Computing optical properties and photo-emission spectra : a new starting point
Calcul des proprietées optiques et des spectres de photo-émission : un nouveau point de départ
Résumé
When a material is irradiated by particles or light, it responds with the excitation of electrons and nuclei. Because of the Coulomb interaction, this gives rise to interesting many-body effects, that cannot be explained in a single-particle picture. In this thesis we are interested in their contribution to the electronic spectra. In particular we will be looking into excitonic effects. These phenomena are due to excitations that can be described as electron-hole pairs that interact.
The Bethe-Salpeter Equation (BSE) for the two-particle Green's function, in an approximation based on the GW approximation to the self-energy, is a well established approach for accounting for excitonic effects in theoretical spectroscopy. However, in its current formulation it is computationally heavy, as its starting point requires the knowledge of the interacting single particle Green's function. Moreover, the existing implementations give access to only the diagonal parts of the microscopic screening function $\varepsilon^{-1}(\mathbf{q},\omega)_{\mathbf{G},\mathbf{G}'}$ and Dynamic Structure Factor $S(\mathbf{q},\omega)_{\mathbf{G},\mathbf{G}'}$, both of which, in their full form, are dense matrices in reciprocal lattice vectors $\mathbf{G}$ and $\mathbf{G}'$. In inhomogeneous systems these off-diagonal elements can be important and, thus, it is highly desirable to be able to describe them.
In this work, on the one hand, we try to make the Bethe-Salpeter Equation approach more efficient. To this end we study the possibility of deriving alternative equations for the two-particle Green's function and modifying the standard Bethe-Salpeter Equation. In particular, we use the fact that the shifts of spectral weight induced by the GW correction to the single-particle energies and by the electron-hole interaction cancel at least partially. The idea is to incorporate these cancelation effects, and moreover to use insight from Time-dependent Density Functional Theory, to render our calculations lighter. Furthermore, based on detailed analysis and comparison of different approaches to theoretical spectroscopy we discuss the importance of various ingredients contained in them.
On the other hand we extend the Bethe-Salpeter Equation to the off-diagonal elements of the microscopic screening function and Dynamic Structure Factor. This allows us, first of all, to reproduce available Coherent Inelastic X-ray Scattering results and make theoretical prediction for new ones. Second, this gives us the possibility to calculate the induced charge distributions due to excitons when the material is subject to an external perturbation. And, third, we demonstrate the existence of exciton satellites, alongside the plasmon ones, in photo-emission spectra of wide gap insulators.
L’equation de Bethe-Salpeter (BSE) pour la fonction de Green a deux particules, basée sur l'approximation GW pour la self-énergie, est une approche bien établie, qui permet de prendre en compte les effets excitoniques en spectroscopie théorique. Néanmoins, dans sa formulation actuelle elle est d'une part lourde du point de vue calculatoire et présente, d'autre part, des annulations, qui ne sont pas prises en compte analytiquement.
Dans cette these, nous avons étudie, dans un premier temps, la possibilité de démontrer des equations alternatives pour la fonction de Green a deux particules et ainsi de modifier l'equation de Bethe-Salpeter, en particulier en utilisant des informations issues de la Théorie de la Fonctionnelle de la Densité Dépendante du Temps (TDDFT) dans l'Approximation de la Densité Locale Adiabatique (ADLDA). Nous avons aussi compare différentes approches anciennes et nouvelles a la spectroscopie théorique et discute l'importance des différents ingredients qu'elle contiennent.
Dans un second temps, nous avons étendu le formalisme existant afin de prendre en compte l'interaction des quasiparticules et des excitons dans la description ab-initio de la fonction spectrale qui décrit par exemple la photo-emission. Nous avons pu le faire grace a l'extension de l’equation de Bethe-Salpeter et cela nous a permis de reproduire les résultats expérimentaux de Coherent Inelastic X-ray Scattering (CIXS) et meme de prédire et de suggérer de nouvelles experiences. Finalement, nous avons pu mettre en evidence l’existence des satellites excitoniques, au cote des satellites plasmoniques dans les spectres de photo-emission d'isolants.