Ferromagnetism in ABC-trilayer graphene

Abstract

Graphene was first realized in its free form in 2004 by the physicists Andre Geim and Konstantin Novoselov. First believed to only exist as a theoretical system, this material has some very unique properties. It is a two dimensional material with an extremely high charge mobility. It turns out that stacking several layers of graphene on top of each other causes the properties of this material to change. This thesis focuses on the ferromagnetic properties of graphene. In the first few chapters, the derivations of the ferromagnetic properties of both monolayer and bilayer graphene will be treated extensively based on existing literature. The results that are presented in the literature will be reproduced by the use of numerical methods. Finally, based on this, a similar set of numerical calculations will be done for ABC-stacked trilayer graphene, which will result in a phase diagram in the electron-electron coupling versus doping plane. Finally, the effects of Coloumb screening will be investigated. Due to the "flatter" low energy bands of ABC-trilayer graphene, it will be shown that this material exhibits stronger ferromagnetism than that seen in monolayer, bilayer and ABA-trilayer graphene. This is experimentally very exciting due to the difficulty of producing graphene samples with very low doping, which makes it a big challenge to detect ferromagnetism in monolayer graphene, bilayer graphene and ABA-trilayer graphene which undergoes a phase transition to paramagnetism at relatively low levels of doping. The increased level of doping needed to make ABC-trilayer graphene paramagnetic makes its realization in the ferromagnetic phase more manageable.