Flat bands in slightly twisted bilayer graphene: Tight-binding calculations

The presence of flat bands near Fermi level has been proposed as an explanation for high transition temperature superconductors. The bands of graphite are extremely sensitive to topological defects which modify the electronic structure. In this Rapid Communication, we found nondispersive flat bands no farther than 10 meV of the Fermi energy in slightly twisted bilayer graphene as a signature of a transition from a parabolic dispersion of bilayer graphene to the characteristic linear dispersion of graphene. This transition occurs for relative rotation angles of layers around $1.5\ifmmode^\circ\else\textdegree\fi{}$ and is related to a process of layer decoupling. We have performed ab initio calculations to develop a tight-binding model with an interaction Hamiltonian between layers that include the $\ensuremath{\pi}$ orbitals of all atoms and takes into account interactions up to third nearest neighbors within a layer.