Direct measurement of the out-of-plane spin texture in the dirac-cone surface state of a topological insulator

We have performed spin- and angle-resolved photoemission spectroscopy of Bi₂Te₃ and present the first direct evidence for the existence of the out-of-plane spin component on the surface state of a topological insulator. We found that the magnitude of the out-of-plane spin polarization on a hexagonally deformed Fermi surface of Bi₂Te ₃ reaches maximally 25% of the in-plane counterpart, while such a sizable out-of-plane spin component does not exist in the more circular Fermi surface of TlBiSe₂, indicating that the hexagonal deformation of the Fermi surface is responsible for the deviation from the ideal helical spin texture. The observed out-of-plane polarization is much smaller than that expected from the existing theory, suggesting that an additional ingredient is necessary for correctly understanding the surface spin polarization in Bi ₂Te₃.