Tunable band gap in twisted bilayer graphene

At large commensurate angles, twisted bilayer graphene which holds even parity under sublattice exchange exhibits a tiny gap. Here, we point out a way to tune this tiny gap into a large gap. We start from comprehensive understanding of the physical origin of gap opening by density functional theory calculations. We reveal that the effective inter-layer hopping, intra-layer CDW, or inter-layer charge imbalance favors a gap. Then, on the basis of tight-binding calculations, we suggest that a periodic transverse inhomogeneous pressure, which can tune inter-layer hoppings in specific regions of the moi$\acute{\mathrm{r}}$e supercell, may open a gap of over $100$~meV, which is further confirmed by first-principles calculations. Our results provide a theoretical guidance for experiments to open a large gap in twisted bilayer graphene.