Charged moir\'e phonons in twisted bilayer graphene

Abstract

Moir\'e phonons describe collective vibrations of a moir\'e superlattice produced by long-wavelength relative displacements of the constituent layers. Despite coming from the backfolding of the acoustic phonons of the individual layers, many of these modes become infrared active when the system is doped. We illustrate this effect by a direct calculation of the optical absorption of twisted bilayer graphene (tBG) around different twist angles, including the magic angle. Several modes -- including the acoustic-like phason -- acquire a dipole moment via interband matrix elements of the electron-phonon coupling (EPC) when the flat band is filled or emptied, giving rise to new resonances in the optical conductivity within the single-electron gap that are strongly affected by relaxation. The phason in particular gains a charge that equals the amount of electrons per moir\'e cell added/removed to/from neutrality. Geometrically, this can be understood as the topological quantization of a sliding Chern number. The charged phason yields a Drude-like conductivity with an effective mass that increases with lattice relaxation. Our findings are testable via THz spectroscopy, and provide an experimental knob to characterize EPC strength and disorder in moir\'e materials at small twist angles.