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We combine state-of-the-art large-scale first principles calculations with alow-energy continuum model to describe the nearly flat bands of twisted bilayergraphene at the first magic angle $\theta =1.08^\circ$. We show that the energywidth of the flat band manifold, as well as the energy gap separating it fromthe valence and conduction bands, can be obtained only if the out-of-planerelaxations are fully taken into account. The results agree both qualitativelyand quantitatively with recent experimental outcomes.

The crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the "magic angle" $\theta\sim 1.08^\circ$