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 ${I}_{\ensuremath{\uparrow}/\ensuremath{\downarrow}}$ may still be produced. Once an amount of spin-up electrons flow into the device region from lead $\ensuremath{\alpha}$ and flow out from lead $\ensuremath{\beta}$ under light irradiation, the same amount of spin-down electrons will flow into the device region from lead $\ensuremath{\beta}$ and flow out from lead $\ensuremath{\alpha}$, which results in ${I}_{c}^{\ensuremath{\alpha}/\ensuremath{\beta}}={I}_{\ensuremath{\uparrow}}^{\ensuremath{\alpha}/\ensuremath{\beta}}+{I}_{\ensuremath{\downarrow}}^{\ensuremath{\alpha}/\ensuremath{\beta}}=0$ and ${I}_{s}^{\ensuremath{\alpha}/\ensuremath{\beta}}={I}_{\ensuremath{\uparrow}}^{\ensuremath{\alpha}/\ensuremath{\beta}}\ensuremath{-}{I}_{\ensuremath{\downarrow}}^{\ensuremath{\alpha}/\ensuremath{\beta}}\ensuremath{\ne}0$ 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.