Rashba Splitting Research Articles

Optical spin injection in graphene with Rashba spin-orbit interaction

We calculate the efficiency of infrared optical spin injection in single-layer graphene with Rashba spin-orbit coupling and for in-plane magnetic field. The injection rate in the photon frequency range corresponding to the Rashba splitting is shown to be proportional to the ratio of the Zeeman and Rashba splittings. As a result, large spin polarization can be controllably achieved for experimentally available values of the spin-orbit coupling and in magnetic fields below 10 Tesla.

Spin orbit splitting of the photon induced Fano resonance in an oscillating graphene electrostatic barrier

We investigate theoretically the effect of a time dependent oscillating potential on the transport property of the Dirac Fermion through a monolayer graphene electrostatic barrier under the influence of the Rashba spin orbit interaction. The time dependent problem is solved in the frame work of the non-perturbative Floquet approach. It is noted that the dynamic condition of the barrier may be controlled by tuning the Rashba parameter. Introduction of the spin orbit interaction causes splitting of the Fano resonance (FR), a characteristic feature in photon assisted tunneling. The separation between the spin split FR's gives an indirect measure of the fine structure of the quasi-hole bound state inside the barrier. The present findings on the Rashba splitting of the FR and its external control by tuning the oscillating field parameters might have potential for applications in spintronic devices, especially in the spin field effect transistors. The spin polarization of different Floquet sidebands is found to be quite sensitive to the spin-pseudospin interaction.

Rashba effect within the space–charge layer of a semiconductor

The observed heavy-hole, light-hole and split-off band edges of a semiconductor are the well known consequence of two physical processes: atomic spin–orbital interaction and solid-state band–band anticrossing. In this work, we examined the four band-edge-like bands in great detail within the Ge space–charge layer with either Pb/Ge(111)- R30° or a 2 ML Pb film on Ge(111). Our results reveal that the conventional picture of band edges for a semiconductor is actually crude. In addition, momentum-dependent Rashba splitting effect can be included to explain the observed non-split-off band, indicating the Rashba effect as an intrinsic property near a semiconductor surface.

Many-body interactions and Rashba splitting of the surface state on Cu(110)

Using high-resolution angle-resolved photoemission spectroscopy, we elucidate the Rashba splitting of $\ensuremath{\Delta}{k}_{F}=0.003$ ${\AA{}}^{\ensuremath{-}1}$ near the Fermi level (${E}_{F}$) in the Shockley surface state of Cu(110) at the $\overline{\mathrm{Y}}$ point of the surface Brillouin zone. The observed energy-band dispersion exhibits a kink structure at $\ensuremath{\sim}\ensuremath{-}20$ meV, which is a clear indication of band renormalization caused by an electron-phonon interaction. The electron-phonon coupling parameter is found to be ${\ensuremath{\lambda}}_{ep}=0.17\ifmmode\pm\else\textpm\fi{}0.02$ based on the experimentally obtained real part of the self-energy. First-principle calculations yield ${\ensuremath{\lambda}}_{ep}=0.160$ and $\ensuremath{\Delta}{k}_{F}=0.004$ ${\AA{}}^{\ensuremath{-}1}$ at ${E}_{F}$, which are fully consistent with the experimental results. In addition, the contributions of the electron-electron and electron-phonon interactions to the linewidth of the surface state at the $\overline{\mathrm{Y}}$ point are experimentally determined to be ${\ensuremath{\Gamma}}_{ee}\ensuremath{\sim}9$ meV and ${\ensuremath{\Gamma}}_{ep}\ensuremath{\sim}7$ meV, respectively. We demonstrate that the Rashba splitting must be resolved by photoemission line-shape analysis for an accurate determination of the electron self-energy and coupling parameters.

Noncentrosymmetric superconductor with a bulk three-dimensional Dirac cone gapped by strong spin-orbit coupling

The layered, noncentrosymmetric heavy element ${\text{PbTaSe}}_{2}$ is found to be superconducting. We report its electronic properties accompanied by electronic-structure calculations. Specific heat, electrical resistivity, and magnetic-susceptibility measurements indicate that PbTaSe${}_{2}$ is a moderately coupled, type-II BCS superconductor (${T}_{c}=3.72$ K, Ginzburg--Landau parameter $\ensuremath{\kappa}=17$) with an electron-phonon coupling constant of ${\ensuremath{\lambda}}_{ep}=0.74$. Electronic-structure calculations reveal a single bulk three-dimensional Dirac cone at the $K$ point of the Brillouin zone derived exclusively from its hexagonal Pb layer; it is similar to the feature found in graphene except there is a 0.8 eV gap opened by spin-orbit coupling. The combination of large spin-orbit coupling and lack of inversion symmetry also results in large Rashba splitting on the order of tenths of an eV.

