Towards an improved description of spectroscopies for materials with localized electrons : Effective potentials and interactions

Abstract : The aim of this thesis is to develop approximations to describe many-body effects in photoemission and optical properties of materials containing localized electrons. This is a tough problem. The full quantum-mechanical treatment is based on the solution of the Schrödinger equation for the many-body wavefunction, which is cumbersome and requires in practice some approximations. One simplified approach is given by Density Functional Theory (DFT) with the Kohn-Sham system of independent particles, but it is difficult to access properties other than the density and total energy. In this thesis we start from an in principle exact framework, the Green's functions. They are intermediate in complexity between DFT and the full wavefunction methods.For the removal or excitation of a localized electron one important point is to avoid self-interaction and self-screening. This is naturally achieved when one uses a generalized Coulomb interaction (Chap.3). Moreover, supposing that the localized electron has little overlap with the others, we can think that their interaction is classical. Then the main many-body effect is the reaction of the other electrons to the removal or excitation of the localized electron: this is screening of the hole or electron-hole pair by the other electrons. However, in many standard approximations in the Green's functions framework, such as GW or the cumulant expansion, screening appears in the linear response approximation. Instead, we can expect that the removal or excitation of a localized electron is a strong perturbation to the other electrons. Therefore, it could be that non-linear contributions to screening are important. How can we verify when this is true? And how can we include these effects? On the other hand, even in linear response one could do better than standard approximations, because the linear response screening itself is often calculated in the Random Phase Approximation (RPA). How much do things improve when one goes beyond the RPA but stays in linear response? We address these points in the thesis.Concerning the screening, in Chap.5 we first use a simple zero-dimensional model to study on one side, effects beyond the RPA within linear reponse and, on the other side, effects beyond linear response but staying within the RPA. Interestingly, we find that we have to treat both at the same time in order to find significant improvement. This means that we have to find promising ways to go beyond the RPA that are simple enough to allow us to go to the non-linear regime. Therefore we develop approximations based on perturbation theory and test some already existent ones in the model.Screening is expressed through the dielectric function, which gives us also directly absorption. This is another reason to study it. In order to be more realistic than the zero-dimensional model, in Chap.6 we study the dielectric function of a simple solid using localized Wannier functions. This allows us to highlight cancellations between self-energy and excitonic effects in the framework of Green's functions and from this derive a simple Kohn Sham exchange-correlation potential and kernel for Time-Dependent DFT (TDDFT).In Chap.7 we go back to the problem of non-linear screening and address the question: how can we make it appear explicitly in the full formulation? We show how to do this,and how to use the approximation of a localized electron in order to derive a cumulant Green's function beyond the standard linear response one. We propose two levels of approximations to evaluate the resulting expression in practice, and show some preliminary results. In both cases, TDDFT is used to describe screening.Since a combination of Green's functions and TDDFT seems to be a good strategy to simplify the many-body problem, Chap.8 contains some more considerations about possible combinations.
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Marilena Tzavala. Towards an improved description of spectroscopies for materials with localized electrons : Effective potentials and interactions. Strongly Correlated Electrons [cond-mat.str-el]. Université Paris-Saclay, 2017. English. ⟨NNT : 2017SACLX100⟩. ⟨tel-01691302⟩

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