Crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the magic angle θ∼1.08

We combine state-of-the-art large-scale first-principles calculations with a low-energy continuum model to describe the nearly flat bands of twisted bilayer graphene at the first magic angle θ=1.08∘. We show that the energy width of the flat-band manifold, as well as the energy gap separating it from the valence and conduction bands, can be obtained only if the out-of-plane relaxations are fully taken into account. The results agree both qualitatively and quantitatively with recent experimental outcomes.