Moire patterns and electronic structure of hBN encapsulated graphene

Hexagonal boron nitride layers are barrier materials for graphene and other 2D materials used to prepare high electrical quality devices. Their surface interaction with graphene becomes most apparent at energy ranges accessible through back-gating in the limit of long period moire patterns in nearly aligned structures. Here we examine the electronic structure of graphene encapsulated by nearly aligned hBN layers that give rise to two moire patterns, one per each G/BN interface, that can add up constructively or cancel out destructively depending on the relative sliding displacement and rotation between the hBN layers. Most of the electronic properties of hBN encapsulated graphene can understood from a linear superposition of the moire pattern effects stemming from each one of the interfaces. By examining the band gaps, density of states, and band structures for different relative arrangements of the top/bottom hBN layers we conclude that an appropriate coupling of graphene with the two hBN interfaces can greatly enhance the electronic structure features of both primary and secondary Dirac points, and influence the degree of particle-hole asymmetry in the system.