Spin-orbit Coupling In Graphene Research Articles

Determining spin-orbit coupling in graphene by quasiparticle interference imaging

Inducing and controlling spin-orbit coupling (SOC) in graphene is key to create topological states of matter, and for the realization of spintronic devices. Placing graphene onto a transition metal dichalcogenide is currently the most successful strategy to achieve this goal, but there is no consensus as to the nature and the magnitude of the induced SOC. Here, we show that the presence of backscattering in graphene-on-WSe2 heterostructures can be used to probe SOC and to determine its strength quantitatively, by imaging quasiparticle interference with a scanning tunneling microscope. A detailed theoretical analysis of the Fourier transform of quasiparticle interference images reveals that the induced SOC consists of a valley-Zeeman (λvZ ≈ 2 meV) and a Rashba (λR ≈ 15 meV) term, one order of magnitude larger than what theory predicts, but in excellent agreement with earlier transport experiments. The validity of our analysis is confirmed by measurements on a 30 degree twist angle heterostructure that exhibits no backscattering, as expected from symmetry considerations. Our results demonstrate a viable strategy to determine SOC quantitatively by imaging quasiparticle interference.

Robust propagating in-gap modes due to spin-orbit domain walls in graphene

Recently, great experimental efforts towards designing topological electronic states have been invested in layered incommensurate heterostructures which form various nano- and meso-scale domains. In particular, it has become clear that a delicate interplay of different spin-orbit terms is induced in graphene on transition metal dichalcogenide substrates. We therefore theoretically study various types of domain walls in spin-orbit coupling in graphene looking for robust one-dimensional propagating electronic states. To do so, we use an interface Chern number and a spectral flow analysis in the low-energy theory and contrast our results to the standard arguments based on valley-Chern numbers or Chern numbers in continuum models. Surprisingly, we find that a sign-changing domain wall in valley-Zeeman spin-orbit coupling binds two robust Kramers pairs, within the bulk gap opened due to a simultaneous presence of Rashba coupling. We also study the robustness to symmetry breaking and lattice backscattering effects in tight-binding models. We show an explicit mapping of our valley-Zeeman domain wall to a domain wall in gated spinless bilayer graphene. We discuss the possible spectroscopic and transport signatures of various types of spin-orbit coupling domain walls in heterostructures.

Electron spin resonance in a proximity-coupled MoS2/graphene van der Waals heterostructure

Coupling graphene’s excellent electron and spin transport properties with a higher spin–orbit coupling (SOC) material allows tackling the hurdle of spin manipulation in graphene due to the proximity to van der Waals layers. Here, we use magneto-transport measurements to study the electron spin resonance on a combined system of graphene and MoS2 at 1.5 K. The electron spin resonance measurements are performed in the frequency range of 18–33 GHz, which allows us to determine the g-factor in the system. We measure the average g-factor of 1.91 for our hybrid system, which is a considerable shift compared to that observed in graphene on SiO2. This is a clear indication of proximity induced SOC in graphene in accordance with theoretical predictions.

Nonvolatile tuning of the spin–orbit coupling in graphene by a ferroelectric dipole

Spin–orbit coupling (SOC) offers an alternative technique for generating pure spin currents in non-magnetic materials and controlling spin precessions for spin-field effect transistors. In addition, introducing SOC into graphene causes pristine graphene to evolve into a new condensed matter phase, such as the topological insulator state (quantum spin Hall state). Thus, the control of SOC in graphene is essential for its functional spin-orbitronic applications. Here, we report the nonvolatile tuning of SOC in graphene through the proximity effect from a ferroelectric substrate, Pb(Zr52,Ti48)O3 (PZT). Ferroelectric poling by applying a gate voltage induces a change in the SOC strength in addition to shifting the charge neutral point in graphene. The variations in SOC were extracted from weak localization within the quantum interference theory of graphene. Our analyses show that the dipole moments from the PZT polarization significantly enhance the z → −z asymmetric and symmetric SOCs of graphene. Unlike the impurity doping and/or gating, our methodology leads to the nonvolatile electrical control of SOC, thereby paving the way for versatile spin-orbitronic applications of graphene.

Spin Hall Effect in Bilayer Graphene Combined with an Insulator up to Room Temperature.

