Rashba-Type Spin-Orbit Splitting of Quantum Well States in Ultrathin Pb Films

A Rashba-type spin-orbit splitting is found for quantum well states formed in ultrathin Pb films on Si(111). The resulting momentum splitting is comparable to what is found for semiconductor heterostructures. The splitting shows no coverage dependency and the sign of the spin polarization is reversed compared to Rashba splitting in the Au(111) surface state. We explain our results by competing effects at the two boundaries of the Pb layer.

Figure 1

(a) Measured spin integrated ARPES data for a 10 ML thick Pb film on $\mathrm{Si}(111)\sqrt{3}$. (b) Measurement geometry and sample coordinates.

Figure 2

SARPES data for an 8 ML thick Pb layer on $\mathrm{Si}(111)\sqrt{3}$ at $k_y=-0.08{\AA }^{-1}$ and $k_x=0$. (a) Measured (open circles) and modeled (solid line) spin polarization in the $x$ direction of the sample. (b) Measured spin polarization along the $y$ (blue circles) and $z$ (green diamonds) direction of the sample. (c) Spin resolved spectra obtained from the spin polarization in the $x$ direction. (d) Schematic representation of a constant energy surface where the arrows of band $A$ and $B$ refer to the direction of the spin polarization axis.

Figure 3

(a) Measured (symbols) and fitted (solid line) polarization spectra for a 10 ML thick Pb film at $k_y=0$. (b) Resulting polarization spectra for two Gaussians with opposite spin (inset) where the energy spacing is varied in steps of 1 meV. (c) Polarization spectrum and resulting spin resolved spectra for a 22 ML thick Pb film obtained at $k_y=-0.08{\AA }^{-1}$ and $k_x=0$. (d) Measured (red diamonds) and calculated (blue crosses) spin splitting as function of coverage at $k_y=-0.08{\AA }^{-1}$ and $k_x=0$, the blue circles show the intuitively expected $1/\mathrm{\text{thickness}}$ dependence.

Figure 4

DFT calculations for 10 ML Pb on Si(111) with the Si (left) and Pb (right) lattice constant. The Si states are shown in gray, Pb states located in the topmost layers in black. The spin-split bands are indicated by colored (or shaded) lines and the size of this splitting is shown in the lower panels together with experimental results. The red (or gray) lines in the lower panels are fits to obtain the Rashba parameter. The oscillations in energy splitting are the result of hybridization between the QWS and substrate bands in the calculations.