Aleksander Hinz

• This study aims to analyze the electrical conductivity properties and thermopower of monolayer and bilayer graphene. After an experimental and theoretical introduction to the effect of thermopower in graphene, we aim to explain the divergence between experiment and theory for thermopower in bilayer graphene in the first part of this work. Several approaches are presented; an extended Mott normalism, diagrammatic calculations in the linear response framework and Boltzmann equation calculations. A comparison of these approaches is provided. These approaches take into account both the diffusion of the electrons as well as electron phonon interaction with a particular focus on the phonon drag component. Within these calculations the detailed analysis of the phonon bath turns out to be of key importance. Therefore, the contribution of phonon-phonon interaction, phonon-boundary interaction and phonon-impurity interaction is examined in detail. Furthermore, the results are compared to competing theories such as the balance equations theory, as well as to other systems, and finally to experimental results. In the second part the quantum corrections to the conductivity and the thermopower in monolayer graphene are studied numerically and analytically. First, we use the recursive Green’s function method to numerically calculate the conductivity and the thermopower of graphene. For conductivity, we obtain changes between weak antilocalization to weak localization as a function of the system’s parameters, namely the correlation strength of the impurities, the width and concentration of the impurities and the Fermi energy of the system. In addition, we find an increase of the quantum correction to the thermopower, and thereby magneto thermopower, which depends on the same parameters weak localization corrections to the conductivity. We analytically reproduce the known results for the conductivity, linking them to the same parameters that we tuned in the numerical calculation.