The influence of morphology and long range interactions in the electronic properties of graphene

Abstract

This thesis is concerned with the physics of graphene, a novel two dimensional material with unique properties that has generated an inmense amount of activity in the last years. The interest in this material relies on a number of features that make it the ideal playground to study some fundamental physics issues, as well as a viable candidate for potential applications. This work has addressed two problems of great interest in the physics of this material: the influence of morphology on its electronic properties and the effects of long range interactions.

In the first part of the thesis the effects of topological defects and smooth curvature have been analyzed. A Hubbard model on the dislocated lattice is presented to account correctly for the magnetic properties, and a continuum model based on the Dirac equation in curved space is employed to describe smooth corrugations.

In the second part, the effects of long range interactions are addressed. Unscreened Coulomb impurities are shown to have characteristic signatures in the spectral properties through a SCBA numerical computation. Finally, the effects of electron-electron interactions on observable quantities are evaluated through a renormalized field theory.