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International audience; We perform a systematic study of the macroscopic dielectric function and electron energy loss (EEL) spectra for graphite. We obtain the dispersion behavior for the π plasmon, as a function of the momentum transfer q for two nonequivalent paths that traverse the first four Brillouin zones. We carry out these calculations within both time-dependent density functional theory (with two exchange-correlation functionals) and the Bethe-Salpeter equation. Additionally, we explore the effects of using the complete excitonic Hamiltonian (with all electron-hole pairs and antipairs), and within the Tamm-Dancoff approximation (neglecting antipairs). By analyzing the behavior of the macroscopic dielectric function, we are able to determine which peaks are predominantly from plasmonic behavior or only interband transitions. We compare the calculated spectra against several experiments that span almost five decades; our results present clear trends that follow the physical origins of the observed peaks. We carry out this study over a large range of momentum transfer in order to better evaluate the different theoretical methods compared to experiment, and predict the plasmonic behavior beyond available experimental data. Our results indicate that including the complete Hamiltonian with the exciton coupling included is essential for accurately describing the observed EEL spectra and plasmon dispersion of graphite, particularly for low values of momentum transfer. However, the solution of the Bethe-Salpeter equation is computationally intensive, so time-dependent density functional theory methods used in conjunction with the complete Hamiltonian may be an attractive alternative.

We conduct a theoretical and numerical study on the second-harmonic (SH) optical response of a nano-structured metamaterial composed of a periodic array of inclusions. Both the inclusions and their surrounding matrix are made of centrosymmetrical materials, for which SH is strongly suppressed, but by appropriately choosing the shape of the inclusions, we may produce a geometrically non-centrosymmetric system which does allow efficient SH generation. Variations in the geometrical configuration allows tuning the linear and quadratic spectra of the optical response of the system. We develop an efficient scheme for calculating the nonlinear polarization, extending a formalism for the calculation of the macroscopic dielectric function using Haydock's recursion method. We apply the formalism developed here to an array of holes within an Ag matrix, but it can be readily applied to any metamaterial made of arbitrary materials and for inclusions of any geometry within the long-wavelength regime., Comment: 16 pages, 7 figures

We present a theoretical study of spin-velocity injection (SVI) of a pure spin current (PSC) induced by a linearly polarized light that impinges normally on the surface of two 50\% hydrogenated noncentrosymmetric two-dimensional (2D) graphene structures. The first structure, hydrogenated at only one side, labeled Up, also known as graphone, and the second, labelled Alt, is 25\% hydrogenated at both sides. The hydrogenation opens an energy gap in both structures. We analyze two possibilities: in the first, the spin is fixed along a chosen direction, and the resulting SVI is calculated; in the second, we choose the SVI direction along the surface plane, and calculate the resulting spin orientation. This is done by changing the energy $\hbar\omega$ and polarization angle $\alpha$ of the incoming light. The results are calculated within a full electronic band structure scheme using the Density Functional Theory (DFT) in the Local Density Approximation (LDA). The maxima of the spin-velocities are reached when $\hbar\omega=0.084$\,eV and $\alpha=35^\circ$ for the Up structure, and $\hbar\omega=0.720$\,eV and $\alpha=150^\circ$ for the Alt geometry. We find a speed of 668\,Km/s and 645\,Km/s for the Up and the Alt structures, respectively, when the spin points perpendicularly to the surface. Also, the response is maximized by fixing the spin-velocity direction along a high symmetry axis, obtaining a speed of 688Km/s with the spin pointing at $13^\circ$ from the surface normal, for the Up, and 906 Km/s and the spin pointing at $60^\circ$ from the surface normal, for the Alt system. These speed values are of order of magnitude larger than those of bulk semiconductors, such as CdSe and GaAs, thus making the hydrogenated graphene structures excellent candidates for spintronics applications., Comment: 22 pages, 10 figures, submitted to Physical Review B

