Determining the Magic Angle in Twisted Bilayer Graphene via Lattice Coherence Splitting

We find that the magic angle in twisted bilayer graphene (tBG) corresponds to a specific small rotation angle that divides the graphene hexagon in in a lattice-coherence within two-dimensional reciprocal space. By repeatedly subdividing the graphene hexagon while preserving this lattice- coherent condition, the magic angle is geometrically determined to be 1.067°. This construction maintains moiré diffraction coherence (MDC), such that the reciprocal-space diffraction pattern associated with the subdivided hexagon forms a flat band relative to the original graphene Brillouin zone. The center of the threefold-subdivided hexagon is rotated by 1.067° with respect to the center of the original hexagon, thereby identifying this angle as the magic angle associated with the emergence of superconductivity in tBG.