Search

International audience; The dynamic structure factor of materials is proportional to their linear electronic response and it displays their excitation spectra. Usually the response is measured on the same length scale as the perturbation. Here we illustrate that much can be gained by studying also the mixed dynamic structure factor, which connects different spatial components of perturbation and response. We extend state-of-the-art ab initio calculations to access the mixed dynamic structure factor, including excitonic effects. Using bulk silicon and lithium fluoride as prototype examples, we show that these effects play a crucial role above and below the quasi-particle gap, and are needed in order to explain coherent inelastic x-ray scattering experiments. Our approach also yields important information concerning the microscopic structure of time-dependent density functional theory. One of the key concepts in condensed matter theory is screening, the modification of a potential felt by a charge due to the rearrangement of other charges [1]. In many cases the dominant contribution to this phenomenon can be described in linear response [2]. This means that the knowledge of the response of a system to an external perturbation is entirely contained in the density-density response function χ,which is determined only by the material.The poles of χ in frequency space are the excitation energies of the system. The density-density response function is measured directly or indirectly in many spectroscopy experiments [3], such as electron energy loss spectroscopy (EELS) [4], optical absorption [5, 6], or inelastic x-ray scattering (IXS) [7], which yields the dynamic structure factor (DSF) that is proportional to the imaginary part of χ. Knowing χ can also help to understand or predict effects such as a significant local rearrangement of charges as response of the system to a perturbation, which can have dramatic effects on the structure, for example self-trapped excitons [8]. Finally, screening is also one of the fundamental processes that govern the behavior of all many-body systems. Therefore it appears naturally as a building block in the formulation of many-body perturbation theory [9], via the screened Coulomb interaction W = v c + v c χv c , where v c is the bare Coulomb interaction. The widely-used GW approximation (GWA) [10], for example, uses W as effective interaction. Some important features of the frequency-dependent screening are captured for the homogeneous electron gas by the Lindhard dielectric function [11] from the random phase approximation (RPA) [12], where only the classical electrostatic potential between charges is taken into account. For small momentum transfer this is sufficient to describe the long-range collective oscillations of the electron gas, called plasmons, even for simple metals and semiconductors (see, e.g., [13-17]). However, in many other cases this approximation yields unsatisfactory results. Prominent examples are materials with localized d-or f-states [18-21], or loss spectra for larger momentum transfer [22-25], where a shorter length scale is probed. Moreover, the RPA cannot yield bound ex-citons [26], which are most clearly seen in optical spectra [27, 28]. Such many-body effects are instead captured by the Bethe-Salpeter equation (BSE) [29], a two-body Dyson equation that correlates the excited electrons and holes [26, 30]. This equation has been successfully used to calculate optical spectra in the framework of semi-empirical calculations since the eighties [31-34], and in first principles calculations since the nineties [35-38]. Loss spectra for vanishing momentum transfer have been looked at more recently [39-41], and a few calculations exist for loss spectra at non-vanishing momentum transfer [42-50]. Optics, EELS and IXS probe the response of the system on the same length scale as the perturbation. Besides the spectroscopic information, this allows one also to reconstruct charge excitations as an averaged function of space and time from experimental IXS spectra [51-55]. However, in an inhomogeneous material even a spatially monochromatic perturbation creates a response on different length scales [56, 57], depending on the local structure of the material. Only when all these components of the response are known can one describe induced charges with spatial resolution, and can one determine important many-body effects that depend on all the components of W. For these reasons, it is highly desirable to extend state-of-the-art advanced theoretical and numerical approaches to the description of the full inhomogeneous response of materials including excitonic effects. This gives access to the mixed DSF (MDSF), which is a matrix in reciprocal space whose diagonal is the ordinary DSF [7]. The MDSF can be measured by coherent IXS (CIXS) [7]. On the theory side, some off-diagonal elements of the MDSF in silicon were calculated in the adiabatic local density approximation (ALDA) of time-dependent den

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.

Combining nonresonant inelastic x-ray scattering experiments with state-of-the-art ab initio many-body calculations, we investigate the electronic screening mechanisms in strongly correlated CuO in a large range of energy and momentum transfers. The excellent agreement between theory and experiment, including the low-energy charge excitations, allows us to use the calculated dynamical screening as a safe building block for many-body perturbation theory and to elucidate the crucial role played by d-d excitations in renormalizing the band gap of CuO. In this way we can dissect the contributions of different excitations to the electronic self-energy which is illuminating concerning both the general theory and this prototypical material. Combining nonresonant inelastic x-ray scattering experiments with state-of-the-art ab initio many-body calculations, we investigate the electronic screening mechanisms in strongly correlated CuO in a large range of energy and momentum transfers. The excellent agreement between theory and experiment, including the low-energy charge excitations, allows us to use the calculated dynamical screening as a safe building block for many-body perturbation theory and to elucidate the crucial role played by d-d excitations in renormalizing the band gap of CuO. In this way we can dissect the contributions of different excitations to the electronic self-energy which is illuminating concerning both the general theory and this prototypical material. Combining nonresonant inelastic x-ray scattering experiments with state-of-the-art ab initio many-body calculations, we investigate the electronic screening mechanisms in strongly correlated CuO in a large range of energy and momentum transfers. The excellent agreement between theory and experiment, including the low-energy charge excitations, allows us to use the calculated dynamical screening as a safe building block for many-body perturbation theory and to elucidate the crucial role played by d-d excitations in renormalizing the band gap of CuO. In this way we can dissect the contributions of different excitations to the electronic self-energy which is illuminating concerning both the general theory and this prototypical material.

