Simulative Investigation on the Electronic, Vibrational and Optical Properties of the Ge2Sb2Te5 Chalcogenide

Chalcogenides are chemical compounds with at least one of the following three chemical elements: Sulfur (S), Selenium (Sn), and Tellurium (Te). As opposed to other materials, chalcogenide atomic arrangement can quickly and reversibly inter-change between crystalline, amorphous and liquid phases. Therefore they are also called phase change materials. As a results, chalcogenide thermal, optical, structural, electronic, electrical properties change pronouncedly and significantly with the phase they are in, leading to a host of different applications in different areas. The noticeable optical reflectivity difference between crystalline and amorphous phases has allowed optical storage devices to be made. Their very high thermal conductivity and heat fusion provided remarkable benefits in the frame of thermal energy storage for heating and cooling in residential and commercial buildings. The outstanding resistivity difference between crystalline and amorphous phases led to a significant improvement of solid state storage devices from the power consumption to the re-writability to say nothing of the shrinkability. This work focuses on a better understanding from a simulative stand point of the electronic, vibrational and optical properties for the crystalline phases (hexagonal and faced-centered cubic). The electronic properties are calculated implementing the density functional theory combined with pseudo-potentials, plane waves and the local density approximation. The phonon properties are computed using the density functional perturbation theory. The phonon dispersion and spectrum are calculated using the density functional perturbation theory. As it relates to the optical constants, the real part dielectric function is calculated through the Drude-Lorentz expression. The imaginary part results from the real part through the Kramers-Kronig transformation. The refractive index, the extinctive and absorption coefficients are analytically calculated from the dielectric function. The transmission and reflection coefficients are calculated using the Fresnel equations. All calculated optical constants compare well the experimental ones.

Resonances in the two centers Coulomb system

In this work we investigate the existence of resonances for two-centers Coulomb systems with arbitrary charges in two and three dimensions, defining them in terms of generalized complex eigenvalues of a non-selfadjoint deformation of the two-center Schrödinger operator. After giving a description of the bifurcation of the classical system for positive energies, we construct the resolvent kernel of the operators and we prove that they can be extended analytically to the second Riemann sheet. The resonances are then defined and studied with numerical methods and perturbation theory.

Quantum integrability as a new method for exact results on N=2 supersymmetric gauge theories and black holes

In this thesis I show a triple new connection we found between quantum integrability, N=2 supersymmetric gauge theories and black holes perturbation theory. I use the approach of the ODE/IM correspondence between Ordinary Differential Equations (ODE) and Integrable Models (IM), first to connect basic integrability functions - the Baxter’s Q, T and Y functions - to the gauge theory periods. This fundamental identification allows several new results for both theories, for example: an exact non linear integral equation (Thermodynamic Bethe Ansatz, TBA) for the gauge periods; an interpretation of the integrability functional relations as new exact R-symmetry relations for the periods; new formulas for the local integrals of motion in terms of gauge periods. This I develop in all details at least for the SU(2) gauge theory with Nf=0,1,2 matter flavours. Still through to the ODE/IM correspondence, I connect the mathematically precise definition of quasinormal modes of black holes (having an important role in gravitational waves’ obervations) with quantization conditions on the Q, Y functions. In this way I also give a mathematical explanation of the recently found connection between quasinormal modes and N=2 supersymmetric gauge theories. Moreover, it follows a new simple and effective method to numerically compute the quasinormal modes - the TBA - which I compare with other standard methods. The spacetimes for which I show these in all details are in the simplest Nf=0 case the D3 brane in the Nf=1,2 case a generalization of extremal Reissner-Nordström (charged) black holes. Then I begin treating also the Nf=3,4 theories and argue on how our integrability-gauge-gravity correspondence can generalize to other types of black holes in either asymptotically flat (Nf=3) or Anti-de-Sitter (Nf=4) spacetime. Finally I begin to show the extension to a 4-fold correspondence with also Conformal Field Theory (CFT), through the renowned AdS/CFT correspondence.

Excitonic properties of transition metal oxide perovskites and workflow automatization of GW schemes

The Many-Body-Perturbation Theory approach is among the most successful theoretical frameworks for the study of excited state properties. It allows to describe the excitonic interactions, which play a fundamental role in the optical response of insulators and semiconductors. The first part of the thesis focuses on the study of the quasiparticle, optical and excitonic properties of \textit{bulk} Transition Metal Oxide (TMO) perovskites using a G$_0$W$_0$+Bethe Salpeter Equation (BSE) approach. A representative set of 14 compounds has been selected, including 3d, 4d and 5d perovskites. An approximation of the BSE scheme, based on an analytic diagonal expression for the inverse dielectric function, is used to compute the exciton binding energies and is carefully bench-marked against the standard BSE results. In 2019 an important breakthrough has been achieved with the synthesis of ultrathin SrTiO3 films down to the monolayer limit. This allows us to explore how the quasiparticle and optical properties of SrTiO3 evolve from the bulk to the two-dimensional limit. The electronic structure is computed with G0W0 approach: we prove that the inclusion of the off-diagonal self-energy terms is required to avoid non-physical band dispersions. The excitonic properties are investigated beyond the optical limit at finite momenta. Lastly a study of the under pressure optical response of the topological nodal line semimetal ZrSiS is presented, in conjunction with the experimental results from the group of Prof. Dr. Kuntscher of the Augsburg University. The second part of the thesis discusses the implementation of a workflow to automate G$_0$W$_0$ and BSE calculations with the VASP software. The workflow adopts a convergence scheme based on an explicit basis-extrapolation approach [J. Klimeš \textit{et al.}, Phys. Rev.B 90, 075125 (2014)] which allows to reduce the number of intermediate calculations required to reach convergence and to explicit estimate the error associated to the basis-set truncation.