Soliton Signature In The Phonon Spectrum Of Twisted Bilayer Graphene

The phonon spectra of twisted bilayer graphene (tBLG) are analyzed for a series of 692 twisting angle values in the [0, 30 degrees] range. The evolution of the phonon bandstructure as a function of twist angle is examined using a band unfolding scheme where the large number of phonon modes computed at the Gamma point for the large moire tBLG supercells are unfolded onto the Brillouin Zone (BZ) of one of the two constituent layers. In addition to changes to the low-frequency breathing and shear modes, a series of well-defined side-bands around high-symmetry points of the extended BZ emerge due to the twist angle-dependent structural relaxation. The results are rationalized by introducing a nearly-free-phonon model that highlights the central role played by solitons in the description of the new phonon branches, which are particularly pronounced for structures with small twist angles, below a buckling angle of theta(B) similar to 3.75 degrees.