Moiré phonons in graphene/hexagonal boron nitride moiré superlattice

We theoretically study the in-plane acoustic phonons of graphene/hexagonal boron nitride moir\'e superlattice using a continuum model. We demonstrate that the original phonon bands of individual layers are strongly hybridized and reconstructed into moir\'e phonon bands consisting of dispersive bands and flat bands. The phonon band structure can be effectively described by a spring-mass network model to simulate the motion of moir\'e domain walls where the flat-band modes are interpreted as vibrations of independent, decoupled strings. We also show that the moir\'e phonon has angular momentum due to the inversion symmetry breaking by hBN, with high amplitudes concentrated near the narrow gap region. Finally, we apply the same approach to twisted bilayer graphene and we find a notable difference between the origins of the flat-band modes in G/hBN and TBG, reflecting distinct geometric structures of the domain pattern.