Localization of lattice dynamics in low-angle twisted bilayer graphene.

Twisted bilayer graphene is created by slightly rotating the two crystal networks in bilayer graphene 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 domain1-3. The resulting superlattice modulates the vibrational3,4 and electronic5,6 structures within the material, leading to changes in the behaviour of electron-phonon coupling7,8 and to the observation of strong correlations and superconductivity9. However, accessing these modulations and understanding the related effects are challenging, because the modulations are too small for experimental techniques to accurately resolve the relevant energy levels and too large for theoretical models to properly describe the localized effects. Here we report hyperspectral optical images, generated by a nano-Raman spectroscope10, of the crystal superlattice in reconstructed (low-angle) twisted bilayer graphene. 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 points1 causing detectable spectral variations. The results are rationalized by an atomistic model that enables evaluation of the local density of the electronic and vibrational states of the superlattice. This evaluation highlights the relevance of solitons and topological points for the vibrational and electronic properties of the structures, particularly for small twist angles. Our results are an important step towards understanding phonon-related effects at atomic and nanometric scales, such as Jahn-Teller effects11 and electronic Cooper pairing12-14, and may help to improve device characterization15 in the context of the rapidly developing field of twistronics16.