  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.
