  Magnetoplasmons on graphene edge in quantizing magnetic field are
investigated at different Landau level filling factors. To find the mode
frequency, the optical conductivity tensor of disordered graphene in magnetic
field is calculated in the self-consistent Born approximation, and the nonlocal
electromagnetic problem is solved using the Wiener-Hopf method. Magnetoplasmon
dispersion relations, velocities and attenuation lengths are studied
numerically and analytically with taking into account the screening by metallic
gate and the energy dissipation in graphene. The magnetoplasmon velocity
decreases in the presence of nearby gate and oscillates as a function of the
filling factor because of the dissipation induced frequency suppression
occurring when the Fermi level is located near the centers of Landau levels, in
agreement with the recent experiments.

Mesoscale and Nanoscale Physics