Plasmon-phonon interactions in twisted bilayer graphene

The Fermi velocity in twisted bilayer graphene (TBG) near a magic angle can be comparable to the sound velocity of the acoustic phonons of graphene. As a result, the phonon acoustic bands coexist with a high density of electron-hole pairs in the momentum-frequency space, leading to two main effects: i) the renormalization of the phonon dispersion and ii) the intrinsic coupling between phonons and the plasmons of the 2d Coulomb gas. We compute the full bosonic excitation spectrum of TBG, accounting for both acoustic phonos and plasmons. We show that the Umklapp processes can not be neglected in magic-angle TBG, and strongly affect the dispersion of the excitations in the meV region of the spectrum. Unexpected features appear at these energy scale and we suggest that their signature can be detected via THz spectroscopic techniques.