Coupled phonons in twisted bilayer graphene

Stacking two layers of two-dimensional materials slightly twisted relative to each other causes significant alternations of the physical properties of the resulting bilayer. For graphene, at the right twist angle, the electronic band structure features a flat band at the Fermi level that gives rise to interesting many-body physics such as correlated insulators or superconducting states. Likewise, a finite twist angle modifies the phonon band structure. A reciprocal space continuum model including lattice reconstruction due to relaxation allows us to investigate the continuous evolution of the phonon band structure with twist angle. At intermediate angles, we find a complicated structure of the phonon density of states around the frequency of the layer breathing mode, that is substantially broadened by the moire-induced interaction with the acoustic phonon branches. We infer optical activities and suggest Raman experiments to validate our predictions. Our results suggest that suitably twisting structures may manipulate both phonon and electron properties of such a system, and thus set the stage to test electron-phonon contributions to the observed correlated states.