initio time-dependent density-functional calculations and nonresonant inelastic x-ray scattering measurements of the dynamical structure factor of rutile ${\mathrm{TiO}}_{2}$. Our calculations are in good agreement with experiment and prove the presence of large crystal local-field effects below the Ti $M$ edge, which yield a sharp loss peak at 14 eV whose intensity features a remarkable nonmonotonic dependence on the wave vector. These effects, which impact the excitation spectra in the oxide more dramatically than in transition metals, provide a signature of the underlying electronic structure.

Band Structure versus Dynamical Exchange-Correlation Effects in Surface Plasmon Energy and Damping: A First-Principles Calculation

A first-principles parameter-free calculation that includes full three-dimensional band structure and dynamical exchange correlations is reported for the dynamical surface response and surface plasmon (SP) on a simple metal prototype surface Mg(0001). We demonstrate that band structure effects have a more profound impact on the SP characteristics than dynamical exchange correlations. A comparison with jellium and one-dimensional potential evaluations shows that the band structure is of paramount importance for the correct description of the SP linewidth and also leads to a better description of the SP energy dispersion. The inclusion of the exchange-correlation kernel results in a better agreement with experimental data. We show that lateral crystal local field effects have a negligible impact on the SP properties. Significant anisotropy is predicted for the SP linewidth.

Ab initioand semiempirical dielectric response of superlattices

We present a study of the dielectric response of ${(\mathrm{Ga}\mathrm{As})}_{p}∕{(\mathrm{Al}\mathrm{As})}_{p}$ (001) superlattices in a wide range of barrier and well widths. We applied density functional theory and a semiempirical method to obtain the superlattice band structures. These were then used as a starting point to evaluate the optical spectra and macroscopic dielectric constants using time-dependent density functional theory. In this context, we investigated the role of crystal local field effects in determining the anisotropy of the dielectric constants. Furthermore, we calculated absorption spectra including the strong continuum excitonic effect through the use of an appropriate model exchange-correlation kernel. We analyzed in detail the complementarity of the ab initio and semiempirical approaches and we compared the successes and limitations of the different approximation schemes.

Ab initiostudy of the optical absorption and wave-vector-dependent dielectric response of graphite

We performed ab initio calculations of the optical absorption spectrum and the wave-vector-dependent dielectric and energy-loss functions of graphite in the framework of the random-phase approximation. In the absorption spectrum, the most prominent peaks were analyzed in terms of interband transitions from specific regions of the Brillouin zone. The inclusion of the crystal local-field effects (LFE) in the response had an important influence on the absorption spectrum for light polarization parallel to the $\mathbf{c}$ axis. The calculated electron energy-loss spectra, even without LFE, were in very good agreement with existing momentum-dependent energy-loss experiments concerning the peak positions of the two valence-electron plasmons. Important aspects of the line shape and anisotropy of the energy-loss function at large momentum transfer $q$ were also well described: the splitting of the total $(\ensuremath{\pi}+\ensuremath{\sigma})$ plasmon and the appearance of peaks originating from interband transitions. Finally, the role of the interlayer interaction was studied, in particular with regard to its effect on the absorption spectrum for light polarization parallel to $\mathbf{c}$, and to the position of the higher-frequency $\ensuremath{\pi}+\ensuremath{\sigma}$ plasmon.