  Surface states in Tl/Si(111) and Bi/Si(111) show non-Rashba-type spin
splitting. We study spin-transport properties in these surface states. First we
construct tight-binding Hamiltonians for Tl/Si and Bi/Si surfaces, which
respect crystallographic symmetries. As a result, we find specific terms in the
Tl/Si surface Hamiltonian responsible for non-Rashba spin splitting. Using this
model we calculate current-induced spin polarization in the Tl/Si Hamiltonian
in order to see the effect of non-Rashba spin-orbit interaction. We found that
the induced spin polarization is in-plane and perpendicular to the current,
which is consequently the same with Rashba systems. We find that it follows
from crystallographic symmetries. Furthermore, we numerically find bound states
at the junction between two surface regions which have different signs of the
spin-orbit interaction parameters in the Bi/Si system and in the Tl/Si system.
We explain these numerical results with the results of our analytical
calculations.