Spin-orbit coupling in graphene can be enhanced by chemical functionalization, adatom decoration, or proximity with a van der Waals material. As it is expected that such enhancement gives rise to a sizable spin Hall effect, a spin-to-charge current conversion phenomenon of technological relevance, it has sparked wide research interest. However, it has only been measured in graphene/transition-metal dichalcogenide van der Waals heterostructures with limited scalability. Here, we experimentally demonstrate the spin Hall effect up to room temperature in graphene combined with a nonmagnetic insulator, an evaporated bismuth oxide layer. The measured spin Hall effect arises most likely from an extrinsic mechanism. With a large spin-to-charge conversion efficiency, scalability, and ease of integration to electronic devices, we show a promising material heterostructure suitable for spin-based device applications.

Quantum Hall Effect Measurement of Spin-Orbit Coupling Strengths in Ultraclean Bilayer Graphene/WSe2 Heterostructures.

We study proximity-induced spin-orbit coupling (SOC) in bilayer graphene/few-layer WSe2 heterostructure devices. Contact mode atomic force microscopy (AFM) cleaning yields ultraclean interfaces and high-mobility devices. In a perpendicular magnetic field, we measure the quantum Hall effect to determine the Landau level structure in the presence of out-of-plane Ising and in-plane Rashba SOC. A distinct Landau level crossing pattern emerges when tuning the charge density and displacement field independently with dual gates, originating from a layer-selective SOC proximity effect. Analyzing the Landau level crossings and measured inter-Landau level energy gaps yields the proximity-induced SOC energy scale. The Ising SOC is ∼2.2 meV, 100 times higher than the intrinsic SOC in graphene, whereas its sign is consistent with theories predicting a dependence of SOC on interlayer twist angle. The Rashba SOC is ∼15 meV. Finally, we infer the magnetic field dependence of the inter-Landau level Coulomb interactions. These ultraclean bilayer graphene/WSe2 heterostructures provide a high mobility system with the potential to realize novel topological electronic states and manipulate spins in nanostructures.

Spin-orbit coupling in elemental two-dimensional materials

The fundamental spin-orbit coupling and spin mixing in graphene and rippled honeycomb lattice materials silicene, germanene, stanene, blue phosphorene, arsenene, antimonene, and bismuthene is investigated from first principles. The intrinsic spin-orbit coupling in graphene is revisited using multi-band $k\cdot p$ theory, showing the presence of non-zero spin mixing in graphene despite the mirror symmetry. However, the spin mixing itself does not lead to the the Elliott-Yafet spin relaxation mechanism, unless the mirror symmetry is broken by external factors. For other aforementioned elemental materials we present the spin-orbit splittings at relevant symmetry points, as well as the spin admixture $b^2$ as a function of energy close to the band extrema or Fermi levels. We find that spin-orbit coupling scales as the square of the atomic number Z, as expected for valence electrons in atoms. For isolated bands, it is found that $b^2\sim Z^4$. The spin-mixing parameter also exhibits giant anisotropy which, to a large extent, can be controlled by tuning the Fermi level. Our results for $b^2$ can be directly transferred to spin relaxation time due to the Elliott-Yafet mechanism, and therefore provide an estimate of the upper limit for spin lifetimes in materials with space inversion center.

Charge-to-Spin Conversion by the Rashba-Edelstein Effect in Two-Dimensional van der Waals Heterostructures up to Room Temperature.

The proximity of a transition-metal dichalcogenide (TMD) to graphene imprints a rich spin texture in graphene and complements its high-quality charge/spin transport by inducing spin–orbit coupling (SOC). Rashba and valley-Zeeman SOCs are the origin of charge-to-spin conversion mechanisms such as the Rashba–Edelstein effect (REE) and spin Hall effect (SHE). In this work, we experimentally demonstrate for the first time charge-to-spin conversion due to the REE in a monolayer WS2-graphene van der Waals heterostructure. We measure the current-induced spin polarization up to room temperature and control it by a gate electric field. Our observation of the REE and the inverse of the effect (IREE) is accompanied by the SHE, which we discriminate by symmetry-resolved spin precession under oblique magnetic fields. These measurements also allow for the quantification of the efficiencies of charge-to-spin conversion by each of the two effects. These findings are a clear indication of induced Rashba and valley-Zeeman SOC in graphene that lead to the generation of spin accumulation and spin current without using ferromagnetic electrodes. These realizations have considerable significance for spintronic applications, providing accessible routes toward all-electrical spin generation and manipulation in two-dimensional materials.

