Twisted bilayer materials, and in particular, twisted bilayer graphene, are created by slightly rotating the two individual crystal networks in a 2D material with respect to each other. For small twist angles, the material undergoes a self-organized lattice reconstruction, leading to the formation of a periodically repeated domain. The resulting superlattice modulates the vibrational and electronic structures within the material, leading to changes in the behavior of electron–phonon coupling and to the observation of strong correlations and superconductivity. In this talk, I will report on the phonon spectra of twisted bilayer graphene (tBLG) and twisted bilayer MoS2 that were computational analyzed for a series of hundreds of twisting angle values. 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 Γ point for the large moiré 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. I will also review how these results have been confirmed experimentally in collaboration with the group of Ado Jorio: Observations of the crystallographic structure with visible light are made possible by the nano-Raman technique, which reveals the localization of lattice dynamics, with the presence of strain solitons and topological points causing detectable spectral variations.
