Selection Rules for Optical Vortex Absorption by Landau-quantized Electrons

An optical vortex beam carries orbital angular momentum $\ell$ in addition to spin angular momentum $\sigma$. We demonstrate that a Landau-quantized two dimensional electron system absorbs the optical vortex beam through modified selection rules, reflecting two kinds of angular momenta. The lowest Landau level electron absorbs the optical vortex beams with $\sigma=1$ (positive helicity) and $\ell=0$ or $\sigma=-1$ (negative helicity) and $\ell=2$ in the electric dipole transition. The induced electric currents survive only along the edge of the sample, due to cancellation of the bulk currents. Thus, the magnetization can be induced by only the edge current. It is shown that the induced orbital magnetization disappears when the dark ring of the beam coincides with the disk edge. This scheme may provide a helicity-dependent absorption using the optical vortex beam.