Engineering giant Rashba spin-orbit splitting in graphene via n−p codoping

Spin-orbit coupling in graphene is able to induce various topological phases and is also crucial for potential application in graphene-based spintronics. However, graphene itself exhibits extremely weak spin-orbit coupling, and it is rather challenging to enhance the spin-orbit coupling without drastically affecting its fundamental physical property in graphene via external means. In this paper, we show that the charge-compensated $n\text{\ensuremath{-}}p$ codoping approach not only can overcome the main shortcomings arising from single-element adsorption in graphene but can also result in a large Rashba spin-orbit splitting. As an example, we codope heavy adatoms with outer-shell $p$ electrons (e.g., Tl atoms acting as $n$-type dopants) on $p$-type doped graphene (e.g., by substituting carbon atoms with B atoms). We find the following: (1) Electrostatic attraction between $n$- and $p$-type dopants effectively enhances the adsorption and diffusion barrier of metallic adatoms and suppresses the undesirable formation of clustering. (2) Large Rashba spin-orbit splitting ($\ensuremath{\sim}130\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ for 6.25% B-Tl-codoped graphene) is produced due to the electrostatic interaction. (3) The charge-compensated nature and mutual screening of $n\text{\ensuremath{-}}p$ codopants preserve the Dirac dispersion of charge carriers to some extent.

Twist-angle dependence of the proximity spin-orbit coupling in graphene on transition-metal dichalcogenides

We theoretically study the proximity spin-orbit coupling in graphene on transition-metal dichalcogenides monolayer stacked with arbitrary twist angles. We find that the relative rotation greatly enhances the spin splitting of graphene, typically by a few to ten times compared to the non-rotated geometry,and the maximum splitting is achieved around $20^\circ$. The induced SOC can be changed from the Zeeman-type to the Rashba-type by rotation. The spin-splitting is also quite sensitive to the gate-induced potential, and it sharply rises when the graphene's Dirac point is shifted toward the TMDC band. The theoretical method does not need the exact lattice matching and it is applicable to any incommensurate bilayer systems. It is useful for the twist-angle engineering of a variety of van der Waals proximity effects.

Proximity-induced spin-orbit coupling in graphene/ Bi1.5Sb0.5Te1.7Se1.3 heterostructures

The weak intrinsic spin-orbit coupling in graphene can be greatly enhanced by proximity coupling. Here we report on the proximity-induced spin-orbit coupling in graphene transferred by hexagonal boron nitride (hBN) onto the topological insulator Bi$_{1.5}$Sb$_{0.5}$Te$_{1.7}$Se$_{1.3}$ (BSTS) which was grown on a hBN substrate by vapor solid synthesis. Phase coherent transport measurements, revealing weak localization, allow us to extract the carrier density-dependent phase coherence length $l_\phi$. While $l_\phi$ increases with increasing carrier density in the hBN/graphene/hBN reference sample, it decreases in BSTS/graphene due to the proximity-coupling of BSTS to graphene. The latter behavior results from D'yakonov-Perel-type spin scattering in graphene with a large proximity-induced spin-orbit coupling strength of at least 2.5 meV.

Spin-orbit coupling in graphene, silicene and germanene: dependence on the configuration of full hydrogenation and fluorination

We investigate the effect of full hydrogenation and fluorination on the spin-orbit coupling (SOC) in graphene, silicene and germanene. In chair conformation, the fluorination of graphene increases the spin-orbit splitting (\(E_{\mathrm{so}})\), while the hydrogenation and fluorination of other structures reduce the \(E_{\mathrm{so}}\) at the \(\Gamma \)-point. In case of boat conformation, the hydrogenation and fluorination reduce the symmetry of honeycomb structure, which in turn remove the degeneracy of valence band maximum at the \(\Gamma \)-point. The change in band gaps due to SOC is very small in boat conformation structures as compared to that in the corresponding chair conformation structures.

Tailoring emergent spin phenomena in Dirac material heterostructures.

