Rashba Spin-Orbit Coupling in Image Potential States

The search in two-dimensional condensed matter systems of Rashba-type spin-polarized electronic states is aimed by the possibility to control and manipulate the spin orientation. In this Letter, for the first time, we report on the experimental evidence of a Rashba-type spin splitting in the $n=1$ image potential state. The image potential state Rashba splitting here measured at the graphene/Ir(111) interface, as confirmed by theoretical considerations, can be detectable to any metal surface with a significant spin-orbit coupling.

Figure 1

(a) Angle-resolved nonlinear photoemission spectra collected with a photon energy of 3.12 eV and $P$-polarized light at the graphene/Ir(111) interface. (b) Angle-resolved linear photoemission spectra collected with a photon energy of 6.24 eV and $P$-polarized light at the graphene/Ir(111) interface. (c) Energy position versus $k_{\parallel }$ momentum for the first image potential state IPS1 and the surface states SS. The parabolic fit (line) of the data gives the effective mass and the Rashba effect reported in the figure.

Figure 2

Comparison between nonlinear photoemission (blue) and linear photoemission (red) spectra collected at a photon energy of 4.64 eV at $k_{\parallel }=0$ and $P$-polarized light. Being that the work function ($\mathrm{\Phi }=4.45\pm 0.05\mathrm{eV}$) is smaller than the laser photon energy, in order to measure the nonlinear contribution in the photoemission spectrum, a positive potential of $+0.7\mathrm{V}$ was applied to the sample. In the inset we report the angular dispersion of the photoemission spectra collected at a photon energy of 4.64 eV.

Figure 3

Comparison between nonlinear photoemission spectra collected at a photon energy of 4.64 eV in right (green) and left (blue) circular polarization, and the difference between the best fit of the corresponding signals (gray). The measurements are acquired at the $\overline{\mathrm{\Gamma }}$ point ($\theta =0°$) and at symmetric angles ($\theta =9°$ and $\theta =-9°$) corresponding to $k_{\parallel }=0$ and $k_{\parallel }=\pm 0.16{\AA }^{-1}$, respectively. In the inset, nonlinear photoemission spectra collected at a different photon energy 3.12 eV by changing the circular polarization from right (green) to left (blue) at the same $k_{\parallel }$ values ($k_{\parallel }=0$ and $k_{\parallel }=-0.16{\AA }^{-1}$, the data at $k_{\parallel }=+0.16{\AA }^{-1}$ are not available for experimental constraint). The dichroic signals measured with the two photon energies are comparable.

Figure 4

Squared amplitude of the wave functions at $\overline{\mathrm{\Gamma }}$ of SS of Ir(111) (green), IPS1 of Ir(111) (red), and IPS1 of graphene/Ir(111) (blue). Vertical lines correspond to the Ir surface layer ($z=0$) and graphene plane. In the inset: plot of the linear screening density $n_1$ of Ir(111) and graphene/Ir(111) due to the application of an external charge. The arrows mark nuclear positions while vertical dashed lines represent the image plane of the two systems.