Pure spin current generation via photogalvanic effect with spatial inversion symmetry

We propose a new idea to generate pure spin current with photogalvanic effect (PGE) by designing devices with spatial inversion symmetry based on two-dimensional spin semiconducting materials. Due to the preservation of spatial inversion symmetry, the electric current generated by the PGE must be zero. However, finite spin-dependent current I_↑/↓ may still be produced. Once an amount of spin-up electrons flow into the device region from lead α and flow out from lead β under light irradiation, the same amount of spin-down electrons will flow into the device region from lead β and flow out from lead α, which results in Ic^α/β=I_↑^α/β+I_↓^α/β=0 and ${I}ₛ^{{α}/{β}}={I}_{{↑}}^{{α}/{β}}{-}{I}_{{↓}}^{{α}/{β}}{≠}0$ simultaneously for each lead and thus finite pure spin current arises. As a concrete example, this idea is demonstrated by calculating the PGE in a photoelectric device constructed with an armchair-edged graphene nanoribbon which is divided into two semi-infinite ribbons. The two semi-infinite ribbons are then periodically and symmetrically patterned with ferromagnetic triangle antidots in the form of ``$▹◃$'' to achieve spatial inversion symmetry of the device. We find that the pure spin current can be robustly generated, neither dependent on the photon energy and polarization/helicity angle, nor dependent on whether it is linearly, circularly, or elliptically polarized.