Topological phase transitions in Sb(111) films driven by external strain and electric field

Using the first-principles calculations, we systematically study the lattice structure and topological phase transitions driven by external strain and electric field in Sb(111) thin films. The results show that 1-bilayer film is a robust trivial semiconductor, and the band gap of a 4-bilayer film can be tuned by strain but without gap closing up to strains of 8%, indicating a robust two-dimensional topological insulator. However, for the remaining bilayers below 9 bilayers, the topological phase transitions are driven if a suitable value of strain is applied. Moreover, the electric field not only can induce the Rashba splitting, but also may induce the gap closing at other points rather than at time-reversal invariant momenta. Our theoretical results provide efficient methods to manipulate topological phase transitions of Sb films.

Orbital dependent Rashba splitting and electron-phonon coupling of 2D Bi phase on Cu(100) surface

A monolayer of bismuth deposited on the Cu(100) surface forms a highly ordered c(2×2) reconstructed phase. The low energy single particle excitations of the c(2×2) Bi/Cu(100) present Bi-induced states with a parabolic dispersion in the energy region close to the Fermi level, as observed by angle-resolved photoemission spectroscopy. The electronic state dispersion, the charge density localization, and the spin-orbit coupling have been investigated combining photoemission spectroscopy and density functional theory, unraveling a two-dimensional Bi phase with charge density well localized at the interface. The Bi-induced states present a Rashba splitting, when the charge density is strongly localized in the Bi plane. Furthermore, the temperature dependence of the spectral density close to the Fermi level has been evaluated. Dispersive electronic states offer a large number of decay channels for transitions coupled to phonons and the strength of the electron-phonon coupling for the Bi/Cu(100) system is shown to be stronger than for Bi surfaces and to depend on the electronic state symmetry and localization.

ZnIr2O4: An efficient photocatalyst with Rashba splitting

Semiconductor-based photocatalysts nowadays are of central interest for the splitting of water into hydrogen and oxygen. However, the efficiency of the known materials is small for direct utilization of the solar energy. Using first-principles calculations, we show that ZnIr2O4 can overcome this shortage. Modified Becke-Johnson calculations give an indirect band of 2.25 eV, which can be reduced to the visible energy range by S doping. For 25% S doping we find a direct band gap of 1.25 eV and a Rashba spin splitting of 220 meV Å. The valence band edge potential is 2.89 V against the standard hydrogen electrode, which is sufficient for photocatalytic water oxidation and pollutant degradation. The optical absorption of S-doped ZnIr2O4 is strongly enhanced, making the material an efficient photocatalyst for visible light.

Tunable Rashba Effect in Two-Dimensional LaOBiS2 Films: Ultrathin Candidates for Spin Field Effect Transistors

Rashba spin splitting is a two-dimensional (2D) relativistic effect closely related to spintronics. However, so far there is no pristine 2D material to exhibit enough Rashba splitting for the fabrication of ultrathin spintronic devices, such as spin field effect transistors (SFET). On the basis of first-principles calculations, we predict that the stable 2D LaOBiS2 with only 1 nm of thickness can produce remarkable Rashba spin splitting with a magnitude of 100 meV. Because the medium La2O2 layer produces a strong polar field and acts as a blocking barrier, two counter-helical Rashba spin polarizations are localized at different BiS2 layers. The Rashba parameter can be effectively tuned by the intrinsic strain, while the bandgap and the helical direction of spin states sensitively depends on the external electric field. We propose an advanced Datta-Das SFET model that consists of dual gates and 2D LaOBiS2 channels by selecting different Rashba states to achieve the on-off switch via electric fields.

