Correlated Insulating States in Twisted Double Bilayer Graphene.

We present a combined experimental and theoretical study of twisted double bilayer graphene with twist angles between 1° and 1.35°. Consistent with moiré band structure calculations, we observe insulators at integer moiré band fillings one and three, but not two. An applied transverse electric field separates the first moiré conduction band from neighboring bands, and favors the appearance of correlated insulators at 1/4, 1/2, and 3/4 band filling. Insulating states at 1/4 and 3/4 band filling emerge only in a parallel magnetic field (B_{||}), whereas the resistivity at half band filling is weakly dependent on B_{||}. Our findings suggest that correlated insulators are favored when a moiré flat band is spectrally isolated, and are consistent with a mean-field picture in which insulating states are established by breaking both spin and valley symmetries at 1/4 and 3/4 band filling and valley polarization alone at 1/2 band filling.