Strong Spin-Orbit Splitting on Bi Surfaces

Using first-principles calculations and angle-resolved photoemission, we show that the spin-orbit interaction leads to a strong splitting of the surface-state bands on low-index surfaces of Bi. The dispersion of the states and the corresponding Fermi surfaces are profoundly modified in the whole surface Brillouin zone. We discuss the implications of these findings with respect to a proposed surface charge density wave on Bi(111) as well as to the surface screening, surface spin-density waves, electron (hole) dynamics in surface states, and to possible applications to the spintronics.

Figure 1

Surface states of Bi(111) calculated without (black) and with (red) spin-orbit splitting included. The shaded areas show the projection of the bulk bands obtained without (violet) and with (yellow) SOC and their superposition (brown).

Figure 2

Calculated and measured electronic structure in the vicinity of two high symmetry points on three surfaces of Bi. (a) $\bar{\Gamma }$ on Bi(111), (b) $\bar{\Gamma }$ on Bi(110), and (c) ${\bar{M}}_1$ on Bi(100). The small black dots are the projected bulk band structure calculated using the tight-binding model of Liu and Allen [17]. The red solid circles are the calculated surface state energies; the thin red line is a guide to the eye. The photoemission intensity is linearly scaled from dark blue (minimum) to white (maximum).