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 Keldysh Green's function formalism. When a dc electric field Ex ∼ 10 3 V/m is applied, a spin polarization σy ≃ 5.2 × 10 −8Å−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 σz ≃ 2 × 10 −10Å−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.

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