Incommensurate transitions and disorder in twisted bilayer graphene
Twisted bilayer graphene near the magic-angle has attracted a considerable amount of attention following the recent discovery of correlated insulating phases and superconductivity. Currently, the main source of disorder in experimental samples appears to come from a non-uniform twist angle across the system. Motivated by this, we construct local, microscopic lattice models that capture the low energy description of twisted bilayer graphene but are able to keep the twist angle as a tunable parameter. This allows us to study the effects of incommensurate twist angles on the low energy eigenstates in twisted bilayer graphene. We demonstrate that at the magic-angle, the system undergoes a single-particle, incommensurate transition where the wavefunctions delocalize in momentum space, concomitant with the onset of a finite density of states at the Dirac node energy. Using these microscopic models of twisted bilayer graphene we study the effects of disorder in the twist angle. Our results show that this qualitatively new type of disorder has a very weak effect on the renormalized Fermi velocity but systematically broadens the minibandwidth and smears out the otherwise sharp van Hove peaks.