Spin-orbit Interaction In Graphene Research Articles

Spin-orbit coupling in monolayer graphene doped by Cd and Te atoms

Using the density functional theory, the electronic band structure of pure and doped by cadmium and tellurium atoms monolayer graphene has been studied. It is shown that doping by cadmium and tellurium leads to the appearance of an energy gap, as well as an enhancement of spin-orbit interaction in graphene. The maximum value of spin-orbit splitting in doped graphene obtained from energy spectra is 0.23 eV. The value of spin-orbit splitting for different doped atoms varies in the range of 0.08 – 0.23 eV. It should also be noted that the enhancement of spin-orbit interaction in graphene depends on the concentration of atoms doped into the lattice. At low concentrations, the energy states splitting caused by spin-orbit interaction is not observed.

Novel transport phenomena in graphene induced by strong spin-orbit interaction

Graphene is known to have small intrinsic spin-orbit Interaction (SOI). In this review, we demonstrate that SOIs in graphene can be strongly enhanced by proximity effect when graphene is deposited on the top of transition metal dichalcogenides. We discuss the symmetry of the induced SOIs and differences between TMD underlayers in the capacity of inducing strong SOIs in graphene. The strong SOIs contribute to bring novel phenomena to graphene, exemplified by robust supercurrents sustained even under tesla-range magnetic fields.

Selective enhancement of Kane Mele-type spin-orbit interaction in graphene

In order to enhance the spin orbit interaction (SOI) in graphene for seeking the dissipationless quantum spin Hall devices, unique Kane-Mele-type SOI and high mobility samples are desired. However, the common external modification of graphene often introduces “extrinsic” Rashba-type SOI, which will destroy the possible topological state, bring a certain degree of impurity scattering and reduce the sample mobility. Here we show that by the EDTA-Dy molecule dressing, the carrier mobility is even improved, and the quantum Hall plateaus are observed more clearly. The Kane-Mele type SOI is mimicked after dressing, which is evidenced by the suppressed weak localization at equal carrier densities and simultaneous Elliot-Yafet spin relaxation. This is attributed to the spin-flexural phonon coupling induced by the enhanced graphene ripples, as revealed by the in-plane magnetotransport measurement.

Absence of a giant spin Hall effect in plasma-hydrogenated graphene

The weak spin-orbit interaction in graphene was predicted to be increased, e.g., by hydrogenation. This should result in a sizable spin Hall effect (SHE). We employ two different methods to examine the spin Hall effect in weakly hydrogenated graphene. For hydrogenation we expose graphene to a hydrogen plasma and use Raman spectroscopy to characterize this method. We then investigate the SHE of hydrogenated graphene in the H-bar method and by direct measurements of the inverse SHE. Although a large nonlocal resistance can be observed in the H-bar structure, comparison with the results of the other method indicate that this nonlocal resistance is caused by a non-spin-related origin.

Spin Proximity Effects in Graphene/Topological Insulator Heterostructures.

Enhancing the spin-orbit interaction in graphene, via proximity effects with topological insulators, could create a novel 2D system that combines nontrivial spin textures with high electron mobility. To engineer practical spintronics applications with such graphene/topological insulator (Gr/TI) heterostructures, an understanding of the hybrid spin-dependent properties is essential. However, to date, despite the large number of experimental studies on Gr/TI heterostructures reporting a great variety of remarkable (spin) transport phenomena, little is known about the true nature of the spin texture of the interface states as well as their role on the measured properties. Here, we use ab initio simulations and tight-binding models to determine the precise spin texture of electronic states in graphene interfaced with a Bi2Se3 topological insulator. Our calculations predict the emergence of a giant spin lifetime anisotropy in the graphene layer, which should be a measurable hallmark of spin transport in Gr/TI heterostructures and suggest novel types of spin devices.

Origin and Magnitude of ‘Designer’ Spin-Orbit Interaction in Graphene on Semiconducting Transition Metal Dichalcogenides

We use a combination of experimental techniques to demonstrate a general occurrence of spin-orbit interaction (SOI) in graphene on transition metal dichalcogenide (TMD) substrates. Our measurements indicate that SOI is ultra-strong and extremely robust, despite it being merely interfacially-induced, with neither graphene nor the TMD substrates changing their structure. This is found to be the case irrespective of the TMD material used, of the transport regime, of the carrier type in the graphene band, and of the thickness of the graphene multilayer. Specifically, we perform weak antilocalization measurements as the simplest and most general diagnostic of SOI, and show that the spin relaxation time is very short in all cases regardless of the elastic scattering time. Such a short spin-relaxation time strongly suggests that the SOI originates from a modification of graphene band structure. We confirmed this expectation by measuring a gate-dependent beating, and a corresponding frequency splitting, in the low-field Shubnikov-de Haas magneto-resistance oscillations in high quality bilayer graphene on WSe$_2$. These measurements provide an unambiguous diagnostic of a SOI-induced splitting in the electronic band structure, and their analysis allows us to determine the SOI coupling constants for the Rashba term and the so-called spin-valley coupling term, i.e., the terms that were recently predicted theoretically for interface-induced SOI in graphene. The magnitude of the SOI splitting is found to be on the order of 10 meV, more than 100 times greater than the SOI intrinsic to graphene. Both the band character of the interfacially induced SOI, as well as its robustness and large magnitude make graphene-on-TMD a promising system to realize and explore a variety of spin-dependent transport phenomena, such as, in particular, spin-Hall and valley-Hall topological insulating states.

