Electromagnetic spin polarization on the surface of topological insulator

We study the spin polarization of the electrons on the surface of topological insulators under a dc electric field or a circularly polarized light by using the Keldysh Green's function formalism. When a dc electric field Eₓ~10³0.28em0exV/m is applied, a spin polarization σy5.2×10^-80.28em0ex^-2 is induced. Furthermore, we also find that a light illumination induces the out-of-plane component of the spin polarization as a result of the inverse Faraday effect. The magnitude of the spin polarization is proportional to the square of the lifetime τ and σz2×10^-100.28em0ex^-2 for typical parameters. Finally, we investigate the spin polarization in the presence of the warping term. By the symmetry consideration of the system, we find that the out-of-plane spin polarization is cubic of the current and that the magnitude of the induced spin polarization depends on the direction of the applied current.