Gate control of the electron spin-diffusion length in semiconductor quantum wells

The spin diffusion length is a key parameter to describe the transport properties of spin polarized electrons in solids. Electrical spin injection in semiconductor structures, a major issue in spintronics, critically depends on this spin diffusion length. Gate control of the spin diffusion length could be of great importance for the operation of devices based on the electric field manipulation and transport of electron spin. Here we demonstrate that the spin diffusion length in a GaAs quantum well can be electrically controlled. Through the measurement of the spin diffusion coefficient by spin grating spectroscopy and of the spin relaxation time by time-resolved optical orientation experiments, we show that the diffusion length can be increased by more than 200% with an applied gate voltage of 5 V. These experiments allow at the same time the direct simultaneous measurements of both the Rashba and Dresselhaus spin-orbit splittings.

Induced Rashba splitting of electronic states in monolayers of Au, Cu on a W(110) substrate

The paper sums up a theoretical and experimental investigation of the influence of the spin–orbit coupling in W(110) on the spin structure of electronic states in deposited Au and Cu monolayers. Angle-resolved photoemission spectroscopy reveals that in the case of monolayers of Au and Cu spin–orbit split bands are formed in a surface-projected gap of W(110). Spin resolution shows that these states are spin polarized and that, therefore, the spin–orbit splitting is of Rashba type. The states evolve from hybridization of W 5d, 6p-derived states with the s, p states of the deposited metal. Interaction with Au and Cu shifts the original W 5d-derived states from the edges toward the center of the surface-projected gap. The size of the spin–orbit splitting of the formed states does not correlate with the atomic number of the deposited metal and is even higher for Cu than for Au. These states can be described as W-derived surface resonances modified by hybridization with the p, d states of the adsorbed metal. Our electronic structure calculations performed in the framework of the density functional theory correlate well with the experiment and demonstrate the crucial role of the W top layer for the spin–orbit splitting. It is shown that the contributions of the spin–orbit interaction from W and Au act in opposite directions which leads to a decrease of the resulting spin–orbit splitting in the Au monolayer on W(110). For the Cu monolayer with lower spin–orbit interaction the resulting spin splitting is higher and mainly determined by the W.

Observation of Rashba splitting on [formula omitted] reconstructed surface

The electronic structure of 3×3−Sb/Si111 reconstructed surface is measured by angle-resolved photoemission spectroscopy. By the first time, band splitting at Γ¯ and M¯ points in the surface Brillouin zone (SBZ) of this system is observed, which could be simply interpreted in the framework of Rashba splitting. Furthermore, first principle calculation is carried out and compared with our experimental results.

Bulk and surface Rashba splitting in single termination BiTeCl

By angle-resolved photoemission spectroscopy (ARPES) we observe a giant Rashba-type spin splitting in the electronic bulk conduction and valence bands of the semiconductor BiTeCl. This material belongs to the group of bismuth tellurohalides BiTeX (X = Cl,Br,I) which are layered non-centrosymmetric materials with strong spin–orbit interaction. By photon energy-dependent ARPES, we separate the bulk and surface contribution of the electronic structure and show that the tellurium-terminated (0001) crystal surface hosts spin-split two-dimensional surface states. On the chlorine-terminated surface at the opposite side of the crystal no surface states are observed due to photon-induced surface chemistry.

Rashba-type spin splitting from interband scattering in quasiparticle interference maps

We have studied the BiCu${}_{2}$/Cu(111) surface alloy using low-temperature scanning tunneling microscopy and spectroscopy. We observed standing waves caused by scattering off defects and step edges. Different from previous studies on similar Rashba-type surfaces, we identified multiple scattering vectors that originate from various intraband as well as interband scattering processes. A detailed energy-dependent analysis of the standing-wave patterns enables a quantitative determination of band dispersions, including the Rashba splitting. The results are in good agreement with angle-resolved photoelectron spectroscopy (ARPES) data and demonstrate the usefulness of this strategy to determine the band structure of Rashba systems. The lack of other possible scattering channels will be discussed in terms of spin conservation and hybridization effects. The results open new possibilities to study spin-dependent scattering on complex spin-orbit coupled surfaces.

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.

