Shear phonon modes in twisted bilayer 2D crystals

Based on large scale first-principles computations and molecular dynamics simulations, we present variation of low energy in-plane phonon modes in twisted bilayer 2D crystals such as graphene and transition metal dichalcogenides. It is shown that the shear phonon modes soften as the twisted angle increases to 30 degrees while layer breathing modes does not. Discussions regarding on relation between the shear phonon softening, stability of quasicrystalline ordering and interlayer friction will be present.