We present the three-layer model to calculate the surface second-harmonic generation (SSHG) yield. This model considers that the surface is represented by three regions or layers. The first layer is the vacuum region with a dielectric function ${\ensuremath{\epsilon}}_{v}(\ensuremath{\omega})=1$ from where the fundamental electric field impinges on the material. The second layer is a thin layer $(\ensuremath{\ell})$ of thickness $d$ characterized by a dielectric function ${\ensuremath{\epsilon}}_{\ensuremath{\ell}}(\ensuremath{\omega})$, and it is in this layer where the SSHG takes place. The third layer is the bulk region denoted by $b$ and characterized by ${\ensuremath{\epsilon}}_{b}(\ensuremath{\omega})$. Both the vacuum and bulk layers are semi-infinite. The model includes the multiple reflections of both the fundamental and the second-harmonic (SH) fields that take place at the thin layer $\ensuremath{\ell}$. We obtain explicit expressions for the SSHG yield for the commonly used $s$ and $p$ polarizations of the incoming $1\ensuremath{\omega}$ and outgoing $2\ensuremath{\omega}$ electric fields, where no assumptions for the symmetry of the surface are made. These symmetry assumptions ultimately determine which components of the surface nonlinear second-order susceptibility tensor $\mathbf{\ensuremath{\chi}}(\ensuremath{-}2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega})$ are different from zero, and thus contribute to the SSHG yield. Then, we particularize the results for the most commonly investigated surfaces, the (001), (110), and (111) crystallographic faces, taking their symmetries into account. We use the three-layer model and compare it against the experimental results of a Si(111)$(1\ifmmode\times\else\texttimes\fi{}1)$:H surface, as a test case, and use it to predict the SSHG yield of a Si(001)$(2\ifmmode\times\else\texttimes\fi{}1)$ surface.

Two-dimensional transition-metal dichalcogenide materials have recently attracted great attention from the scientific community due to their interesting properties such as the presence of an energy band gap and the support of spin-polarized states. In particular, monolayer molybdenum disulfide has a structure with no inversion symmetry and, thus, presents a large spin-splitting of the top valence bands. This latter fact makes it favorable for studies of optical spin injection, a phenomenon that, under incidence of circularly polarized light, creates spin-polarized electrons in the conduction bands. Here, we perform a theoretical study of the one-photon optical spin and current injection on transition-metal dichalcogenide monolayers of molybdenum disulfide. In particular, we present calculations for spectra of the degree of spin polarization, which are calculated in a full-band structure scheme employing density functional theory; besides the so-called quasiparticle GW approximation is applied for the calculation of the band gap energy correction. Our results show 100% of spin polarization of the electrons for the one monolayer structure at the K valley. The degree of spin polarization also presents a net maximum value at the direct energy band gap at K as the number of monolayers increases.

We formulate a theoretical approach of surface second-harmonic generation from semiconductor surfaces based on the length gauge and the electron density operator. Within the independent particle approximation, the nonlinear second-order surface susceptibility tensor ${\ensuremath{\chi}}^{\mathrm{a}\mathrm{b}\mathrm{c}}(\ensuremath{-}2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega})$ is calculated, including in one unique formulation (i) the scissors correction, needed to have the correct value of the energy band gap, (ii) the contribution of the nonlocal part of the pseudopotentials, routinely used in ab initio band-structure calculations, and (iii) the derivation for the inclusion of the cut function, used to extract the surface response. The first two contributions are described by spatially nonlocal quantum-mechanical operators and are fully taken into account in the present formulation. As a test case of the approach, we calculate ${\ensuremath{\chi}}^{xxx}(\ensuremath{-}2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega})$ for the clean $\mathrm{Si}(001)2\ifmmode\times\else\texttimes\fi{}1$ reconstructed surface. The effects of the scissors correction and of the nonlocal part of the pseudopotentials are discussed in surface nonlinear optics. The scissors correction shifts the spectrum to higher energies though the shifting is not rigid and mixes the $1\ensuremath{\omega}$ and $2\ensuremath{\omega}$ resonances, and has a strong influence in the line shape. The effects of the nonlocal part of the pseudopotentials keeps the same line shape of $|{\ensuremath{\chi}}_{2\ifmmode\times\else\texttimes\fi{}1}^{xxx}(\ensuremath{-}2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega})|$, but reduces its value by 15%--20%. Therefore the inclusion of the three aforementioned contributions is very important and makes our scheme unprecedented and opens the possibility to study surface second-harmonic generation with more versatility and providing more accurate results.

