Denis Kochan

Spin-orbit coupling in hydrogenated graphene.

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.

Spin relaxation mechanism in graphene: resonant scattering by magnetic impurities

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.

Theory of spin-orbit coupling in bilayer graphene

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.

Model spin-orbit coupling Hamiltonians for graphene systems

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, C-6v, and C-3v that represent, for example, pristine graphene, graphene miniripple, 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 C-6v -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 C-6v, C-3v, and C-2v, 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.

Resonant scattering by magnetic impurities as a model for spin-relaxation in bilayer graphene

We propose that the observed spin relaxation in bilayer graphene is due to resonant scattering by magnetic impurities. We analyze a resonant scattering model due to adatoms on both dimer and nondimer sites, finding that only the former give narrow resonances at the charge neutrality point. Opposite to single-layer graphene, the measured spin-relaxation rate in the graphene bilayer increases with carrier density. Although it has been commonly argued that a different mechanism must be at play for the two structures, our model explains this behavior rather naturally in terms of different broadening scales for the same underlying resonant processes. Not only do our results-using robust and first-principles inspired parameters-agree with experiment, they also predict an experimentally testable sharp decrease of the spin-relaxation rate at high carrier densities.

Spin-orbit coupling in fluorinated graphene

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

Spin-orbit coupling in methyl-functionalized graphene

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Theory of the ac Spin-Valve Effect

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, fluorines own spin-orbit coupling is the principal cause of the giant induced local spin-orbit coupling in graphene. The

Theory of spin-orbit-induced spin relaxation in functionalized graphene

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Spin-orbit coupling in graphene structures

hybridization induced transfer of spin-orbit coupling from graphenes