Relationship between Fermi surface warping and out-of-plane spin polarization in topological insulators: A view from spin- and angle-resolved photoemission

We have performed spin- and angle-resolved photoemission spectroscopy of the topological insulator Pb(Bi,Sb)(2)Te-4 and observed significant out-of-plane spin polarization on the hexagonally warped Dirac-cone surface state. To put this into context, we carried out quantitative analysis of the warping strengths for various topological insulators [Pb(Bi,Sb)(2)Te-4, Bi2Te3, Bi2Se3, and TlBiSe2] and elucidated that the out-of-plane spin polarization P-z is systematically correlated with the warping strength. However, the magnitude of P-z is found to be only half that expected from the k . p theory when the warping is strong. Besides confirming a universal relationship between the spin polarization and the surface state structure, our data provide an empirical guiding principle for tuning the spin polarization in topological insulators.