Interaction between electronic and vibrational edge states in graphene

Abstract: A sheet of graphene in a magnetic field perpendicular to the sheet has electronic edge states with nonzero velocities. These edge states are localized to the edge of the sheet on the order of the magnetic length. In addition, there are also vibrational edge states — mechanical waves which propagate along the edge and decay exponentially into the bulk. These edge waves are analogous to the well-known surface acoustic waves in 3D systems; the edge being a 1D surface. This thesis considers a zigzag edge of a graphene sheet in a perpendicular magnetic field and investigates the interaction of in-plane vibrational edge waves with electronic edge states. It is found that propagation of low-amplitude vibrational edge waves is significantly blocked for certain acoustic wave vectors — those leading to resonant absorption due to electronic-acoustic interaction. For a finite gate voltage and a fixed acoustic frequency, tuning the magnetic field can bring the system through a number of such electronic resonances. Considering vibrational edge waves of larger amplitude, so that nonlinear effects become important, it is further demonstrated that the coupled system of electronic and acoustic equations has a family of solutions in which the mechanical displacement is in the shape of a localized and stable profile traveling along the edge — a soliton. This type of acoustic soliton can attain velocities significantly higher than the speed of sound.