Cyclotron resonance in antidot arrays

We study the dynamical properties of an electron gas scattered by impenetrable antidots in the presence of a strong magnetic field. We find that the lineshape of the cyclotron resonance is very different from the Lorentzian and is not characterized by the Drude scattering rate. We show that the dissipative dynamical response of skipping orbits, $S_c(\omega)$, is broadened on a scale of the cyclotron frequency $\omega_c$ and has a sharp dip $\propto |\omega-\omega_c|$. For small antidots, $S_c(\omega)$ is strongly modulated with a period equal to $\omega_c$ and has sharp square-root singularities for a series of resonant frequencies. For large antidots, $S_c(\omega)$ has a hard gap at $\omega<\omega_c$ between two sharp peaks, associated respectively with edge states and free cyclotron orbits.