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-up arrow/down arrow may still be produced. Once an amount of spin-up electrons flow into the device region from lead alpha and flow out from lead beta under light irradiation, the same amount of spin-down electrons will flow into the device region from lead beta and flow out from lead alpha, which results in I-c(alpha/beta) = I-up arrow(alpha/beta) + I-down arrow(alpha)/beta = 0 and I-s(alpha)/beta = I-up arrow(alpha)/beta-I-down arrow(alpha)/beta not equal 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 (sic)(sic) 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.