Rashba Splitting Research Articles

Large-gap quantum spin Hall states in decorated stanene grown on a substrate

Two-dimensional stanene is a promising candidate material for realizing room-temperature quantum spin Hall (QSH) effect. Monolayer stanene has recently been fabricated by molecular beam epitaxy, but shows metallic features on Bi$_2$Te$_3$(111) substrate, which motivates us to study the important influence of substrate. Based on first-principles calculations, we find that varying substrate conditions considerably tunes electronic properties of stanene. The supported stanene gives either trivial or QSH states, with significant Rashba splitting induced by inversion asymmetry. More importantly, large-gap (up to 0.3 eV) QSH states are realizable when growing stanene on various substrates, like the anion-terminated (111) surfaces of SrTe, PbTe, BaSe and BaTe. These findings provide significant guidance for future research of stanene and large-gap QSH states.

Significantly enhanced giant Rashba splitting in a thin film of binary alloy

Dirac cones in a two-dimensional environment have attracted much attention not only because of the massless Dirac fermions but also due to their capability to lock the spin direction with the momentum. Here we demonstrate that the Rashba effect within a single layer of a binary alloy composed of heavy atoms, Pb and Au, can be driven by and even tweaked with the adjacent top and bottom layers to yield cone-like structures and further enhance the Rashba coupling strength. Two cones are observed at the surface zone center with giant Rashba parameters 1.53 and 4.45 eVÅ; an anisotropic giant Rashba splitting at the surface zone boundary has a great value, 6.26 eVÅ, inferring the critical role of p-d hybridization between Pb and Au. Our results reveal not only an interesting natural phenomenon but also a feasible method of tweaking the Rashba effect of a two-dimensional system.

Spin splitting of Dirac fermions in graphene on Ni intercalated with alloy of Bi and Au

By angle- and spin-resolved photoemission we have studied electronic structure and spin–orbit splitting in graphene/Ni(111) intercalated with alloy of high spin–orbit materials Bi and Au. Results are compared to ultimate cases of (i) graphene/Ni intercalated only with Au which shows giant Rashba splitting (∼100meV) and (ii) graphene/Ni intercalated only with Bi for which spin splitting of the Dirac cone is nearly zero (⩽10meV). Our results demonstrate that partial substitution of intercalated Au with Bi reduces spin splitting of the Dirac cone in graphene and even allows for its systematic adjustment through concentration of Bi. Observed effects are ascribed to peculiar electronic structure of Bi which has in the valence band no d electronic states responsible for the onset of giant Rashba effect through electronic hybridization with π band of graphene. We also report in details electronic properties of graphene/Ni(111) intercalated only with Bi in various concentrations. Such graphene reveals undistorted band structure characteristic to quasifreestanding graphene with small n-doping and a minor band gap at the Dirac point (∼200meV) which depends weakly on the concentration of Bi. It has been shown that this gap is related to the symmetry breaking rather than to the topological phase formation.

Magnetization-dependent Rashba splitting of quantum well states at the Co/W interface

Exchange and Rashba spin-orbit interactions are expected to couple at ferromagnetic-metal/heavy-metal interfaces and influence their electronic structure. We examine these largely unexplored effects in Co(0001) films on W(110) by angle-resolved photoemission spectroscopy. We find breaking of inversion symmetry in the band dispersion of magnetic quantum well states along structurally equivalent directions of the Co films. Ab initio calculations ascribe this unusual band behavior to the relative orientation of coexisting exchange and Rashba fields. These findings elucidate fundamental interface electronic effects, which are associated to spin-orbit phenomena at ferromagnetic-metal/heavy-metal junctions.

Spin pumping and inverse Rashba-Edelstein effect in NiFe/Ag/Bi and NiFe/Ag/Sb

The Rashba effect is an interaction between the spin and the momentum of electrons induced by the spin-orbit coupling in surface or interface states. We measured the inverse Rashba-Edelstein effect via spin pumping in Ag/Bi and Ag/Sb interfaces. The spin current is injected from the ferromagnetic resonance of a NiFe layer towards the Rashba interfaces, where it is further converted into a charge current. Using spin pumping theory, we quantify the conversion parameter of spin to charge current to be 0.11 ± 0.02 nm for Ag/Bi and a factor of ten smaller for Ag/Sb. The relative strength of the effect is in agreement with spectroscopic measurements and first principles calculations. We also vary the interlayer materials to study the voltage output in relation to the change of the effective spin mixing conductance. The spin pumping experiment offers a straight-forward approach of using spin current as an efficient probe for detecting interface Rashba splitting.

