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 Keldysh Green's function formalism. When a dc electric field $E_x \sim 10^{3} {\rm V/m}$ is applied, a spin polarization $<\sigma_{y}> \simeq 5.2 \times 10^{-8}{\rm \AA^{-2}}$ 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 $\tau$ and $<\sigma_{z}> \simeq 2 \times 10^{-10}{\rm \AA^{-2}}$ 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. 
Tetsuro Misawa, Takehito Yokoyama, Shuichi Murakami
cond-mat.mes-hall