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

The electronic properties of twisted bilayer graphene are being intensely investigated. The flat bands emerging at the first ``magic angle'' are responsible for anomalous insulating behavior at half-filling and superconductivity. Using state-of-the-art $a\phantom{\rule{0}{0ex}}b\phantom{\rule{0.333em}{0ex}}i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ calculations, it is shown that the energy gaps and band dispersion are captured correctly only when the atomic corrugation, arising as a result of the interlayer interaction, is considered. The atomic corrugation shows a wave profile with maximum atomic out-of-plane displacements of about 0.1 angstrom.