Graphene Moiré Magic-Angle Phase Map (2D)

The 3D twisted-bilayer sim renders one real-space snapshot of the moiré density landscape at a time. This 2D companion instead maps the whole parameter space at once: every point in the twist-angle/interlayer-coupling plane is colored by the renormalized Dirac velocity v*/v_F from the Bistritzer–MacDonald continuum model, with the magic-angle locus — the curve where v*/v_F crosses exactly zero — traced analytically as a contour rather than read off a single simulation run. A second panel computes the real-space AA-puddle density directly as a 2D grid at whatever (θ,w) point the sliders select, so you can watch the electron-density proxy sharpen into puddles at the same moment the crosshair crosses the magic-angle contour.