A scheme to realize the quantum spin-valley Hall effect in monolayer graphene

Quantum spin Hall effect was first predicted in graphene. However, the weak spin orbit interaction in graphene meant that the search for quantum spin Hall effect in graphene never fructified. In this work we show how to generate the quantum spin-valley Hall effect in graphene via quantum pumping by adiabatically modulating a magnetic impurity and an electrostatic potential in a monolayer of strained graphene. We see that not only exclusive spin polarized currents can be pumped in the two valleys in exactly opposite directions but one can have pure spin currents flowing in opposite directions in the two valleys, we call this novel phenomena the quantum spin-valley Hall effect. This means that the twin effects of quantum valley Hall and quantum spin Hall can both be probed simultaneously in the proposed device. This work will significantly advance the field of graphene spintronics, hitherto hobbled by the lack of spin-orbit interaction. We obviate the need for any spin orbit interaction and show how graphene can be manipulated to posses features exclusive to topological insulators.

Gate-Tunable Spin-Charge Conversion and the Role of Spin-Orbit Interaction in Graphene.

The small spin-orbit interaction of carbon atoms in graphene promises a long spin diffusion length and the potential to create a spin field-effect transistor. However, for this reason, graphene was largely overlooked as a possible spin-charge conversion material. We report electric gate tuning of the spin-charge conversion voltage signal in single-layer graphene. Using spin pumping from an yttrium iron garnet ferrimagnetic insulator and ionic liquid top gate, we determined that the inverse spin Hall effect is the dominant spin-charge conversion mechanism in single-layer graphene. From the gate dependence of the electromotive force we showed the dominance of the intrinsic over Rashba spin-orbit interaction, a long-standing question in graphene research.

Gauge transformations of spin-orbit interactions in graphene

Inclusion of spin-dependent interactions in graphene in the vicinity of the Dirac points can be posed in terms of non-Abelian gauge potentials. Such gauge potentials being surrogates of physical electric fields and material parameters, only enjoy a limited gauge freedom. A general gauge transformation thus changes the physical model. We argue that this property can be useful in connecting reference physical situations, such as free particle or Rashba interactions to non-trivial physical Hamiltonians with a new set of spin-orbit interactions, albeit constrained to being isoenergetic. We analyse different combinations of spin-orbit interactions in the case of monolayer graphene and show how they are related by means of selected non-Abelian gauge transformations.

Engineering quantum spin Hall effect in graphene nanoribbons via edge functionalization

Kane and Mele predicted that in the presence of spin-orbit interaction graphene realizes the quantum spin Hall state [Phys. Rev. Lett. 95, 226801 (2005)]. However, exceptionally weak intrinsic spin-orbit splitting in graphene ($\ensuremath{\approx}$${10}^{\ensuremath{-}5}$ eV) inhibits experimental observation of this topological insulating phase. To circumvent this problem, we propose an approach towards controlling spin-orbit interactions in graphene by means of covalent functionalization of graphene edges with functional groups containing heavy elements. Proof-of-concept first-principles calculations show that very strong spin-orbit coupling can be induced in realistic models of narrow graphene nanoribbons with tellurium-terminated edges. We demonstrate that electronic bands with strong Rashba splitting as well as the quantum spin Hall state spanning broad energy ranges can be realized in such systems. Our work thus helps pave the way towards engineering topological electronic phases in nanostructures based on graphene and other materials by means of locally introduced spin-orbit interactions.

Rashba spin-orbit interaction and birefringent electron optics in graphene

Electron optics exploits the analogies between rays in geometrical optics and electron trajectories, leading to interesting insights and potential applications. Graphene, with its two-dimensionality and photon-like behavior of its charge carriers, is the perfect candidate for the exploitation of electron optics. We show that a circular gate-controlled region in the presence of Rashba spin-orbit interaction in graphene may indeed behave as a Veselago electronic lens but with two different indices of refraction. We demonstrate that this birefringence results in complex caustics patterns for a circular gate, selective focusing of different spins, and the possible direct measurement of the Rashba coupling strength in scanning probe experiments.

