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Damping, satellites and multiple excitations in oxides and nanostructures: efficient theoretical and numerical approaches towards a dynamical many-body theory

Abstract : My Ph.D. thesis is about the development of novel theoretical and numerical approaches for a comprehensive description of dielectric response in in ultra thin films. After an introductory part (chapters 1 to 5), I present investigations of electronic excitations in specific systems (SrTiO3 in chapter 6 and graphite-related systems in chapters 7 and 8). In the last two chapters I present a numerical development for the simulation of isolated nano films (chapter 9) and a formal derivation of a dynamical theory for 2-particle excitations (chapter 10). In chapter 6, I employ several theories and approximations to analyse the absorption spectra of bulk SrTiO3. The most remarkable result is the observation of an exceptionally sharp peak at 6.4 eV of excitonic origin, absent in actual measurements. Its sharpness is ascribed to peculiar dispersion properties of Ti 3eg states, while its absence in measured data is ascribed to the lack of dynamical coupling between excitations in state-of-the-art computational methods. In order to overcome this limitation, in chapter 10 I derive an approach to compute the 2-particle correlation function equivalent but alternative to the Bethe-Salpeter equation (BSE). This is inspired by the cumulant ansatz for the 1-particle Green’s function. In this framework, the 2-particle equation can be solved without altering its dependence on time variables. The resulting formula for the polarizability presents three corrective terms to the static BSE solution: The first is a weight renormalization, the second implies a shift of the BSE peaks and the third creates additional peaks at higher energy accounting for the coupling with other neutral excitations of the system (e.g. exciton-exciton or exciton-phonons). I also investigate the influence of the environment on the dielectric response of graphite-based materials. In chapter 7 I focus on the differences induced by the staking of graphene layers (AA, ABA and ABC), while in chapter 8 I focus on the evolution of spectral properties when passing from bulk graphite (inter-plane distance d0) to isolated graphene (d0 tending to infinite). In isolated films, optical spectra and loss function coincide. However the speed of convergence to the isolated spectrum depends on the quantity computed (absorption/loss function) and on the direction and the amplitude of the exchanged momentum q. The comparison of calculations in several configurations allows me to indicate which spectrum converges faster. Calculations in chapters 7 and 8 are done within the supercell approach, which actually increase enormously the computational workload of plane-wave based calculations. So in chapter 9 I make a thorough study of the Coulomb cutoff method, which permits calculations of isolated systems by artificially extinguishing all out of plane interactions. I implemented successfully the technique in the DP and EXC simulation codes, adding an analytical algorithm to treat the q=0 limit, and I apply it successfully to compute the loss function and the spectral function of isolated graphene sheets. Moreover, I thoroughly discuss some delicate analytical aspects, which make the method meaningful when sums over q-points are involved (like in the Dyson equation of the polarizability, or calculations of the self-energy) but ill-defined when specific values of q are required.
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Submitted on : Monday, October 15, 2018 - 5:10:36 PM
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Lorenzo Sponza. Damping, satellites and multiple excitations in oxides and nanostructures: efficient theoretical and numerical approaches towards a dynamical many-body theory. Materials Science [cond-mat.mtrl-sci]. Ecole Polytechnique (EDX), 2013. English. ⟨tel-01883527⟩

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