Non-linear effects in the cyclotron resonance of a massless quasi-particle in graphene

We consider the classical motion of a massless quasi-particle in a magnetic field and under a weak electromagnetic radiation with the frequency $\omega$. Due to the non-parabolic, linear energy dispersion, the particle responds not only at the frequency $\omega$ but generates a broad frequency spectrum around it. The linewidth of the cyclotron resonance turns out to be very broad even in a perfectly pure material which allows one to explain recent experimental data in graphene. It is concluded that the linear response theory does not work in graphene in finite magnetic fields.