Systèmes auxiliaires pour les observables : approximation du connecteur dynamique locale pour les spectres d'addition et d'émission d'électrons

Abstract : This thesis proposes an innovative theoretical method for studying one-electron excitation spectra, as measured in photoemission and inverse photoemission spectroscopy.The current state-of-the-art realistic calculations rely usually on many-body Green’s functions and complex, non-local self energies, evaluated specifically for each material. Even when the calculated spectra are in very good agreement with experiments, the computational cost is very large. The reason is that the method itself is not efficient, as it yields much superfluous information that is not needed for the interpretation of experimental data.In this thesis we propose two shortcuts to the standard method. The first one is the introduction of an auxiliary system that exactly targets, in principle, the excitation spectrum of the real system. The prototypical example is density functional theory, in which the auxiliary system is the Kohn-Sham system: it exactly reproduces the density of the real system via a real and static potential, the Kohn-Sham potential. Density functional theory is, however, a ground state theory, which hardly yields excited state properties: an example is the famous band-gap problem. The potential we propose (the spectral potential), local and frequency-dependent, yet real, can be viewed as a dynamical generalisation of the Kohn-Sham potential which yields in principle the exact spectrum.The second shortcut is the idea of calculating this potential just once and forever in a model system, the homogeneous electron gas, and tabulating it. To study real materials, we design a connector which prescribes the use of the gas results for calculating electronic spectra.The first part of the thesis deals with the idea of auxiliary systems, showing the general framework in which they can be introduced and the equations they have to fulfill. We then use exactly-solvable Hubbard models to gain insight into the role of the spectral potential; in particular, it is shown that a meaningful potential can be defined wherever the spectrum is non-zero, and that it always yields the expected spectra, even when the imaginary or the non-local parts of the self energy play a prominent role.In the second part of the thesis, we focus on calculations for real systems. We first evaluate the spectral potential in the homogeneous electron gas, and then import it in the auxiliary system to evaluate the excitation spectrum. All the non-trivial interplay between electron interaction and inhomogeneity of the real system enters the form of the connector. Finding an expression for it is the real challenge of the procedure. We propose a reasonable approximation for it, based on local properties of the system, which we call dynamical local connector approximation.We implement this procedure for four different prototypical materials: sodium, an almost homogeneous metal; aluminum, still a metal but less homogeneous; silicon, a semiconductor; argon, an inhomogeneous insulator. The spectra we obtain with our approach agree to an impressive extent with the ones evaluated via the computationally expensive self energy, demonstrating the potential of this theory.
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Marco Vanzini. Systèmes auxiliaires pour les observables : approximation du connecteur dynamique locale pour les spectres d'addition et d'émission d'électrons. Matière Condensée [cond-mat]. Université Paris-Saclay, 2018. Français. ⟨NNT : 2018SACLX012⟩. ⟨tel-01803435⟩

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