Spin-resolved photoemission and ab initio theory of graphene/SiC

The spin-orbit splitting of graphene $\pi$ states can be strongly enhanced by external influences such as corrugation or proximity to heavier atoms. Here we investigate experimentally and theoretically whether such strong enhancement is possible for graphene on SiC(0001). By spin- and angle-resolved photoemission we found for two independently grown samples no resolvable spin-orbit splitting with an upper limit of our analysis of 20 meV. Our ab initio calculations predict a low spin-orbit splitting of 0.05 meV with small anisotropy but a local tenfold enhancement where hybridization with SiC substrate bands occurs.

Figure 1

Region near the $\overline{\mathrm{K}}$ point of the graphene Brillouin zone with calculated constant energy surface (at $\sim 0.8$ eV below the Dirac point) and measurements of the spin-orbit splitting from sample A (green, $+$) and sample B (yellow, $\times$). The upper limit of the spin splitting of each measurement (${\delta }_{UL}$, in meV) is given at each measured k point separately for spin quantization axes (a) along $x$ (parallel to $\overline{\Gamma }$$\overline{\mathrm{K}}$) and (b) along $y$ (perpendicular to $\overline{\Gamma }$$\overline{\mathrm{K}}$). Labels $k_1$, $k_2$, and $k_3$ denote the data points corresponding to Fig. 2.

Figure 2

(a),(b) Spin- and angle-resolved photoemission for sample A with k along the $\overline{\Gamma }$$\overline{\mathrm{K}}$ line where no splitting was predicted. Parts (a) and (b) refer to the two orthogonal spin quantization axes in the graphene plane. (c),(d) Same as (a),(b) but for sample B and k along $\overline{\mathrm{K}}$$\overline{\mathrm{M}}$ where maximum spin-orbit splitting has been predicted. (e),(f) Same as (c),(d) but for k along the direction perpendicular to $\overline{\Gamma }$$\overline{\mathrm{K}}$ where 200 meV spin-orbit splitting has been reported. The spin splitting in the present figure is less than 10 meV.

Figure 3

Lower panel: $p_z$ band of graphene on a C-terminated SiC substrate with a C-deficient interface layer. The inset shows the structural model (the lower surface of the film is passivated with hydrogen) with Si, C, and H atoms indicated by large, medium, and small spheres. $k_{\parallel }=0$ indicates the $\overline{\mathrm{K}}$ point, negative $k_{\parallel }$ values signify the direction towards $\overline{\Gamma }$, positive $k_{\parallel }$ values towards $\overline{\mathrm{M}}$. Upper panel: Spin-orbit splitting of the upper (blue) and lower branch (red) of the Dirac cone formed by the $p_z$ band. At the $\overline{\mathrm{K}}$ point, the splitting reduces to about 20 $\mu$eV; at a band crossing at around $0.15$ Å${}^{-1}$ it can reach more than 0.1 meV.