Spin-orbit Coupling In Graphene Research Articles

Sizeable Kane–Mele-like spin orbit coupling in graphene decorated with iridium clusters

The spin-orbit coupling strength of graphene can be enhanced by depositing iridium nanoclusters. Weak localization is intensely suppressed near zero fields after the cluster deposition, rather than changing to weak anti-localization. Fitting the magnetoresistance gives the spin relaxation time, which increases by two orders with the application of a back gate. The spin relaxation time is found to be proportional to the electronic elastic scattering time, demonstrating the Elliot–Yafet spin relaxation mechanism. A sizeable Kane–Mele-like coupling strength of over 5.5 meV is determined by extrapolating the temperature dependence to zero.

Extrinsic spin Hall effect from anisotropic Rashba spin-orbit coupling in graphene

The study of the spin Hall effect in graphene is an active field of research, but its experimental realization is proven to be difficult due to the inherently weak intrinsic spin-orbit interaction. Thus, one needs to rely on extrinsic spin-orbit scattering to be able to probe this effect in graphene. The authors of this paper have reported some progress in this direction. They predict that adatoms on graphene can induce an anisotropic Rashba spin-orbit coupling, and the degree of anisotropy has a noticeable effect on the energy dependence of the spin Hall angle.

Electron-spin to phonon coupling in graphene decorated with heavy adatoms

The naturally weak spin-orbit coupling in Graphene can be largely enhanced by adatom deposition (e.g. Weeks et al. Phys. Rev. X 1, 021001 (2011)). However, the dynamics of the adatoms also induces a coupling between phonons and the electron spin. Using group theory and a tight-binding model, we systematically investigate the coupling between the low-energy in-plane phonons and the electron spin in single-layer graphene uniformly decorated with heavy adatoms. Our results provide the foundation for future investigations of spin transport and superconductivity in this system. In order to quantify the effect of the coupling to the lattice on the electronic spin dynamics, we compute the spin-flip rate of electrons and holes. We show that the latter exhibits a strong dependence on the quasi-particle energy and system temperature.

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 $10 \times 10$ 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 $\sigma$ 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.

Controllable magnetic correlation between two impurities by spin-orbit coupling in graphene.

Two magnetic impurities on the edge of a zigzag graphene nanoribbon strongly interact with each other via indirect coupling, which can be mediated by conducting carriers. By means of Quantum Monte Carlo (QMC) simulations, we find that the spin-orbit coupling λ and the chemical potential μ in system can be used to drive the transition of local-spin exchange from ferromagnetism to anti-ferromagnetism. Since the tunable ranges for λ and μ in graphene are experimentally reachable, we thus open the possibilities for its device application. The symmetry in spatial distribution is broken by the vertical and the transversal spin-spin correlations due to the effect of spin-orbit coupling, leading to the spatial anisotropy of spin exchange, which distinguish our findings from the case in normal Fermi liquid.

Transport study of graphene adsorbed with indium adatoms

Enhancement of the spin-orbit coupling in graphene may lead to various topological phenomena and also find applications in spintronics. Adatom adsorption has been proposed as an effective way to achieve the goal. In particular, great hope has been held for indium in strengthening the spin-orbit coupling and realizing the quantum spin Hall effect. To search for evidence of the spin-orbit coupling in graphene adsorbed with indium adatoms, we carry out extensive transport measurements. It is found that indium adatoms dope graphene and introduce significant Coulomb scattering. No signature of the spin-orbit coupling is observed in the weak localization magnetoconductance and nonlocal spin Hall effect. Possible explanations are discussed.

Spin Force on Pseudo Spin Current in Graphene

The present study investigated spin force by using pseudo spin-orbit coupling in an artificial atomic structure for graphene. This spin force, which is applied on pseudo spin current, can be controlled by graphene gap and electric field due to charged nanodot. It seems that, by this force can be constructed a logical system from graphene and semiconductors. In addition, this force can be used for understanding the Zitterbewegung of electron wave packet with pseudo spin-orbit coupling in graphene and create of the charge Hall effect in semiconductors and graphene.

