For the past decade, graphene has been among the most heavily researched materials in condensed matter physics. In particular, its unusual electronic properties have spurred researchers to investigate new applications and theoretical insights. In this thesis, we focus on a system consisting of two sheets of graphene at a relative twist angle. The physics of this system has proved surprisingly rich and non-trivial. We summarize the current state of theoretical work on this system and extend this theory to cover a new twist angle regime, finding an exotic flat band state in the process. Finally, we investigate the possiblity of Peierls-like transitions in all regimes.
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MATIN Development Team