Dirac materials such as graphene and topological insulators (TIs) are known to have unique electronic and spintronic properties. We combine graphene with TIs in van der Waals heterostructures to demonstrate the emergence of a strong proximity-induced spin-orbit coupling in graphene. By performing spin transport and precession measurements supported by ab initio simulations, we discover a strong tunability and suppression of the spin signal and spin lifetime due to the hybridization of graphene and TI electronic bands. The enhanced spin-orbit coupling strength is estimated to be nearly an order of magnitude higher than in pristine graphene. These findings in graphene-TI heterostructures could open interesting opportunities for exploring exotic physical phenomena and new device functionalities governed by topological proximity effects.

Effect of Distance on Photoluminescence Quenching and Proximity-Induced Spin-Orbit Coupling in Graphene/WSe2 Heterostructures.

Spin-orbit coupling (SOC) in graphene can be greatly enhanced by proximity coupling it to transition metal dichalcogenides (TMDs) such as WSe2. We find that the strength of the acquired SOC in graphene depends on the stacking order of the heterostructures when using hexagonal boron nitride ( h-BN) as the capping layer, i.e., SiO2/graphene/WSe2/ h-BN exhibiting stronger SOC than SiO2/WSe2/graphene/ h-BN. We utilize photoluminescence (PL) as an indicator to characterize the interaction between graphene and monolayer WSe2 grown by chemical vapor deposition. We observe much stronger PL quenching in the SiO2/graphene/WSe2/ h-BN stack than in the SiO2/WSe2/graphene/ h-BN stack and, correspondingly, a much larger weak antilocalization (WAL) effect or stronger induced SOC in the former than in the latter. We attribute these two effects to the interlayer distance between graphene and WSe2, which depends on whether graphene is in immediate contact with h-BN. Our observations and hypothesis are further supported by first-principles calculations, which reveal a clear difference in the interlayer distance between graphene and WSe2 in these two stacks.

Protected Pseudohelical Edge States in Z_{2}-Trivial Proximitized Graphene.

We investigate topological properties of models that describe graphene on realistic substrates which induce proximity spin-orbit coupling in graphene. A Z_{2} phase diagram is calculated for the parameter space of (generally different) intrinsic spin-orbit coupling on the two graphene sublattices, in the presence of Rashba coupling. The most fascinating case is that of staggered intrinsic spin-orbit coupling which, despite being topologically trivial, Z_{2}=0, does exhibit edge states protected by time-reversal symmetry for zigzag ribbons as wide as micrometers. We call these states pseudohelical as their helicity is locked to the sublattice. The spin character and robustness of the pseudohelical modes is best exhibited on a finite flake, which shows that the edge states have zero g factor, carry a pure spin current in the cross section of the flake, and exhibit spin-flip reflectionless tunneling at the armchair edges.

Trigonal warping induced unusual spin texture and strong spin polarization in graphene with the Rashba effect

We study the electronic and scattering properties of graphene with moderate Rashba spin-orbit coupling (SOC). The Rashba SOC in graphene tends to distort the band structure and gives rise to a trigonally warped Fermi surface. For electrons at a pronouncedly warped Fermi surface, the spin direction exhibits a staircase profile as a function of the momentum, making an unusual spin texture. We also study the spin-resolved scattering on a Rashba barrier and find that the trigonal warping is essential for producing spin polarization of the transmitted current. Particularly, both the direction and strength of the spin polarization can be controlled by kinds of electric methods. Our work unveils that not only SOC but also the geometry of the Fermi surface is important for generating spin polarization.

Strong electron-hole symmetric Rashba spin-orbit coupling in graphene/monolayer transition metal dichalcogenide heterostructures

