Photoinduced pure spin-current injection in graphene with Rashba spin-orbit interaction

We propose a photoexcitation scheme for pure spin-current generation in graphene subject to a Rashba spin-orbit coupling. Although excitation using circularly polarized light does not result in optical orientation of spins in graphene unless an additional magnetic field is present, we show that excitation with linearly polarized light at normal incidence yields spin-current injection without magnetic field. Spins are polarized within the graphene plane and are displaced in opposite directions, with no net charge displacement. The direction of the spin current is determined by the linear polarization axis of the light, and the injection rate is proportional to the intensity. The technique is tunable via an applied bias voltage and is accessible over a wide frequency range. We predict a spin-current polarization as high as 75% for photon frequencies comparable to the Rashba frequency. Spin-current injection via optical methods removes the need for ferromagnetic contacts, which have been identified as a possible source of spin scattering in electrical spin injection in graphene.

Figure 1

(a) Energy-momentum dispersion of graphene with Rashba spin-orbit coupling; (b) vectors defining the orientation in the graphene plane; and (c) magnitude of the spin expectation value as a function of crystal momentum.

Figure 2

Spin-current injection strength for graphene with Rashba spin-orbit interaction. The single independent component ${\mu }_1^{xyxx}\left(\omega \right)$ of the total spin-current injection tensor [Eq. (11)], as well as the individual contributions ${\overline{\mu }}_{1a–c}\left(\omega \right)$ [Eq. (12)], are shown as a function of the light frequency $\omega$ for the case of intrinsic graphene $\left(E_F=0\right)$.

Figure 3

Photoinduced pure spin-current injection schemes. (a) Intrinsic graphene at low energy, ${\omega }_a<{\Omega }_R$, yields the strongest spin-current injection. (b) For midrange energy, ${\Omega }_R<{\omega }_b<2{\Omega }_R$, the spin-current injection strength improves by tuning the Fermi level to $\left|E_F\right|=\frac{1}{2}\hslash {\Omega }_R$ to Pauli block half of the transitions involving a split-off band. (c) For the same frequency range, further increasing the Fermi level to $\left|E_F\right|=\hslash {\Omega }_R$ results in the Pauli blocking of transitions involving the gapless bands. This yields a reversal of the spin-current injection.

Figure 4

Spin-current injection strength ${\mu }_1^{xyxx}\left(\omega \right)$ for graphene with Rashba spin-orbit interaction [Eq. (11)] for varying values of the Fermi level $\left(E_F=0,\frac{1}{2}\hslash {\Omega }_R,\hslash {\Omega }_R,\frac{3}{2}\hslash {\Omega }_R\right)$.

Figure 5

Spin-current polarization per carrier, $P$, for graphene with Rashba spin-orbit interaction [Eq. (15)] for intrinsic graphene $\left(E_F=0\right)$ and for the maximal case making use of Pauli blocking [$E_F=(2\hslash \omega -\hslash {\Omega }_R)/4$].