Twist Angle-Dependent Bands and Valley Inversion in 2D Materials/hBN Heterostructures

The use of relative twist angle between adjacent atomic layers in a van der Waals heterostructure, has emerged as a new degree of freedom to tune electronic and optoelectronic properties of devices based on 2D materials. Using ABA-stacked trilayer (TLG) graphene as the model system, we show that, contrary to conventional wisdom, the band structures of 2D materials are systematically tunable depending on their relative alignment angle between hexagonal BN (hBN), even at very large twist angles. Moreover, addition or removal of the hBN substrate results in an inversion of the K and K' valley in TLG's lowest Landau level (LL). Our work illustrates the critical role played by substrates in van der Waals heterostructures and opens the door towards band structure modification and valley control via substrate and twist angle engineering.