We present a theoretical study of the optical generation of one-photon spin and current injection onto In-adsorbed Si(111) surfaces with $4\ifmmode\times\else\texttimes\fi{}2$ and $8\ifmmode\times\else\texttimes\fi{}2$ reconstructions. The spin injection, under incidence of circularly polarized light into nonmagnetic semiconductors, creates spin-polarized electrons in the conduction bands. The current injection is a nonlinear second-order effect that is allowed in materials without inversion symmetry. In bulk centrosymmetric crystals, the optical injection of current can only be observed at the surface wherein the inversion of symmetry might be broken. We report calculations for the degree of spin polarization and current-injection spectra which are calculated in a full electronic band structure scheme at the level of GW scissor-energy correction. Our results show an anisotropic behavior of the spin- and current-injection optical response. We obtain maximum percentages of the degree of spin polarization of 30% and 35% for the $4\ifmmode\times\else\texttimes\fi{}2$ and $8\ifmmode\times\else\texttimes\fi{}2$ surface reconstructions, respectively. It is also possible to optically generate injection current coming mainly from the first two top layers on both In-adsorbed surface reconstructions.

We present ab initio calculations to investigate second harmonic generation (SHG) response of single wall zigzag pristine boron-nitride nanotubes (BNNTs) and BNNTs modified by the molecular hydrogen adsorption. Calculations have been performed using density functional theory (DFT) within the local-density approximation (LDA) together with the GW Green function method to determine the band gap. A length gauge approach has been used to calculate the nonlinear optical response with the scissors correction to obtain the nonlinear susceptibility ${\ensuremath{\chi}}^{zzz}(\ensuremath{-}2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega})$ of the zigzag BNNTs. We have found that, contrary to reports in the literature, the (5,0) and (9,0) BNNTs have a nonvanishing SHG response. We have also found that SHG intensity decreases with the increase of the molecular hydrogen coverage.

Many ab initio calculations, in particular in solid state physics, rely on the antiresonant approximation. In this paper we discuss the derivation, the validity, and the accuracy of this approximation, analyzing how the optical properties of several bulk semiconducting materials and surfaces can be affected. We present accurate results for different spectroscopic quantities in the linear and nonlinear responses and we analyze the discrepancies between approximated and exact formulas. An investigation is made of the effect of the approximation on absorption spectra for different materials, showing the reliability of the approximation even in the presence of local field and excitonic effects. The energy loss is shown to be drastically affected. The effect of the band gap of materials on the quality of the approximation is also discussed. Finally, we report on the influence of the antiresonant approximation on second harmonic generation spectra.

We calculate the nonlinear dipole and quadrupole moments induced at the second-harmonic (SH) frequency $2\ensuremath{\omega}$ in a small dielectric sphere by an inhomogeneous monochromatic electric field of frequency $\ensuremath{\omega}.$ We neglect finite-size effects and assume that the selvedge region of the sphere is thin enough so that the surface may be considered locally flat. The second-order dipole displays resonances corresponding to the excitation of dipolar and quadrupolar plasmons at $\ensuremath{\omega}$ and a dipolar plasmon at $2\ensuremath{\omega},$ besides the resonances in the nonlinear surface response parameters a, b, and f. The second-order quadrupole, on the other hand, has resonances corresponding to those of a, b, and f, and to the excitation of dipolar surface plasmons at $\ensuremath{\omega}$ only. Depending on the relation between the size of the sphere and the spatial scale of variation of the field, the SH radiation may be dominated by either dipolar or quadrupolar scattering, with a crossover region. As an application, we calculate the SH scattering of a Si sphere lying at various distances above a dielectric substrate.

In order to study the effects of disorder in surface second-harmonic generation (SHG), we perform a numerical simulation on an infinite one-dimensional array of polarizable entities embedded in a homogeneous host. The position of each entity within the unit cell is generated by using two different types of disorder algorithms, and periodic boundary conditions are applied to generate an infinite chain. The contribution of the coherent and the incoherent radiation to the SHG radiated efficiency is calculated including the dipolar and quadrupolar interaction among the polarizable units in a self-consistent treatment, and within the long-wavelength approximation. The induced linear and nonlinear dipolar and quadrupolar moments on each entity are calculated by solving a set of linear algebraic equations. We consider that the entities are identical to each other and that each responds to the local field and to the gradient of the local field, like an isotropic harmonic oscillator.

We develop a model for sum and difference frequency generation (SFG/DFG) at the interface of an isotropic centrosymmetric nonsimple metal covered by a noncentrosymmetric adsorbate. We separate the nonlinear response of the surface into a free-electron contribution that characterizes the intraband transitions, a bound-electron contribution that characterizes the interband transitions, and a cross term due to the interaction among free and bound electrons. For the former we introduce an adjustable parameter consistent with semi-infinite jellium calculations, whereas for the others we apply a screened dipollium model that gives the nonlinear response in terms of the bound- and free-electron contributions to the substrate's bulk dielectric function. The nonlinear response of the adsorbate is described through the Raman and IR response of its stretch mode. We calculate SFG/DFG spectra for a ${\mathrm{CN}}^{\ensuremath{-}}$ covered Au-electrolyte interface choosing the direction of the dipole moment of the adsorbate either toward or away from the surface. The interference between the substrate's and overlayer's responses allows the extraction of orientational information from a comparison of our model calculations to recently obtained experimental spectra.

