Electromagnetic spin polarization on the surface of topological insulator

TL;DR

This paper investigates how electric fields and circularly polarized light induce spin polarization on the surface of topological insulators, revealing the effects of external stimuli and system symmetry on spin behavior.

Contribution

It provides a theoretical analysis of spin polarization mechanisms on topological insulator surfaces under electric and optical stimuli, including effects of warping and symmetry considerations.

Findings

Electric field induces measurable in-plane spin polarization.

Circularly polarized light causes out-of-plane spin polarization via inverse Faraday effect.

Out-of-plane polarization depends on current direction and is cubic in current magnitude.

Abstract

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.