  We study the electronic and spin structures of the giant Rashba-split surface
states of the Bi/Si(111)-($\sqrt{3} \times \sqrt{3}$)R30 trimer phase by means
of spin- and angle-resolved photoelectron spectroscopy (spin-ARPES). Supported
by tight-binding calculations of the surface state dispersion and spin
orientation, our findings show that the spin experiences a vortex-like
structure around the $\bar{\Gamma}$-point of the surface Brillouin zone - in
accordance with the standard Rashba model. Moreover, we find no evidence of a
spin vortex around the $\bar{\mathrm{K}}$-point in the hexagonal Brillouin
zone, and thus no peculiar Rashba split around this point, something that has
been suggested by previous works. Rather the opposite, our results show that
the spin structure around $\bar{\mathrm{K}}$ can be fully understood by taking
into account the symmetry of the Brillouin zone and the intersection of spin
vortices centered around the $\bar{\Gamma}$-points in neighboring Brillouin
zones. As a result, the spin structure is consistently explained within the
standard framework of the Rashba model although the spin-polarized surface
states experience a more complex dispersion compared to free-electron like
parabolic states.
