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.

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...

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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.

We report on theoretical investigations of the spin-orbit coupling effects in fluorinated graphene. First-principles density functional calculations are performed for the dense and dilute adatom coverage limits. The dense limit is represented by the single-side semifluorinated graphene, which is a metal with spin-orbit splittings of about 10 meV. To simulate the effects of a single adatom, we also calculate the electronic structure of a 10 × 10 supercell, with one fluorine atom in the top position. Since this dilute limit is useful to study spin transport and spin relaxation, we also introduce a realistic effective hopping Hamiltonian, based on symmetry considerations, which describes the supercell bands around the Fermi level. We provide the Hamiltonian parameters which are best fits to the first-principles data. We demonstrate that, unlike for the case of hydrogen adatoms, fluorine's own spin-orbit coupling is the principal cause of the giant induced local spin-orbit coupling in graphene. The sp 3 hybridization induced transfer of spin-orbit coupling from graphene's σ bonds, important for hydrogenated graphene, contributes much less. Furthermore, the magnitude of the induced spin-orbit coupling due to fluorine adatoms is about 1000 times more than that of pristine graphene, and 10 times more than that of hydrogenated graphene. Also unlike hydrogen, the fluorine adatom is not a narrow resonant scatterer at the Dirac point. The resonant peak in the density of states of fluorinated graphene in the dilute limit lies 260 meV below the Dirac point. The peak is rather broad, about 300 meV, making the fluorine adatom only a weakly resonant scatterer.

A theory of spin-orbit coupling in bilayer graphene is presented. The electronic band structure of the AB bilayer in the presence of spin-orbit coupling and a transverse electric field is calculated from first principles using the linearized augmented plane-wave method implemented in the WIEN2K code. The first-principles results around the K points are fitted to a tight-binding model. The main conclusion is that the spin-orbit effects in bilayer graphene derive essentially from the single-layer spin-orbit coupling which comes almost solely from the d orbitals. The intrinsic spin-orbit splitting (anticrossing) around the K points is about 24 μeV for the low-energy valence and conduction bands, which are closest to the Fermi level, similarly as in the single-layer graphene. An applied transverse electric field breaks space inversion symmetry and leads to an extrinsic (also called Bychkov-Rashba) spin-orbit splitting. This splitting is usually linearly proportional to the electric field. The peculiarity of graphene bilayer is that the low-energy bands remain split by 24 μeV independently of the applied external field. The electric field, instead, opens a semiconducting band gap separating these low-energy bands. The remaining two high-energy bands are spin split in proportion to the electric field; the proportionality coefficient is given by the second intrinsic spin-orbit coupling, whose value is 20 μeV. All the band-structure effects and their spin splittings can be explained by our tight-binding model, in which the spin-orbit Hamiltonian is derived from symmetry considerations. The magnitudes of intra-and interlayer couplings-their values are similar to the single-layer graphene ones-are determined by fitting to first-principles results.

We investigate an effective model of proximity modified graphene (or symmetrylike materials) with broken time-reversal symmetry. We predict the appearance of quantum anomalous Hall phases by computing bulk band gap and Chern numbers for benchmark combinations of system parameters. Allowing for staggered exchange field enables quantum anomalous Hall effect in flat graphene with Chern number C = 1. We explicitly show edge states in zigzag and armchair nanoribbons and explore their localization behavior. Remarkably, the combination of staggered intrinsic spin-orbit and uniform exchange coupling gives topologically protected (unlike in time-reversal systems) pseudohelical states, whose spin is opposite in opposite zigzag edges. Rotating the magnetization from out of plane to in plane makes the system trivial, allowing to control topological phase transitions. We also propose, using density functional theory, a material platform-graphene on Ising antiferromagnet MnPSe3-to realize staggered exchange (pseudospin Zeeman) coupling.