Valley separation in graphene by polarized light

We show that the optical excitation of graphene with polarized light leads to pure valley current for which carriers in the valleys counterflow. The current in each valley originates from the asymmetry of optical transitions and electron scattering by impurities owing to the warping of the electron energy spectrum. The valley current has strong polarization dependence; its direction is opposite for normally incident beams of orthogonal linear polarizations. In undoped graphene on a substrate with high susceptibility, electron-electron scattering leads to an additional contribution to the valley current that can dominate.

Figure 1

(a) Brillouin zone of graphene. The circles indicate the neighborhood of the $K$ and $K^{\prime }$ points in which the electron states have trigonal symmetry allowing for the photocurrent. (b) Mechanisms of photocurrent formation in the $K$ valley. Solid, dashed, and dotted arrows of different thicknesses indicate anisotropy of velocity, optical generation, and scattering rate, respectively, in $\mathit{p}$ space.

Figure 2

Dependence $F\left(\gamma \right)$ that determines the magnitude of the valley current caused by electron-electron scattering [Eq. (17)]. The left inset sketches the scattering of electrons with momenta $\mathit{p}$ and $\mathit{k}$ into states with momenta ${\mathit{p}}^{\prime }$ and ${\mathit{k}}^{\prime }$, respectively. The right inset shows the momentum space in the $K$ valley. Sectors where the Auger-like electron relaxation is allowed are colored, and the ellipses depict the alignment of the photoelectron momenta by linearly polarized light.