Landau level splitting in rotationally faulted multilayer graphene

We show that valley degeneracy in rotationally faulted multilayer graphene may be broken in the presence of a magnetic field and interlayer commensurations. This happens due to a simultaneous breaking of both time-reversal and inversion symmetries leading to a splitting of Landau levels linear in the field. Our theoretical work is motivated by an experiment [Y. J. Song et al., Nature (London) 467, 185 (2010), 10.1038/nature09330] on epitaxially grown multilayer graphene where such linear splitting of Landau levels was observed at moderate fields. We consider both bilayer and trilayer configurations and, although a linear splitting occurs in both cases, we show that the latter produces a splitting that is in quantitative agreement with the experiment.