Substrate-Dependent Band Structures in Trilayer Graphene/h-BN Heterostructures

The tight-binding model has been spectacularly successful in elucidating the electronic and optical properties of a vast number of materials. Within the tight-binding model, the hopping parameters that determine much of the band structure are often taken as constants. Here, using ABA-stacked trilayer graphene as the model system, we show that, contrary to conventional wisdom, the hopping parameters and therefore band structures are not constants, but are systematically variable depending on their relative alignment angle between h-BN. Moreover, the addition or removal of the h-BN substrate results in an inversion of the K and K^{'} valley in trilayer graphene's lowest Landau level. Our work illustrates the oft-ignored and rather surprising impact of the substrates on band structures of 2D materials.