(Received 30 November 2011; revised manuscript received 31 January 2012; published 14 March 2012)We use a very efficient recursive method to calculate the effective optical response of materials made up ofarbitrarily shaped dielectric inclusions arranged in periodic 2D arrays within a metal matrix with a lattice constantmuch smaller than the wavelength of the incident light, so that we may neglect retardation. The starting point ofthe calculation is a digitized image of the system. The geometrical shape of the inclusions and their orientation inthe2Darrayinduceabirefringentopticalresponseofthewholemetamaterialthatcanbetailoredtospecificneeds.DOI: 10.1103/PhysRevB.85.125418 PACS number(s): 78

We present a study of optical coherent control of injection currents at surfaces of cubic semiconductors, predicting that this new optical effect will serve as a surface-sensitive probe of fundamentally and technologically important crystals with both bulk inversion symmetry (such as cubic diamond $\overline{6}m2$ or $\overline{6}$) and noncentrosymmetric systems (such as zinc-blende symmetry $\overline{4}\overline{3}m$). In crystals with any of these symmetries, this effect vanishes in the bulk, but it is allowed in surface regions due to the breaking of the bulk symmetry there. We present the results of ab initio calculations for injected currents at prototypical clean and Sb-covered GaAs(110)($1\ifmmode\times\else\texttimes\fi{}1$) and clean Si(111)($2\ifmmode\times\else\texttimes\fi{}1$) surfaces, which have well-understood and experimentally reproducible reconstructions. The effects are shown to be essentially sensitive to surface structure, and the injected currents can be interpreted in terms of the surface electronic structure. Calculated magnitudes indicate that the currents should be easily observable, and the calculated spectra of all of the surfaces demonstrate interesting behavior as a function of the energy of the incident light. Finally, layer-by-layer analysis provide detailed access to the surface properties through explicit separation of the contributions coming from different layers.

Recent observation of efficient light emission from porous silicon has attracted much attention and renewed interests in the study of nonlinear optical properties of nanometer-sized quantum systems. In this paper, we study the third-order nonlinear optical susceptibility of semiconductor quantum wires. The quantum wires are taken to be circular columns with a cross section size of \ensuremath{\sim}1 nm. The excitonic effects are taken to be the major electronic excitations. We find that the quantum confinement of the excitons greatly enhances the third-order optical nonlinear susceptibility in a quantum wire. The source of the enhancement is primarily the confinement-induced localization of excitons. The large enhancement of the third-order optical nonlinearity estimated here is consistent with the recent observation of the efficient infrared-up-conversion luminescence in porous silicon.

A model for second-harmonic generation from materials with inversion symmetry is developed. The reflecting medium is treated as an ordered array of localized, polarizable entities and the self-consistent relations between induced multipole moments and local fields are derived. The resulting equations are evaluated for a simple model of an entity's response, yielding microscopic estimates of both surface and bulk susceptibility components. The difficulties of applying the model to describe real materials are discussed.

A full band-structure ab initio calculation of the degree of spin polarization (DSP) in stressed bulk Si and bulk GaAs is reported. For Si, we found that compressive stress causes the DSP signal peak to decrease slightly in magnitude and to shift to higher energies.

Calculations of the second-harmonic susceptibility tensor ${\ensuremath{\chi}}^{abc}(\ensuremath{-}2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega})$ are presented for bulk semiconductors within both the $\mathbf{v}\ensuremath{\cdot}\mathbf{A}$ and the $\mathbf{r}\ensuremath{\cdot}\mathbf{E}$ gauges. The description of the semiconductor states incorporates the ``scissors'' Hamiltonian commonly used to obtain the correct band gap. The nonlocality of the scissors correction leads to terms in ${\ensuremath{\chi}}^{abc}(\ensuremath{-}2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega})$ not considered before within a sum-over-states approach to the $\mathbf{v}\ensuremath{\cdot}\mathbf{A}$ gauge. Using this expression, we show that the results of the two gauges give the same result for ${\ensuremath{\chi}}^{abc}(\ensuremath{-}2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega})$, within very good numerical accuracy. As part of the derivation, we clarify the well-known result for the linear optical response which states that the scissors correction rigidly shifts the spectrum along the energy axis, keeping the line-shape intact. The calculation is presented for GaAs using an all-electron scheme and a pseudopotential scheme.

