Optically tunable spin texture of the surface state for Bi₂Se₃ and SmB₆ topological insulators

The spin texture of the surface state for topological insulators can be manipulated by the polarization of light, which might play a potential role in the applications in spintronics. However, the study so far in this direction mainly focuses on the classical light-topological-insulators interactions; TIs coupled to quantized light remains barely explored. In this paper, we develop a formalism to deal with this issue of spin texture of the surface state for topological insulators (for example Bi₂Se₃ and SmB₆) irradiated by a quantum field, and we find that the coupling between an electron and a single-mode quantum field modulates only the arrow length that represents the spin polarization of a topological surface state. Specifically, when the photon number of a single-mode quantum field is fixed, the azimuth angle between the quantum light and the material surface manipulates the spin textures along the constant energy contour rotating (clockwise or counterclockwise) around the high symmetry point, and the polar angle controls the magnitude of the spin polarization. These results are quite different from the situation where an external field is not applied to an electron in a crystal or where a classical external field is utilized to control the spin polarization of a photoemitted electron in a vacuum. Our results have potential applications in quantum optics and condensed-matter physics.