Despite its extremely weak intrinsic spin-orbit coupling (SOC), graphene has been shown to acquire considerable SOC by proximity coupling with exfoliated transition metal dichalcogenides (TMDs). Here we demonstrate strong induced Rashba SOC in graphene that is proximity coupled to a monolayer TMD film, MoS2 or WSe2, grown by chemical vapor deposition with drastically different Fermi level positions. Graphene/TMD heterostructures are fabricated with a pickup-transfer technique utilizing hexagonal boron nitride, which serves as a flat template to promote intimate contact and therefore a strong interfacial interaction between TMD and graphene as evidenced by quenching of the TMD photoluminescence. We observe strong induced graphene SOC that manifests itself in a pronounced weak anti-localization (WAL) effect in the graphene magnetoconductance. The spin relaxation rate extracted from the WAL analysis varies linearly with the momentum scattering time and is independent of the carrier type. This indicates a dominantly Dyakonov-Perel spin relaxation mechanism caused by the induced Rashba SOC. Our analysis yields a Rashba SOC energy of ~1.5 meV in graphene/WSe2 and ~0.9 meV in graphene/MoS2, respectively. The nearly electron-hole symmetric nature of the induced Rashba SOC provides a clue to possible underlying SOC mechanisms.

Gate-dependent spin Hall induced nonlocal resistance and the symmetry of spin-orbit scattering in Au-clustered graphene

Engineering the electron dispersion of graphene to be spin-dependent is crucial for the realization of spin-based logic devices. Enhancing spin-orbit coupling in graphene can induce spin Hall effect, which can be adapted to generate or detect a spin current without a ferromagnet. Recently, both chemically and physically decorated graphenes have shown to exhibit large nonlocal resistance via the spin Hall and its inverse effects. However, these nonlocal transport results have raised critical debates due to the absence of field dependent Hanle curve in subsequent studies. Here, we introduce Au clusters on graphene to enhance spin-orbit coupling and employ a nonlocal geometry to study the spin Hall induced nonlocal resistance. Our results show that the nonlocal resistance highly depends on the applied gate voltage due to various current channels. However, the spin Hall induced nonlocal resistance becomes dominant at a particular carrier concentration, which is further confirmed through Hanle curves. The obtained spin Hall angle is as high as $\ensuremath{\sim}0.09$ at 2 K. Temperature dependence of spin relaxation time is governed by the symmetry of spin-orbit coupling, which also depends on the gate voltage: asymmetric near the charge neutral point and symmetric at high carrier concentration. These results inspire an effective method for generating spin currents in graphene and provide important insights for the spin Hall effect as well as the symmetry of spin scattering in physically decorated graphene.

Copper adatoms on graphene: Theory of orbital and spin-orbital effects

We present a combined DFT and model Hamiltonian analysis of spin-orbit coupling in graphene induced by copper adatoms in the bridge and top positions, representing isolated atoms in the dilute limit. The orbital physics in both systems is found to be surprisingly similar, given the fundamental difference in the local symmetry. In both systems the Cu p and d contributions at the Fermi level are very similar. Based on the knowledge of orbital effects we identify that the main cause of the locally induced spin-orbit couplings are Cu p and d orbitals. By employing the DFT+U formalism as an analysis tool we find that both the p and d orbital contributions are equally important to spin-orbit coupling, although p contributions to the density of states are much higher. We fit the DFT data with phenomenological tight-binding models developed separately for the top and bridge positions. Our model Hamiltonians describe the low-energy electronic band structure in the whole Brillouin zone and allow us to extract the size of the spin-orbit interaction induced by the local Cu adatom to be in the tens of meV. By application of the phenomenological models to Green's function techniques, we find that copper atoms act as resonant impurities in graphene with large lifetimes of 50 and 100~fs for top and bridge, respectively.

Direct coupling between charge current and spin polarization by extrinsic mechanisms in graphene

Spintronics---the all-electrical control of the electron spin for quantum or classical information storage and processing---is one of the most promising applications of the two-dimensional material graphene. Although pristine graphene has negligible spin-orbit coupling (SOC), both theory and experiment suggest that SOC in graphene can be substantially enhanced by extrinsic means, such as functionalization by adatom impurities. We present a theory of transport in graphene that accounts for the full spin-coherent dynamics of the carriers, including hitherto-neglected spin precession processes during resonant scattering with dilute impurities. We identify a novel "anisotropic spin precession scattering" process, specific to two dimensions and extrinsic SOC, which contributes to a large current-induced spin polarization in graphene. The theory also yields a comprehensive description of the spin relaxation mechanisms in impurity-decorated graphene: the Elliot-Yafet and Dyakonov-Perel relaxation rates are both present, and we find that the latter can dominate for some choices of carrier density and impurity strength. This provides theoretical foundations for designing future graphene-based integrated spintronic devices.