We use a homogenization procedure for Maxwell’s equations in order to obtain in the local limit the frequency-dependent macroscopic dielectric-response tensor ij of metamaterials made of a matrix with inclusions of any geometrical shape repeated periodically with any lattice structure. We illustrate the formalism calculating ij for several structures. For dielectric rectangular inclusions within a conducting material we obtain an anisotropic response that may change from conductorlike at low to dielectriclike with resonances at large , attaining a very small reflectance at intermediate frequencies which can be tuned through geometrical tailoring. A simple explanation allowed us to predict and confirm similar behavior for other shapes, even isotropic, close to the percolation threshold.

Dans ces systemes il peut y avoir plus d'un mode collectif associe a une transition inter-sous-bande unique si les deux sous-bandes impliquees sont partiellement occupees. On calcule leur dispersion et leur force de signal

We present a study of optical electron spin-injection (optical orientation) in the bulk semiconductors GaAs, Si, and CdSe from direct optical excitation with circularly polarized light. For GaAs and Si, we compare pseudopotential calculations with calculations of a recent full-zone $\mathbf{k}∙\mathbf{p}$ model. For GaAs, we find that there can be up to 30% spin-injection at energies well above the band gap. For Si, which has very weak spin-orbit coupling, we find that there can be up to 30% spin polarization from direct transitions. The relatively low symmetry of wurtzite CdSe leads to an orientation dependent spin-injection, which can be up to 100% polarized at the band edge. For each of these systems, full-zone calculations are made, which allow us to consider excitation well above the band gap. An adaptive Brillouin zone sampling scheme is used, which allows us to obtain rapid convergence of our spectra. A derivation of the spin-injection rate, which accounts for the coherences excited in a semiconductor with spin-split bands, is also included.

We calculate the reflectance anisotropy and the reflectance-difference spectra for a clean Si(100) surface and two hydrogen- (H-) covered Si(100) surfaces. The clean surface is a $2\ifmmode\times\else\texttimes\fi{}1$ surface reconstruction, characterized by a tilted dimer formed between the two topmost Si atoms. One of the H-covered surfaces is a monohydride surface in which the two dangling bonds of the dimer are H saturated to give a flat dimer, and the other surface is a dihydride surface in which the H saturates each of the two dangling bonds leading to a bulk ideally terminated surface. The optical response is calculated with a pseudopotential framework using the local-density-plus-scissors approximation. A ``layer-by-layer'' analysis of the response is implemented with the pseudopotential calculation.

We directly compare experimental second-harmonic generation (SHG) spectra and reflectance-anisotropy spectra (RAS) of native-oxidized vicinal Si(001) interfaces with off-cut angles $\ensuremath{\zeta}=0\ifmmode^\circ\else\textdegree\fi{}$, 4\ifmmode^\circ\else\textdegree\fi{}, 6\ifmmode^\circ\else\textdegree\fi{}, 8\ifmmode^\circ\else\textdegree\fi{}, and 10\ifmmode^\circ\else\textdegree\fi{} from (001) toward [110]. We fit the measured azimuthal rotational-dependence of $p$-in/$p$-out SHG at two-photon energies $2.8\phantom{\rule{0.3em}{0ex}}\mathrm{eV}l\ensuremath{\hbar}\ensuremath{\omega}l3.5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ including the ${E}_{1}$ critical point resonance using a simplified bond hyperpolarizability model. The model includes dipolar contributions from tetrahedrally coordinated interfacial bonds as well as quadrupolar contributions from the Si bulk. The fit yields complex axial hyperpolarizability spectra ${\ensuremath{\beta}}_{\ensuremath{\Vert},\ensuremath{\Vert},\ensuremath{\Vert}}(2\ensuremath{\omega})$ and averaged bond angles of the interfacial back-edge, terrace-edge and step-edge bonds, and bulk quadrupolar hyperpolarizability ${\ensuremath{\delta}}_{\ensuremath{\Vert},\ensuremath{\Vert},\ensuremath{\Vert}}(2\ensuremath{\omega})$. The fitted microscopic model accurately reproduces measured $s$-in/$p$-out SHG spectra. We then used a Miller's rule approximation to generate axial linear polarizability spectra ${\ensuremath{\alpha}}_{\ensuremath{\Vert}}(\ensuremath{\omega})$ from the fitted ${\ensuremath{\beta}}_{\ensuremath{\Vert},\ensuremath{\Vert},\ensuremath{\Vert}}(2\ensuremath{\omega})$. The measured RAS was satisfactorily reproduced within the same photon energy range. Including the bulk quadrupole contribution to SHG was crucial to accurately retrieving the RAS and to achieving fitted real and imaginary $\ensuremath{\beta}(2\ensuremath{\omega})$ spectra consistent with a nonlinear Kramers-Kronig relation. The results demonstrate the possibility of formulating a common microscopic model of SHG and RAS responses of complicated interfaces.

