  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.
