Spin Polarization of Photoelectrons in GaAs Excited by Twisted Photons

Inter-band photo-excitation of electron states with the twisted photons in GaAs, a direct band-gap bulk semiconductor, is considered theoretically. Assuming linearity of the quantum transition amplitudes and applying Wigner-Eckart theorem, we derive a plane-wave expansion of twisted-photon amplitudes and obtain relative probabilities for magnetic sub-level population of the photo-electrons in conduction band. The approach for calculating the position dependent electron polarization, resulting from photo-absorption of twisted light, is described for vertical transitions in the $\Gamma$ - point. Theoretical predictions for GaAs show the interplay of spin and orbital angular momentum of the twisted photons that alters the magnitude and the sign of photoelectron polarization in the region near photon's phase singularity.