We calculate the optical second harmonic (SH) radiation generated by small spheres made up of a homogeneous centrosymmetric material illuminated by inhomogeneous transverse and/or longitudinal electromagnetic fields. We obtain expressions for the hyperpolarizabilities of the particles in terms of the multipolar bulk susceptibilities and dipolar surface susceptibilities of their constitutive material. We employ the resulting response functions to obtain the nonlinear susceptibilities of a composite medium made up of an array of such particles and to calculate the radiation patterns and the efficiency of SH generation from the bulk and the edge of thin composite films illuminated by finite beams. Each sphere has comparable dipolar and quadrupolar contributions to the nonlinear radiation, and the composite has comparable bulk and edge contributions which interfere among themselves yielding nontrivial radiation and polarization patterns. We present numerical results for Si spheres and we compare our results with recent experiments.

We propose a method to obtain the layer-resolved contributions to the reflectance anisotropy signal of semiconductor surfaces which are modeled using the slab approach. Following this method, a microscopic formulation based on the semiempirical tight-binding approach is used to calculate the reflectance anisotropy of two InP(001) surface structures possibly relevant to standard gas-phase epitaxy conditions. It is shown that (i) the elimination of the anisotropy signal from the bottom layers of the slab is essential to correctly compare with the experiment and (ii) the strong low-energy anisotropy characteristic for gas-phase-grown InP surfaces arises from the uppermost atomic layers.

We present a simple model for surface disordering and study its consequences on reflectance anisotropy spectroscopy (RAS). Large unit cells are taken as a basis to introduce disorder by means of displacing the atoms from their equilibrium positions. Different displacement schemes are employed and ensemble averages are calculated in order to study the influence on the optical response. For reasons of computing time the semiempirical tight binding approach with an ${\mathrm{sp}}^{3}{s}^{*}$ basis is used to calculate the microscopic dielectric response of the surface, through which RAS is obtained. The well studied clean GaAs(110)(1\ifmmode\times\else\texttimes\fi{}1) surface is used as an example. We find that the spectral RAS structures of GaAs(110)(1\ifmmode\times\else\texttimes\fi{}1) follow a well defined behavior as a function of disorder and that a rather small number of surface atoms are needed only at equilibrium positions to produce already the RAS signal specific for the fully ordered surface reconstruction. This is a consequence of nearest neighbor interactions dominating the polarizability response and explains the fast dynamic response of RAS as compared to the diffraction methods which are limited by their large coherence length (low energy and reflection high energy electron diffraction).

Comparing calculations of the second-harmonic generation (SHG) from the monohydride-terminated Si(111)(1 A— 1)H surface with experimental spectra covering the two-photon energy range from 2.4 eV to 5.0 eV, we present a quantitative test of available state-of-the-art theory of surface SHG from a well-characterized semiconductor surface. We conclude that the density-functional theory within the local-density approximation approach with quasiparticle corrections leads to a semiquantitative agreement between theory and experiment and that the SHG arises from transition across bulk states which are perturbed by the surface. The calculations show that the spectra are sensitive to relaxations of the second-layer Si atoms.

We present a microscopic, first-principles calculation of the second-harmonic spectra of clean and Hydrogenated Si(100) surfaces. The differences between theoretical spectra obtained for different reconstructions, namely the 2×1 and the c(4×2) ones, are dramatically enhanced with respect to those obtained in linear optical response. The calculated spectral features are analyzed in detail, studying their relations with those of bulk and surface linear optical spectra. The inclusion of quasiparticle effects within the scissors operator approximation yields theoretical spectra in good agreement with the experiments.