Tunable correlated insulator behavior in twisted double bilayer graphene

Recent evidence for correlated physics in moire superlattice systems has motivated numerous theoretical studies and predictions relating flat bands, interactions, topology, and the underlying dependence on twist angle. In particular, twisted structures of two Bernal-stacked graphene bilayers display transport signatures of correlated insulating states at quarter- and half-filling of the superlattice bands that appear at finite displacement fields. Here, we explore the detailed evolution of these features in the electronic structure via sensitive measurements of the electronic compressibility. By varying carrier density and displacement field in a dual-gate capacitor geometry, we tune the bands into the various incompressible regimes to shed light on the possible correlations. By applying in- and out-of-plane magnetic fields, we probe the spin character and Landau level spectrum of the moire bands and comment on the correspondence to existing theoretical predictions.