Plasmons in twisted bilayer graphene across dispersive and flat bands

Abstract: The dynamical dielectric response of twisted bilayer graphene is explored in large-angle dispersive-band and small-angle quasi-flat-band regimes using time-dependent density-functional theory within the random-phase approximation. At the reference bilayer-graphene interlayer distance, weak coupling in the largest-angle structures preserves Dirac dispersions and the intrinsic $π$ plasmon. Electron doping activates a two-dimensional Dirac plasmon with energies obeying approximate geometric twist-angle scaling, while acoustic-like branches remain embedded in the single-particle continuum. The prohibitively large first-magic-angle supercell is represented by a tractable cell with its interlayer separation reduced to the angle-dependent magic distance, where four quasi-flat bands emerge around the Fermi level. Their partial occupation produces a dispersive low-energy plasmon-like excitation without a clear dielectric zero at resonance. A distinct interband plasmon is instead identified, supported by transitions involving the quasi-flat manifold and neighboring high-density-of-states regions. Band-energy rescaling places its characteristic energy in the mid-infrared range of interband collective excitations measured near the magic angle.