Interlayer vibration of twisted bilayer graphene: A first-principles study

Multi-layered structures of graphene and other two dimensional materials are novel organizations with fascinating properties. In this work, we investigate the interlayer lattice dynamics of the Moiré superlattice of twisted bilayer graphene (tBLG) using first-principles calculations. Due to the structural complexity, we calculate the frequencies of the interlayer breathing and shear vibrational modes of the tBLG without exploring all the degree of freedoms of the tBLG. Our calculation shows that the frequencies of breathing and shear modes display pronounced dependence on twisting angle, and compare well with the state of arts experimental measurements. We hint that the strategy employed here paves a route to the study of the interlayer vibrational properties of double layered two dimensional systems.