We present a screened exact-exchange (SXX) method for the efficient and accurate calculation of the optical properties of solids, where the screening is achieved through the zero-wave-vector limit of the inverse dielectric function. The SXX approach can be viewed as a simplification of the Bethe-Salpeter equation (BSE) or, in the context of time-dependent density-functional theory, as a first step towards a new class of hybrid functionals for the optical properties of solids. SXX performs well for bound excitons and continuum spectra in both small-gap semiconductors and large-gap insulators, with a computational cost much lower than that of the BSE.

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.

A large number of today's ab initio calculations, in particular in solid-state physics, are based on density-functional theory using first-principles pseudopotentials. This approach, initially developed for the ground state, is nowadays widely used as a starting point for the calculation of excited-state properties, as, for instance, those involved in optical spectroscopy. In this paper we investigate the validity and the accuracy of the pseudopotential approximation, analyzing how different choices within the latter can influence the calculated electronic response of silicon and silicon carbide. We consider norm-conserving first-principles pseudopotentials, both in the fully nonlocal (Kleinman-Bylander) and the semilocal forms, with different choices for the reference (local) component. The effects of the inclusion of outer-core states in the valence shell are analyzed in order to obtain a detailed comparison with all-electron calculations. We present accurate results for different pseudopotential descriptions of Kohn-Sham and quasiparticle band structures and of many spectroscopic quantities in the linear and the nonlinear response regimes for different momentum transfers $\mathbf{Q}$. Moreover, the effects of the pseudopotential nonlocality have been analyzed for electron-energy-loss spectra in the limit of vanishing momentum transfer. Our results show that the pseudopotential approximation can be quite safely applied to excited-state calculations, even when they involve Kohn-Sham eigenvalues and eigenvectors several tens of eV above the Fermi energy.

We present calculations of the absorption spectrum of semiconductors and insulators comparing various approaches: (i) the two-particle Bethe-Salpeter equation of many-body perturbation theory; (ii) time-dependent density-functional theory using a recently developed kernel that was derived from the Bethe-Salpeter equation; and (iii) a mapping scheme that we propose in the present work and that allows one to derive different parameter-free approximations to (ii). We show that all methods reproduce the series of bound excitons in the gap of solid argon, as well as continuum excitons in semiconductors. This is even true for the simplest static approximation, which allows us to reformulate the equations in a way such that the scaling of the calculations with the number of atoms equals the one of the random phase approximation.

We show the application of an efficient numerical scheme to obtain the independent-particle dynamic polarizability matrix chi((0))(r,r('),omega), a key quantity in modern ab initio excited-state calculations. The method has been applied to the study of the optical response of a realistic oxidized silicon surface, including the effects of crystal local fields. The latter are shown to substantially increase the surface optical anisotropy in the energy range below the bulk band gap. Our implementation in a large-scale ab initio computational code allows us to make a quantitative study of the CPU time scaling with respect to the system size, and demonstrates the real potential of the method for the study of excited states in large systems.

We consider two commonly used approaches for the ab initio calculation of optical-absorption spectra, namely, many-body perturbation theory based on Green's functions and time-dependent density-functional theory (TDDFT). The former leads to the two-particle Bethe-Salpeter equation that contains a screened electron-hole interaction. We approximate this interaction in various ways, and discuss in particular the results obtained for a local contact potential. This, in fact, allows us to straightforwardly make the link to the TDDFT approach, and to discuss the exchange-correlation kernel ${f}_{\mathrm{xc}}$ that corresponds to the contact exciton. Our main results, illustrated in the examples of bulk silicon, GaAs, argon, and LiF, are the following. (i) The simple contact exciton model, used on top of an ab initio calculated band structure, yields reasonable absorption spectra. (ii) Qualitatively extremely different ${f}_{\mathrm{xc}}$ can be derived approximatively from the same Bethe-Salpeter equation. These kernels can however yield very similar spectra. (iii) A static ${f}_{\mathrm{xc}},$ both with or without a long-range component, can create transitions in the quasiparticle gap. To the best of our knowledge, this is the first time that TDDFT has been shown to be able to reproduce bound excitons.