Renormalized Magic Angles in Twisted Asymmetric Graphene Bilayers

The process of stacking graphene multilayers with a small relative twist angle between each of the layers has been found to produce flat bands at a series of “magic angles.” A number of recent studies have investigated the effects that varying the number of layers or changing the stacking arrangement (AA/AB/ABC etc.) has on the values of the magic angles. Here, by contrast, we consider how magic angles and flat bands are affected when the Fermi velocity at the Dirac points at the corners of a moire Brillouin zone are different. This can occur through differing Fermi velocity renormalizations due to differing dielectrics near the two layers. Such models are also approximately realized in 4-layer structures where the twist angles are not all the same. We model each system using a low-energy theory based on a renormalized Bistritzer-MacDonald model that involves two different renormalized Fermi velocities. We find that our renormalized BM model supports significantly larger magic angles than the magic angles that are present in TBG.