New development in twisted bilayer graphene

Abstract
Narrow-band systems are a natural platform where exotic physics can emerge. Twisted bilayer graphene (tBLG) is a paradigmatic example. For this system, extremely narrow bands appear at low energies for small “magic” twist angles between the two graphene layers. In the narrow-band regime, superconductivity and correlated insulating phases were observed experimentally. These phases are not yet fully understood. Incommensurability effects are often neglected in theoretical studies of tBLG. However, our numerical results suggest that these are of crucial importance in the narrow-band regime, giving rise to sub-ballistic states. In this talk, I will review some of the most important results on tBLG and present our results on incommensurability effects in the narrow-band regime.