Current-induced spin polarization in graphene due to Rashba spin-orbit interaction

Spin polarization induced by an external electric field in graphene is considered theoretically in the linear-response regime. The graphene is assumed to be deposited on a substrate which leads to the spin-orbit interaction of Rashba type. The induced spin polarization is shown to be in the graphene plane and perpendicular to the electric field. However, orientation of the spin polarization becomes reversed when the Fermi level, the position of which can be controlled by an external gate voltage, crosses the Dirac points.

Figure 1

Scheme of the device based on graphene, where the electric field (or charge current) flowing along the stripe (axis $y$) can induce spin polarization of conduction electrons. This spin polarization, induced by the Rashba spin-orbit coupling $\lambda$, is in the graphene plane and normal to the electric field. Orientation of the induced spin polarization becomes reversed when the Fermi level crosses the Dirac points. External gate voltage can be used to control the position of the Fermi level in graphene.

Figure 2

Diagram representing the $x$ component of the current-induced spin polarization in the linear response regime. Here, ${\Sigma }_x$ is defined as ${\Sigma }_x=\hslash I\otimes {\sigma }_x/2$, while $H_A$ is the perturbation due to external field, as described in the text.

Figure 3

Spin polarization $S_x$ induced by electric field, presented as a function of the chemical potential $\mu$ for indicated values of the spin-orbit Rashba coupling parameter (a), and as a function of the Rashba parameter $\lambda$ for indicated values of the chemical potential (b). The other parameters are $a=1.4\AA$, $t=2.9$ eV, $\tau ={10}^{-10}$ s, and $E_y=0.1$ V/m.

Figure 4

Spin polarization $S_x$ induced by electric field, presented as a function of the chemical potential $\mu$ and Rashba spin-orbit coupling parameter $\lambda$, calculated for $a=1.4\AA$, $t=2.9$ eV, $\tau ={10}^{-10}$ s, and $E_y=0.1$ V/m. Local maxima in $|S_x|$ as a function of $\mu$ are marked by the dashed lines.