Rashba Effect and Beating Patterns in the THz Magneto-Photoresponse of a HgTe-Based Two-Dimensional Electron Gas

HgTe quantum wells with a gapped single Dirac cone electronic dispersion relation have been investigated by THz magneto-photoresponse (PR) and magneto-transport measurements. The QW sample has the conventional band alignment with the well thickness (6.1 nm) slightly smaller than the critical thickness for the topological phase transition. The effective gap of this structure is roughly 10 meV, and the large sheet density ([Formula: see text] m-2) of the two-dimensional electron gas (2DEG) results in a very large Fermi energy ([Formula: see text] meV). We have found several interesting effects at these high densities. In this paper we focus on an observed beating of quantum oscillations in the PR signal (at 1.83 THz) and compare it with direct measurements of oscillations in the longitudinal magneto-resistance (Rxx). The mechanism for the PR is cyclotron resonance absorption heating of the electrons (an electron bolometric effect). We attribute the beating to Rashba splitting of the spin states, which is barely observable in direct Rxx measurements under strong gate-induced electric fields.

Strongly anisotropic spin-orbit splitting in a two-dimensional electron gas

Near-surface two-dimensional electron gases on the topological insulator Bi$_2$Te$_2$Se are induced by electron doping and studied by angle-resolved photoemission spectroscopy. A pronounced spin-orbit splitting is observed for these states. The $k$-dependent splitting is strongly anisotropic to a degree where a large splitting ($\approx 0.06$ \AA$^{-1}$) can be found in the $\bar{\Gamma}\bar{M}$ direction while the states are hardly split along $\bar{\Gamma}\bar{K}$. The direction of the anisotropy is found to be qualitatively inconsistent with results expected for a third-order anisotropic Rashba Hamiltonian. However, a $\mathbf{k} \cdot \mathbf{p}$ model that includes the possibility of band structure anisotropy as well as both isotropic and anisotropic third order Rashba splitting can explain the results. The isotropic third order contribution to the Rashba Hamiltonian is found to be negative, reducing the energy splitting at high $k$. The interplay of band structure, higher order Rashba effect and tuneable doping offers the opportunity to engineer not only the size of the spin-orbit splitting but also its direction.

Landau level crossing in a spin-orbit coupled two-dimensional electron gas

We have studied experimentally the Landau level (LL) spectrum of a two-dimensional electron gas (2DEG) in an In0.53Ga0.47As/InP quantum well structure by means of low-temperature magneto-transport coincidence measurement in vector magnetic fields. It is well known that LL crossing occurs in tilted magnetic fields due to a competition between cyclotron energy and Zeeman effect. Remarkably, here we observe an additional type of level-crossing resulting from a competition between Rashba and Zeeman splitting in a small magnetic field, consistent with the theoretical prediction for strongly spin-orbit coupled 2DEG.

Nontrivial spin structure of graphene on Pt(111) at the Fermi level due to spin-dependent hybridization

The electronic and spin structure of a graphene monolayer synthesized on Pt(111) has been investigated experimentally by angle- and spin-resolved photoemission with different polarizations of incident synchrotron radiation and using density functional theory calculations. It is shown that despite the observed total quasifreestanding character of the dispersion of the graphene $\ensuremath{\pi}$ state remarkable local distortions and breaks in the dispersions take place due to hybridization between the graphene $\ensuremath{\pi}$ and Pt $d$ states. Corresponding spin-dependent avoided-crossing effects lead to significant modification of the spin structure and cause an enhanced induced spin-orbit splitting of the graphene $\ensuremath{\pi}$ states near the Fermi level in the region of the $\overline{\mathrm{K}}$ point of the graphene Brillouin zone (BZ) with a magnitude of 80--200 meV depending on the direction in the BZ. Using $p$, $s$, and elliptical polarizations of the synchrotron radiation, the contributions of the graphene $\ensuremath{\pi}$ and Pt $d$ states were separated and their intersection at the Fermi level, which is important for effective spin injection between these states, was shown. Moreover, analysis of the data allows us to conclude that in the region of the Dirac point the spin structure of the system cannot be described by a Rashba splitting, and even a spin-orbit gap between lower and upper Dirac cones is observed.

