Single particle and collective electronic excitations in topological insulator nano- wires

The thesis presents a theoretical study of the confinement effects on the electronic properties of three-dimensional topological insulators (TIs). The focus has been on nano-wires of the prototype compound Bi2Se3. By means of analytical and numerical approaches, starting from a bulk Hamiltonian based on a two-orbital model for the compound, analyzing not only single-electron but also collective electronic excitations such as Dirac magneto-plasmons.We find interesting features with varying the cross-section area, the electron surface density and the strength of an axial magnetic field. An original aspect has been the study of the role played by the Berry phase. It's role in the characterization of both spectral and electronic dielectric properties of TI nano-wires is discussed.