1. Rashba splitting of graphene on Ni, Au, or Ag(111) substrates
Z. Y. Li, S. Qiao and Z. Q. Yang
State Key Laboratory of Surface Physics and Department of Physics,
Fudan University, Shanghai , China
Introduction: For pure graphene, the spin-orbit (SO) splitting at the Dirac points is too small (less than 0.1meV) to be used to manipulate the spin in the carbon based material[1]. In 2008, Dedkov et al. reported an extraordinarily large Rashba splitting (225 meV) of graphene pi-band on Ni(111) substrate[2]. The effect was attributed by them to the large effective electric field at the graphene/Ni(111) (Gr/Ni) interface[2]. However, Rader et al. gave totally opposite conclusions about the graphene grown on metal 3d ferromagnets[3]. They did not observed any sizable Rashba-type SO effect or spin polarization of the graphene on both Ni and Co(111) substrates, and the sums of Rashba and exchange splitting were estimated to be less than 45 meV for the two systems[3].
Method: Ab initio calculations within density functional theory (DFT). The slab model is used to simulate the metallic substrate under graphene.
Fig.1: The most stable geometries of graphene (a) on Ni(111) and (b) on Au or Ag(111). 
Results
Fig.2: Graphene pi-band dispersion on Ni(111). The wave vector k is in the unit of the vector ΓM. The number of metal layer N=13 (a, b, c) and N=1 (d, e, f), respectively. The layer distance between graphene and Ni d=2.0 Å, which is also the equilibrium separation in the two structures. C
Metal
Fig. 3: Graphene pi-band dispersion on (a, b, c) Au(111) and (d, e, f) Ag(111). The layer distances d are shown in figures. The equilibrium separations are about 2.5 Å and 2.4 Å for the Gr/Au and Gr/Ag structures, respectively. The surface states (SSs) of Au(111) and Ag(111) are also shown in figures. The configuration of the two ideal structures is shown in Fig. 1(a).
Fig. 4: The dispersion of the most stable Gr/Au structure with 9 layers Au(111) along ΓM [(a), (b) and (c)] and ΓKM [(d), (e) and (f)]. The equilibrium separation is about 3.3 Å. The configuration is shown in Fig. 1(b). The Fermi level is at zero. The thick red lines on the right-half panel show the Dirac points. The inset in (d) shows the SO splitting of the Dirac point.
Conclusion
The monolayer graphene does have Rashba splitting when it is deposited on Ni(111) surface. However, the Rashba splitting is just about 10 meV. The SO splitting of graphene on metals is just from the interaction between graphene and a few layer metals near the interface. For the practical Gr/Au(111) structure, the splitting can be up to about 25 meV. The effect is rationalized by the asymmetrical potential distributions at the two sides of graphene induced by the substrates and the hybridization of the pi electrons of graphene with the d electrons of metals. The Rashba splitting is not found to relate closely to the charge transfer between the graphene and the substrates.
References:
[1] Y. Yao, F. Ye, X.-L. Qi, S.-C. Zhang, and Z. Fang, Phys. Rev. B 75, (R) (2007).
[2] Yu. S. Dedkov, M. Fonin, U. Rüdiger, and C. Laubschat, Phys. Rev. Lett. 100, (2008).
[3] O. Rader, A. Varykhalov, J. Sánchez-Barriga, D. Marchenko, A. Rybkin, and A. M. Shikin, Phys. Rev. Lett. 102, (2009).