The motion of an electron in graphene in a magnetic field in the presence of an external electromagnetic wave of circular polarization is studied. Electron in graphene has linear momentum energy spectrum corresponding to the dispersion law for massless quasiparticles. The solution corresponding to cyclotron resonance when a frequency of radiation coincides with a `` cyclotron frequency '' of quasiparticles in the absence electromagnetic wave is obtained in the limit of a weak field. Since a rotational frequency of massless quasiparticles in magnetic field depends on its energy a cyclotron resonance line turns out to be very broad. For the special case, where the frequency of radiation is twice the `` cyclotron '' frequency, the exact solution of the equation of motion of quasiparticle in a magnetic field and field of the wave is obtained. Thus in this case in terms of describing the electron motion we obtain a kind of the wave frequency halving in a magnetic field.
78.67.-n Optical properties of low-dimensional, mesoscopic, and nanoscale materials and structures
73.50.Fq High-field and nonlinear effects
$^1$Department of Theoretical Physics, Faculty of Physics, M.V.Lomonosov Moscow State University
Science News of the Faculty of Physics, Lomonosov Moscow State University
This new information publication, which is intended to convey to the staff, students and graduate students, faculty colleagues and partners of the main achievements of scientists and scientific information on the events in the life of university physicists.