Band Engineering in van der Waals Heterostructures Graphene/h-BN

Graphene/h-BN is a prototypical van der Waals heterostructure and exhibits novel electronic properties. The substrate-hexagonal Boron nitride (h-BN) shares similar honeycomb lattice structure with graphene, yet with 1.8% lattice mismatch and large band gap (5.97 eV) due to the inversion symmetry breaking of distinct boron and nitrogen atoms. Due to the flatness of h-BN, graphene devices on h-BN exhibit greatly improved properties including reduced ripples, suppressed charge inhomogeneities and higher mobility. More interestingly, the moire superlattice potential induced by the lattice mismatch and crystal orientation provides new method to engineer the band structure of graphene and lead to the realization of many novel quantum phenomena, such as self-similar Hofstadter butterfly states [1, 2, 3, 4], topological currents [5] (see Fig. 3.1). The Hofstadter butterfly states refer to the fractal spectrum under magnetic field which resemble the butterfly. The experimental attempts to realize this effect have been limited by two facts, on one hand, the typical atomic-scale superstructure requires unfeasible large magnetic field to reach the commensurability condition, on the other hand, the period of artificially constructed superstructures is too large that the corresponding field is too small to overcome the disorder completely.