Ab Initio study of graphene/hBN Van der Waals heterostructures: effect of electric field, twist angles and p-n doping on the electronic properties

In this work, we study the structural and electronic properties of boron nitride bilayers sandwiched between graphene sheets. Different stacking, twist angles, doping, as well as an applied external gate voltage, are reported to induce important changes in the electronic band structure near the Fermi level. Small electronic lateral gaps of the order of few meV can appear near the Dirac points K. We further discuss how the bandstructures change applying a perpendicular external electric field, showing how its application lifts the degeneracy of the Dirac cones and, in the twisted case, moves their crossing points away from the Fermi energy. Then, we consider the possibility of co-doping, in an asymmetric way, the two external graphene layers. This is a situation that could be realized in heterostructures deposited on a substrate. We show that the co-doping acts as an effective external electric field, breaking the Dirac cones degeneracy. Finally, our work demonstrates how, by playing with field strength and p-n co-doping, it is possible to tune the small lateral gaps, pointing towards a possible application of C/BN sandwich structures as nano-optical terahertz devices.