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In this work, we discuss the connections between pseudo spin, real spin ofelectrons in material and spin polarization of photo-emitted electrons out ofmaterial. By investigating these three spin textures for Bi$_2$Se$_3$ andSmB$_6$ compounds, we find that the spin orientation of photo-electrons forSmB$_6$ has different correspondence to pseudo spin and real spin compare toBi$_2$Se$_3$, due to the different symmetry properties of the photo-emissionmatrix between initial and final states. We calculate the spin polarization andcircular dichroism spectra of photo-emitted electrons for both compounds, whichcan be detected by spin-resolved and circular dichroism angle resolvedphoto-emission spectroscopy experiment.

Pseudo-Spin, Real-Spin and Spin Polarization of Photo-emitted Electrons