Proximity orbital and spin-orbital effects of graphene on monolayer transition-metal dichalcogenides (TMDCs) are investigated from first-principles. The Dirac band structure of graphene is found to lie within the semiconducting gap of TMDCs for sulfides and selenides, while it merges with the valence band for tellurides. In the former case, the proximity-induced staggered potential gaps and spin-orbit couplings (all on the meV scale) of the Dirac electrons are established by fitting to a phenomenological effective Hamiltonian. While graphene on MoS 2 , MoSe 2 , and WS 2 has a topologically trivial band structure, graphene on WSe 2 exhibits inverted bands. Using a realistic tight-binding model we find topologically protected helical edge states for graphene zigzag nanoribbons on WSe 2 , demonstrating the quantum spin Hall effect. This model also features "half-topological states," which are protected against time-reversal disorder on one edge only.

First-principles calculations of the spin-orbit coupling in graphene with hydrogen adatoms in dense and dilute limits are presented. The chemisorbed hydrogen induces a giant local enhancement of spin-orbit coupling due to sp(3) hybridization which depends strongly on the local lattice distortion. Guided by the reduced symmetry and the local structure of the induced dipole moments, we use group theory to propose realistic minimal Hamiltonians that reproduce the relevant spin-orbit effects for both single-side semihydrogenated graphene (graphone) and for a single hydrogen adatom in a large supercell. The principal linear spin-orbit band splittings are driven by the breaking of the local pseudospin inversion symmetry and the emergence of spin flips on the same sublattice.

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We propose that the observed small (100 ps) spin relaxation time in graphene is due to resonant scattering by local magnetic moments. At resonances, magnetic moments behave as spin hot spots: the spin-flip scattering rates are as large as the spin-conserving ones, as long as the exchange interaction is greater than the resonance width. Smearing of the resonance peaks by the presence of electron-hole puddles gives quantitative agreement with experiment, for about 1 ppm of local moments. Although magnetic moments can come from a variety of sources, we specifically consider hydrogen adatoms, which are also resonant scatterers. The same mechanism would also work in the presence of a strong local spin-orbit interaction, but this would require heavy adatoms on graphene or a much greater coverage density of light adatoms. To make our mechanism more transparent, we also introduce toy atomic chain models for resonant scattering of electrons in the presence of a local magnetic moment and Rashba spin-orbit interaction. DOI: 10.1103/PhysRevLett.112.116602 PACS numbers: 72.80.Vp, 72.25.Rb Graphene [1,2] has been considered an ideal spintronics [3,4] material. Its spin-orbit coupling being weak, the spin lifetimes of Dirac electrons are expected to be long, on the order of microseconds [5]. Yet experiments find tenths of a nanosecond [6][7][8][9][10][11][12][13]. This vast discrepancy has been the most outstanding puzzle of graphene spintronics. Despite intense theoretical efforts [14][15][16][17][18][19][20][21], the mechanism for the spin relaxation in graphene has remained elusive. Recently, mesoscopic transport experiments [22] found evidence that local magnetic moments could be the culprits. Here we propose a mechanism of how even a small concentration of such moments can drastically reduce the spin lifetime of Dirac electrons. If the local moments sit at resonant scatterers, such as vacancies [23][24][25] and adatoms [25,26], they can act as spin hot spots [27]: while contributing little to momentum relaxation, they can dominate spin relaxation. Our mechanism is general, but to obtain quantitative results we use model parameters corresponding to hydrogen adatoms which yield both resonant scattering and local moments [26,28,29]. The calculated spin relaxation rates for 1 ppm of local moments, when averaged over electron density fluctuations due to electron-hole puddles, are in quantitative agreement with experiment. Our theory shows that in order to increase the spin lifetime in graphene, local magnetic moments at resonant scatterers need to be chemically isolated or otherwise eliminated.In graphene the presence of local magnetic moments is not obvious, unless the magnetic sites (vacancies or adatoms) [30] are intentionally produced [24,25]. It is reasonable to expect that there are not more magnetic sites than, say, 1 ppm, in "clean" graphene samples investigated for spin relaxation in experiments [6][7][8][9][10][11][12][13]. For this concentration a simple estimate gives a weak spin relaxation rate, similar to wha...

We present a detailed theoretical study of effective spin-orbit coupling (SOC) Hamiltonians for graphene based systems, covering global effects such as proximity to substrates and local SOC effects resulting, for example, from dilute adsorbate functionalization. Our approach combines group theory and tight-binding descriptions. We consider structures with global point group symmetries D 6h , D 3d , D 3h , C6v, and C3v that represent, for example, pristine graphene, graphene mini-ripple, planar boron-nitride, graphene on a substrate and free standing graphone, respectively. The presence of certain spin-orbit coupling parameters is correlated with the absence of the specific point group symmetries. Especially in the case of C6v-graphene on a substrate, or transverse electric field-we point out the presence of a third SOC parameter, besides the conventional intrinsic and Rashba contributions, thus far neglected in literature. For all global structures we provide effective SOC Hamiltonians both in the local atomic and Bloch forms. Dilute adsorbate coverage results in the local point group symmetries C6v, C3v, and C2v which represent the stable adsorption at hollow, top and bridge positions, respectively. For each configuration we provide effective SOC Hamiltonians in the atomic orbital basis that respect local symmetries. In addition to giving specific analytic expressions for model SOC Hamiltonians, we also present general (no-go) arguments about the absence of certain SOC terms.