Rashba splitting of graphene-covered Au(111) revealed by quasiparticle interference mapping

We report on low-temperature scanning tunneling spectroscopy measurements on epitaxial graphene flakes on Au(111). We show that using quasiparticle interference (QPI) mapping, we can discriminate between the electronic systems of graphene and Au(111). Beyond the scattering vectors, which can be ascribed to the elastic scattering within each of the systems, we observe QPI features related to the scattering process between graphene states and the Au(111) surface state. This additional interband scattering process at the graphene/Au(111) interface allows the direct quantitative determination of the Rashba-splitting of the Au(111) surface state, which cannot be evaluated from QPI measurements on pure Au(111). This experiment demonstrates a unique local spectroscopic approach to investigate the Rashba-split bands at weakly interacting epitaxial graphene/substrate interfaces.

Rashba effect of bismuth thin film on silicon studied by spin-resolved ARPES

We report high-resolution spin- and angle-resolved photoemission spectroscopy of bismuth thin film on Si(111) to discuss the spin structure of surface states. We found that, unlike conventional picture of the Rashba splitting, the magnitude of the in-plane spin polarization is asymmetric between two hole pockets across the Brillouin-zone center. In addition, these pockets exhibit a giant out-of-plane spin polarization as large as the in-plane counterpart, which changes the sign across the Γ¯ M¯ line. We also revealed that the spin polarization of the Rashba surface states near the Brillouin-zone boundary (the M¯ point) is gradually reduced on decreasing the film thickness. Our result provides a new pathway to generate and control spin-polarized electrons in the Rashba system.

Rashba splitting and dichroism of surface states in Bi/Ag surface alloy

The Rashba effect plays an important role in various spin-related phenomena in two-dimensional electronic systems. In this work we present a theoretical analysis of the Rashba effect both analytically and numerically for the prototypical Rashba system Bi/Ag surface alloy, which shows a giant Rashba spin splitting. The results reveal the critical influence of atomic spin-orbit coupling and structural inversion asymmetry. In addition, we demonstrate a theoretical route to interpret the prominent circular dichroic patterns observed by angle-resolved photoemission spectroscopy in this system. The results reveal a close connection between the experimentally observed dichroic patterns and the Rashba spin texture.

Electric tuning of the surface and quantum well states in Bi2Se3 films: a first-principles study

Based on first-principles calculations in the framework of van der Waals density functional theory, we find that giant, Rashba-like spin splittings can be induced in both the surface states and quantum well states of thin Bi2Se3 films by application of an external electric field. The charge is redistributed so that the Dirac cones of the upper and lower surfaces become nondegenerate and completely gapless. Interestingly, a momentum-dependent spin texture is developed on the two surfaces of the films. Some of the quantum well states, which reside in the middle of the Bi2Se3 film under zero field, are driven to the surface by the electric field. The Rashba splitting energy has a highly non-linear dependence on the momentum and the electric field due to the large contribution of the high-order Rashba terms, which suggests complex spin dynamics in the thin films of Bi2Se3 under an electric field.

Overview of theoretical studies of Rashba effect in polar perovskite surfaces

Theoretical studies with the help of first-principles electronic structure calculations and tight-binding based Hamiltonian models aimed to understand the Rashba effect in the 2D electron gas at the surfaces and interfaces of polar perovskite oxides are discussed. First-principles calculations on a slab of KTaO3 show that the spin-splitting is orbital dependent and is greatly suppressed by the lattice relaxation close to the surface. However, the electron gas is amenable to tuning by external potentials perpendicular to the surface and can be used to control Rashba splitting. Construction of a minimal model Hamiltonian to study d orbitals under uniform electric field is explained. The potential introduces new matrix elements between orbitals by breaking the symmetry and distorting the lattice. When coupled with spin–orbit interaction, this results in lifting the spin degeneracy.

Optical properties of BiTeBr and BiTeCl

We present a comparative study of the optical properties - reflectance, transmission and optical conductivity - and Raman spectra of two layered bismuth-tellurohalides BiTeBr and BiTeCl at 300 K and 5 K, for light polarized in the a-b planes. Despite different space groups, the optical properties of the two compounds are very similar. Both materials are doped semiconductors, with the absorption edge above the optical gap which is lower in BiTeBr (0.62 eV) than in BiTeCl (0.77 eV). The same Rashba splitting is observed in the two materials. A non-Drude free carrier contribution in the optical conductivity, as well as three Raman and two infrared phonon modes, are observed in each compound. There is a dramatic difference in the highest infrared phonon intensity for the two compounds, and a difference in the doping levels. Aspects of the strong electron-phonon interaction are identified. Several interband transitions are assigned, among them the low-lying absorption $\beta$ which has the same value 0.25 eV in both compounds, and is caused by the Rashba spin splitting of the conduction band. An additional weak transition is found in BiTeCl, caused by the lower crystal symmetry.

