Challenges for first-principles methods in theoretical and computational physics : multiple excitations in many-electrons systems and the Aharonov-Bohm effect in carbon nanotubes

Abstract

The present thesis is divied in two parts. In the first part of the thesis we develop a theoretical method able to describe double excitations in absorption experiments. In particular a coherent approach to the description of double excitations in correlated materials is presented: we derive stringent mathematical conditions on the algebraical structure of the Bethe-Salpeter and TDDFT kernels that avoid the occurrence of spurious and non-physical excitations. We discuss how these conditions need to be respected at any level of approximation, including the commonly used local density and static screening approximations. We propose a correlated kernel for the BSE equation, and we illustrate several aspects of our approach with numerical calculations for model molecular systems.In the second part instead we describe the Aharono-Bohm effect in carbon nanotubes. The gap oscillations caused by a magnetic flux penetrating a carbon nanotube represent one of the most spectacular observation of the Aharonov–Bohm effect at the nano–scale. Our understanding of this effect is, however, based on the assumption that the electrons are stricktly confined on the tube surface, on trajectories that are not modifed by curvature effects. Using an ab–initio approach based on Density Functional Theory we show that this assumption fails at the nano–scale inducing important corrections to the physics of the Aharonov–Bohm effect. Curvature effects and electronic density spilled out of the nanotube surface are shown to break the periodicity of the gap oscillations and to induce a large metallic phase in the low flux regime of Multi-walled nanotubes. We predict the key phenomenological features of this anomalous Aharonov–Bohm effect in semiconductive and metallic tubes, also suggesting possible experiments to validate our results.