Properties of quasi particles on two dimensional materials and related structures

Abstract

In this thesis, we use analytical techniques to study properties of two dimensional systems for which the carriers can be described as quasi particles. In the first part, we consider confinement of quasi electrons on AA-stacked bilayer graphene quantum dots. In order to describe this confinment, an appropriate boundary condition is derived. Then, we use this condition for the calculation of the energy levels of the quantum dot with and without an external applied perpendicular magnetic field. Finally, we compare our analytical result with numerical tight-binding calculations. Our results show that due to the nature of the boundary conditions there is intrisic symmetry in the system related with the Dirac K and K 0 states. Also, we see that the dependence of the energy levels on the radius of the system is inversely proportinal to the radius, which is a direct consequence of the Dirac nature of electrons in AA-stacked bilayers. Motivated by recent experimental observations, in the second part we investigate properties of acoustic plasmons. Plasmons are quasi particles describing a collective modes of electrons in the presence of an external electric field. Here, we consider a 2D electron liquid for which plasmon modes can be achieved in the presence of a top gate. Using a semiclassical approach we calculate the plasmon dispersion with many-body corrections beyond Random Phase Approximation. Another important result is the calculation of the damping of acoustic plasmon modes identifying the crossover between the collisionless and hydrodynamic regime. Finally, we calculate the coupling to a near-field probe. This allow the identification of how efficiently observe these modes experimentaly. In the last part, we extend the results obtained in the second part by adding an external perpendicular magnetic field to the structure. The presence of the field generates hybridization of the plasmon modes, known as Bernstein modes. Finally, we show thate electron-electron interactions have fundamental role in the observation of these hybrid modes.