Electronic properties of low-angle twisted bilayer graphene

This dissertation investigates the electronic properties of twisted bilayer graphene, built, as its name suggests, by stacking two sheets of graphene and twisting them with respect to each other. Theoretical studies identified a series of twist angles at which the material displays unusual properties, namely strongly correlated electrons. These special angles are called magic angles, with the first being around 1.1° and the rest being smaller. Experimentally, the existence of the first magic angle was demonstrated by identifying Mott insulating and superconducting phases resulting from the highly correlated electronic states at this particular angle. The subsequent question one may ask is whether the higher order magic angles, predicted theoretically, do in fact exist in practice. In the scope of this master thesis, an attempt to clarify this question is made using the tight binding approximation. The electronic problem of twisted bilayer graphene is thus numerically simulated at tiny twists. However, in order to make the system as realistic as possible, atomic relaxation is taken into account. Relaxation is significant below the first magic angle, which substantially alters the electronic structure and is thus relevant in the quest for secondary magic angles. The tight binding simulation of the system requires solving a computationally expensive problem. This challenge is faced by using a recursive Green function algorithm. The outcome of the simulations provides evidence that the second magic angle, in spite of existing for ideal systems, is suppressed when structural relaxation is taken into account. This conclusion has deep repercussions as it argues that apart from the first one, no other magic angle exists in practice, which calls for experimental verification.