Surface versus bulk contributions to the Rashba splitting in surface systems

We report on a quantitative investigation on the Rashba effect in the Shockley state of the model system Ag/Au(111) by means of angle-resolved photoemission spectroscopy with high-energy resolution. The spectra are discussed in detail in comparison with results of one-step photoemission calculations. The systematic overestimation in the wave-vector splitting present in all actual theoretical studies is explained in terms of an insufficient description of the surface potential. Also, we conclude that the coupling between the semi-infinite bulk and the surface potential mediated by the bulk reflection matrix $B$ is of major importance for a quantitative description of the Rashba effect.

Figure 1

Calculated dispersion of the Au(111) Shockley surface state as a function of the coupling strength. Left panel: 0.25$\left|B\right|$; middle panel: 0.50$\left|B\right|$; right panel: 1.0$\left|B\right|$.

Figure 2

Comparison of calculated and second derivative of measured ARUPS spectra containing surface states of different Ag coverages on Au(111). From left to right 0, 1, 2 monolayers of Ag on Au(111). Upper panel: calculations; lower panel: experiment.

Figure 3

Comparison of calculated and measured dispersions of the spin-orbit (SO)-split surface state of different Ag coverages on Au(111). Shown are the parabolic functions defined by $k_F$ and $E_0$.

Figure 4

Maximum binding energy $E_0$, SO splitting $\Delta k$, effective band mass $m_{\mathrm{eff}}$, and Rashba parameter ${\alpha }_R$ evaluated from ARUPS measurements and calculations. The errors bars result from the determination accuracy of peak positions in $E$ and $k_{\parallel }$ and error propagation.