Designer quantum spin Hall phase transition in molecular graphene

Graphene was the first material predicted to be a time-reversal-invariant topological insulator; however, the insulating gap is immeasurably small owing to the weakness of spin-orbit interactions in graphene. A recent experiment [1] demonstrated that designer honeycomb lattices with graphene-like "Dirac" band structures can be engineered by depositing a regular array of carbon monoxide atoms on a metallic substrate. Here, we argue that by growing such designer lattices on metals or semiconductors with strong spin-orbit interactions, one can realize an analog of graphene with strong intrinsic spin-orbit coupling, and hence a highly controllable two-dimensional topological insulator. We estimate the range of substrate parameters for which the topological phase is achievable, and consider the experimental feasibility of some candidate substrates.

Tunable Spin–Orbit Interaction in Trilayer Graphene Exemplified in Electric-Double-Layer Transistors

Taking advantage of ultrahigh electric field generated in electric-double-layer transistors (EDLTs), we investigated spin-orbit interaction (SOI) and its modulation in epitaxial trilayer graphene. It was found in magnetotransport that the dephasing length L(φ) and spin relaxation length L(so) of carriers can be effectively modulated with gate bias. As a direct result, SOI-induced weak antilocalization (WAL), together with a crossover from WAL to weak localization (WL), was observed at near-zero magnetic field. Interestingly, among existing localization models, only the Iordanskii-Lyanda-Geller-Pikus theory can successfully reproduce the obtained magnetoconductance well, serving as evidence for gate tuning of the weak but distinct SOI in graphene. Realization of SOI and its large tunability in the trilayer graphene EDLTs provides us with a possibility to electrically manipulate spin precession in graphene systems without ferromagnetics.

Spin dephasing and pumping in graphene due to random spin-orbit interaction

We consider spin effects related to the random spin-orbit interaction in graphene. Such a random interaction can result from the presence of ripples and/or other inhomogeneities at the graphene surface. We show that the random spin-orbit interaction generally reduces the spin dephasing (relaxation) time, even if the interaction vanishes on average. Moreover, the random spin-orbit coupling also allows for spin manipulation with an external electric field. Due to the spin-flip interband as well as intraband optical transitions, the spin density can be effectively generated by periodic electric field in a relatively broad range of frequencies.

Rashba spin-orbit interaction in graphene and zigzag nanoribbons

We investigate the effects of Rashba spin-orbit (RSO) interactions on the electronic band structure and corresponding wave functions of graphene. By exactly solving a tight-binding model Hamiltonian we obtain the expected splitting of the bands---due to the SU(2) spin symmetry breaking---that is accompanied by the appearance of additional Dirac points. These points are originated by valence-conduction-band crossings. By introducing a convenient gauge transformation we study a model for zigzag nanoribbons with RSO interactions. We show that RSO interactions lift the quasidegeneracy of the edge band while introducing a state-dependent spin separation in real space. Calculation of the average magnetization perpendicular to the ribbon plane suggest that RSO could be used to produce spin-polarized currents. Comparisons with the intrinsic spin-orbit interaction proposed to exist in graphene are also presented.

Spin-orbit gap of graphene: First-principles calculations

Even though graphene is a low energy system consisting of the two dimensional honeycomb lattice of carbon atoms, its quasi-particle excitations are fully described by the 2+1 dimensional relativistic Dirac equation. In this paper we show that while the spin-orbit interaction in graphene is of the order of $4 meV$, it opens up a gap of the order of $10^{-3} meV$ at the Dirac points. We present the first principle calculation of the spin-orbit gap, and explain the behavior in terms of a simple tight-binding model. Our result also shows that the recently predicted quantum spin Hall effect in graphene can only occur at unrealistically low temperature.

Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps

A continuum model for the effective spin orbit interaction in graphene is derived from a tight-binding model which includes the $\pi$ and $\sigma$ bands. We analyze the combined effects of the intra-atomic spin-orbit coupling, curvature, and applied electric field, using perturbation theory. We recover the effective spin-orbit Hamiltonian derived recently from group theoretical arguments by Kane and Mele. We find, for flat graphene, that the intrinsic spin-orbit coupling $\Hi \propto \Delta^ 2$ and the Rashba coupling due to a perpendicular electric field ${\cal E}$, $\Delta_{\cal E} \propto \Delta$, where $\Delta$ is the intra-atomic spin-orbit coupling constant for carbon. Moreover we show that local curvature of the graphene sheet induces an extra spin-orbit coupling term $\Delta_{\rm curv} \propto \Delta$. For the values of $\cal E$ and curvature profile reported in actual samples of graphene, we find that $\Hi < \Delta_{\cal E} \lesssim \Delta_{\rm curv}$. The effect of spin-orbit coupling on derived materials of graphene, like fullerenes, nanotubes, and nanotube caps, is also studied. For fullerenes, only $\Hi$ is important. Both for nanotubes and nanotube caps $\Delta_{\rm curv}$ is in the order of a few Kelvins. We reproduce the known appearance of a gap and spin-splitting in the energy spectrum of nanotubes due to the spin-orbit coupling. For nanotube caps, spin-orbit coupling causes spin-splitting of the localized states at the cap, which could allow spin-dependent field-effect emission.