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. In particular it is shown that propagation is significantly blocked for certain frequencies defined by the resonant absorption due to electronic-acoustic interaction. We study absorption of acoustic energy as a function of magnetic field and find that, for a finite gate voltage and fixed acoustic frequency, tuning the magnetic field may bring the system through a number of electronic resonances. We suggest that the strong interaction between the acoustic and electronic edge states in graphene may generate significant nonlinear effects leading to the existence of acoustic solitons in such systems