Tuning of the Rashba effect in Pb quantum well states via a variable Schottky barrier

Spin-orbit interaction (SOI) in low-dimensional systems results in the fascinating property of spin-momentum locking. In a Rashba system the inversion symmetry normal to the plane of a two-dimensional (2D) electron gas is broken, generating a Fermi surface spin texture reminiscent of spin vortices of different radii which can be exploited in spin-based devices. Crucial for any application is the possibility to tune the momentum splitting through an external parameter. Here we show that in Pb quantum well states (QWS) the Rashba splitting depends on the Si substrate doping. Our results imply a doping dependence of the Schottky barrier which shifts the Si valence band relative to the QWS. A similar shift can be achieved by an external gate voltage or ultra-short laser pulses, opening up the possibility of terahertz spintronics.

Surface and substrate induced effects on thin films of the topological insulators Bi2Se3and Bi2Te3

Based on van der Waals density functional calculations, we have studied few-quintuple-layer (QL) films of Bi${}_{2}$Se${}_{3}$ and Bi${}_{2}$Te${}_{3}$. The separation between the QLs near the surface is found to have a large increase after relaxation, whereas, the separation between the inner QLs is smaller and approaches the bulk value as the thickness grows, showing a two-dimensional to three-dimensional structural crossover. Accordingly, the surface Dirac cone of the Bi${}_{2}$Se${}_{3}$ film is evidently gapped for small thicknesses (two to four QLs), and the gap is reduced and, finally, is closed with the increasing thickness, agreeing well with the experiments. We further studied the substrate effect by investigating the Bi${}_{2}$Se${}_{3}$/graphene system. It is found that the underlying graphene induces a giant thickness-dependent Rashba splitting and Dirac point shift. Because Bi${}_{2}$Te${}_{3}$ films have smaller relative inter-QL expansion and stronger spin-orbit coupling, the topological features start to appear in the film as thin as two QLs in good accord with the experiments.

Quantum Interference Mapping of Rashba-Split Bloch States inBi/Ag(111)

We report on low-temperature scanning tunneling spectroscopy investigations of the (sqrt[3]×sqrt[3]) Bi/Ag(111)R30° surface alloy which provides a giant Rashba-type spin splitting. We observed spectroscopic features that are assigned to two Rashba-split bands. Quantum interference mapping shows that backscattering is not only allowed below but also above the Rashba energy. We argue that the observed behavior can be understood within the Bloch picture where k refers to the crystal momentum and the velocity of an electronic state is defined as v(n)(E) = 1/ℏ ∇(k)E(n)(k). The analysis of the energy dispersion of scattering channels reveals a conventional Rashba splitting for the unoccupied Rashba bands, while hybridization is observed in the occupied states.

Quantum oscillations and optical conductivity in Rashba spin-splitting BiTeI

We report the observation of Shubnikov--de Haas oscillations in single crystals of the Rashba spin-splitting compound BiTeI, from both longitudinal [${R}_{xx}(B)$] and Hall [${R}_{xy}(B)$] magnetoresistance. Under magnetic fields up to 65 T, we resolved unambiguously only one frequency $F=284.3\ifmmode\pm\else\textpm\fi{}1.3$ T, corresponding to a Fermi momentum ${k}_{F}=0.093\ifmmode\pm\else\textpm\fi{}0.002$ \AA{}${}^{\ensuremath{-}1}$. The amplitude of oscillations is strongly suppressed by a tilting magnetic field, suggesting a highly two-dimensional Fermi surface. Combining with optical spectroscopy, we show that quantum oscillations may be consistent with a bulk conduction band having a Rashba splitting momentum ${k}_{R}=0.046\ifmmode\pm\else\textpm\fi{}0.0005$ \AA{}${}^{\ensuremath{-}1}$.

Controlling Rashba spin splitting in Au(111) surface states through electric field

Combining density-functional theory (DFT) calculations and theoretical analyses, we demonstrate the high-order Rashba spin-orbit coupling in the Au(111) surface and the electric field manipulation of the Rashba splitting energy. A good linear relationship between the Rashba splitting energy and applied electric field is revealed by DFT calculations. The effect is attributed to the linear response of the first-order Rashba parameter to the applied electric field. The nonlinear relationship between Rashba splitting energy and the wave vectors identifies the higher-order Rashba components, which, however, are found to be less influenced by the external electric field. Our investigation provides an in-depth understanding of the tunability of Rashba splitting in a metal surface, which is of great interest in the area of electrical control of spin states.