Strong gate-tunability of flat bands in multilayer graphene due to moiré encapsulation between hBN monolayers

When using hBN as a substrate for graphene devices, the resulting moiré pattern generates secondary Dirac points. Recent experimental advances have enabled the possibility to precisely control the stacking and twist-angle of the individual layers within van Der Waals heterostructures. By encapsulating a multilayer graphene within aligned hBN sheets the controlled moiré stacking may offer even richer benefits. Using advanced tight-binding simulations on atomistically-relaxed heterostructures, we show that the gap at the secondary Dirac point can be opened in selected moiré-stacking configurations, and is independent of any additional vertical gating of the heterostructure. On the other hand, gating can broadly tune the gap at the principal Dirac point, and may thereby strongly compress the first moiré mini-band in width against the moiré-induced gap at the secondary Dirac point. We reveal that in hBN-encapsulated bilayer graphene this novel mechanism can lead to bands flatter than 10 meV under moderate gating, hence presenting a convenient pathway towards electronically-controlled strongly-correlated states on demand.