Electrons in graphene heterostructures with hexagonal boron nitride

We discuss the prospects for the development of new applications and uncovering new physics in graphene heterostructures with hexagonal boron nitride (hBN). On the one hand, the use of hBN as insulating layers allows one to achieve control on electrostatics in graphene-based devices at the few-nm scale, without reducing the transport characteristics of graphene itself, opening ways towards making new generations of ballistic electron devices and quantum dot circuits. On the other hand, Dirac-type electrons in highly-oriented graphene-hBN heterostructures experience a long-period superlattice due to the moire pattern created by a slight incommensurability of the honeycomb lattices of the two crystals. For such superlattice, we investigate the properties of graphene miniband spectrum at zero and strong magnetic fields, where we find several generations of Dirac-type electrons systematically reappearing at the edges of minibands at B=0 and Zak’s magnetic bands in the fractal Hofstadter spectrum. Relation of our modeling of moire superlattice in graphene and Zak’s minibands at high magnetic field to the recent experiments by the Manchester, MIT and Columbia groups will be discussed.