Band structure of twisted bilayer graphene on hexagonal boron nitride

The effect of a hexagonal boron nitride (hBN) layer closely aligned with twisted bilayer graphene (TBG) is studied. At sufficiently low angles between twisted bilayer graphene and hBN, theta(hBN) less than or similar to 2 degrees, the graphene electronic structure is strongly disturbed. The width of the low-energy peak in the density of states changes from W similar to 5-10 meV for a decoupled system to similar to 20-30 meV. Spikes in the density of states due to van Hove singularities are smoothed out. We find that for a realistic combination of the twist angle in the TBG and the twist angle between the hBN and the graphene layer the system can be described using a single moire unit cell.