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-orbit force in graphene with Rashba spin-orbit coupling

The observation of Rashba spin splitting in graphene on the Ni (111) substrate, motivates the studies to manipulate electron spin via Rashba spin-orbit coupling in graphene. We derive the effective spin-orbit force in Rashba coupled graphene from the Heisenberg equation of motion. The spin-orbit force, different from that in conventional semiconductors, can provide us a physical picture of unusual spin separation due to Rashba spin-orbit coupling in graphene. Finally, we numerically calculate spin Hall conductance and qualitatively explain the result by the spin-orbit force picture in graphene.

SPIN-ORBIT COUPLING IN GRAPHENE UNDER UNIAXIAL STRAIN: TIGHT-BINDING APPROACH AND FIRST-PRINCIPLES CALCULATIONS

Tuning the spin-orbit coupling (SOC) in graphene is highly desired for its application in spintronics. In this paper, we calculated the band gap induced by SOC in graphene under uniaxial strain from a tight-binding model, and found that the band gap has a monotonic increasing dependence on the strain in the range of -20% to 15%. Our results suggest that strain can be used as a reversible and controllable way to tune the SOC in graphene. First-principles calculations were performed, confirming the results of tight-binding approximation.

Tight-binding theory of the spin-orbit coupling in graphene

The spin-orbit coupling in graphene induces spectral gaps at the high-symmetry points. The relevant gap at the $\ensuremath{\Gamma}$ point is similar to the splitting of the $p$ orbitals in the carbon atom, being roughly 8.5 meV. The splitting at the $\mathrm{K}$ point is orders of magnitude smaller. Earlier tight-binding theories indicated the value of this intrinsic gap of $1\text{ }\ensuremath{\mu}\text{eV}$, based on the $\ensuremath{\sigma}\text{\ensuremath{-}}\ensuremath{\pi}$ coupling. All-electron first-principles calculations give much higher values, between 25 and $50\text{ }\ensuremath{\mu}\text{eV}$, due to the presence of the orbitals of the $d$ symmetry in the Bloch states at $\mathrm{K}$. A realistic multiband tight-binding model is presented to explain the effects the $d$ orbitals play in the spin-orbit coupling at $\mathrm{K}$. The $\ensuremath{\pi}\text{\ensuremath{-}}\ensuremath{\sigma}$ coupling is found irrelevant to the value of the intrinsic spin-orbit-induced gap. On the other hand, the extrinsic spin-orbit coupling (of the Bychkov-Rashba type), appearing in the presence of a transverse electric field, is dominated by the $\ensuremath{\pi}\text{\ensuremath{-}}\ensuremath{\sigma}$ hybridization, in agreement with previous theories. Tight-binding parameters are obtained by fitting to first-principles calculations, which also provide qualitative support for the model when considering the trends in the spin-orbit-induced gap in graphene under strain. Finally, an effective single-orbital next-nearest-neighbor hopping model accounting for the spin-orbit effects is derived.

Spontaneous persistent currents in a quantum spin Hall insulator

We present a new mechanism for dissipationless persistent charge current. Two dimensional topological insulators hold dissipationless spin currents in their edges so that, for a given spin orientation, a net charge current flows which is exactly compensated by the counter-flow of the opposite spin. Here we show that ferromagnetic order in the edge upgrades the spin currents into persistent charge currents, without applied fields. For that matter, we study an interacting graphene zigzag ribbon with spin-orbit coupling. We find three electronic phases with magnetic edges that carry currents reaching 0.4nA, comparable to persistent currents in metallic rings, for the small spin orbit coupling in graphene. One of the phases is a valley half-metal.

Impurity-Induced Spin-Orbit Coupling in Graphene

We study the effect of impurities in inducing spin-orbit coupling in graphene. We show that the sp3 distortion induced by an impurity can lead to a large increase in the spin-orbit coupling with a value comparable to the one found in diamond and other zinc-blende semiconductors. The spin-flip scattering produced by the impurity leads to spin scattering lengths of the order found in recent experiments. Our results indicate that the spin-orbit coupling can be controlled via the impurity coverage.