Propagation of acoustic edge waves in graphene under quantum Hall effect

We consider a graphene sheet with a zigzag edge subject to a perpendicular magnetic field and investigate the propagation of in-plane acoustic edge waves under the influence of magnetically induced electronic edge states. In particular is is shown that propagation is significantly blocked for certain frequencies defined by the resonant absorption due to electronic-acoustic interaction. We suggest that strong interaction between the acoustic and electronic edge states in graphene may generate significant non-linear effects leading to the existence of acoustic solitons in such systems.