Surface states in $\mathrm{Tl}/\mathrm{Si}\left(111\right)\text{−}\left(1\times 1\right)$ and $\beta \text{−}\mathrm{Bi}/\mathrm{Si}\left(111\right)\text{−}\left(\sqrt{3}\times \sqrt{3}\right)$ 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.

• Received 23 April 2015
• Revised 5 June 2015

DOI:https://doi.org/10.1103/PhysRevB.91.245428