Dissertation Committee Chair: Victor Galitski
Committee:
Mohammad Hafezi
Christopher Jarzynski
Kartik Srinivasan
Alexey Gorshkov
Abstract: In general wave-functions spread and propagate. However, there are certain situations where they cease to do so. Those situations are equivalently interpreted as frozen or localized quantum particles. In the context of condensed matter physics, this localization---the vanishing of the group velocity for a large class of states---is related to the appearance of flat bands in the band structure of a quantum system. The flat bands are important occurrences for multiple reasons. One of them is that on a flat band the kinematics of a system is non-existent and therefore the physics is completely governed by the interaction terms which are responsible for many exotic states of matter. Therefore, one expects that a flat band is a bedrock for finding exotic states. The appearance of flat bands is also, at times, a puzzling phenomenon. For example, the recurrent flat bands in twisted bilayer graphene for different twist angles are not yet completely understood, even at the single particle level, and they are surprising enough that the angles at which they appear are called “magic” angles. Here, the field theoretic approach to these interesting phenomena is presented.