Exchange interaction between magnetic impurities on surfaces of CuxPd1−x and CuxAu1−x random substitutional alloys

We present fully relativistic first principles calculations of the exchange interactions between magnetic impurities deposited on the (1 1 1) surfaces of CuxPd1−x and CuxAu1−x random substitutional alloys, described using the coherent potential approximation. We show that as with pure surfaces of Cu and Au, where Shockley-type surface states mediate an RKKY-type interaction, a surface state and its dispersion can be obtained from studying the Bloch spectral function. In the second part of the paper we show how the details of the interaction are determined by the properties and dispersion of the surface states of the host material. We find an extra exponential decay in the range of the interactions compared to the 1/R2 decay on surfaces of pure metals. The similar topology of the Fermi surface of Cu and Au allows us to scale the spin–orbit coupling and to study the Bychkov–Rashba splitting. Alternatively, the entirely different topology of the Cu and Pd Fermi surfaces allows us to study changes in the surface-state dispersion of the RKKY interaction between surface impurities.

Switchable S = 1/2 and J = 1/2 Rashba bands in ferroelectric halide perovskites.

The Rashba effect is spin degeneracy lift originated from spin-orbit coupling under inversion symmetry breaking and has been intensively studied for spintronics applications. However, easily implementable methods and corresponding materials for directional controls of Rashba splitting are still lacking. Here, we propose organic-inorganic hybrid metal halide perovskites as 3D Rashba systems driven by bulk ferroelectricity. In these materials, it is shown that the helical direction of the angular momentum texture in the Rashba band can be controlled by external electric fields via ferroelectric switching. Our tight-binding analysis and first-principles calculations indicate that S = 1/2 and J = 1/2 Rashba bands directly coupled to ferroelectric polarization emerge at the valence and conduction band edges, respectively. The coexistence of two contrasting Rashba bands having different compositions of the spin and orbital angular momentum is a distinctive feature of these materials. With recent experimental evidence for the ferroelectric response, the halide perovskites will be, to our knowledge, the first practical realization of the ferroelectric-coupled Rashba effect, suggesting novel applications to spintronic devices.

Rashba splitting and relativistic energy shifts in In/Si(111) nanowires

A numerically efficient methodology that allows for relativistic calculations including spin-orbit coupling for spatially anisotropic potentials is employed to study the energetics and electronic properties of In/Si(111)($4\ifmmode\times\else\texttimes\fi{}1$)/($8\ifmmode\times\else\texttimes\fi{}2$) nanowires within density-functional theory. For the subtle total energy balance between the metallic In zigzag chain structure observed at room temperature and the insulating In hexagons that form below the critical temperature, scalar-relativistic corrections to the kinetic energy are clearly far more important than the spin-orbit coupling. On the other hand, a relativistic treatment including spin-orbit coupling is required to describe correctly the electronic band structure that shows a large, strongly anisotropic $k$-point-dependent spin splitting of the In-related states at the $X$ point of the surface Brillouin zone. Suitably combined with the metal-insulator transition, the resulting quasi-1D Rashba effect may be used for spin filtering.

Tunable Rashba effect on strained ZnO: First-principles density-functional study

We investigated the Rashba effect on the conduction band of strained ZnO using first-principles calculations. We found that the Rashba spin rotations can be inversed by applying biaxial strain. This rotation inversion is due to the biaxial strain changing the direction of the electric polarization around the Zn atom. We also found that the amount of Rashba splitting can be controlled by tuning the strain. These findings suggest that the strained ZnO is suitable for spintronics applications.

One-dimensional weak antilocalization due to the berry phase in HgTe wires.

We study the weak antilocalization (WAL) effect in the magnetoresistance of narrow HgTe wires fabricated in quantum wells with normal and inverted band ordering. Measurements at different gate voltages indicate that the WAL is only weakly affected by Rashba spin-orbit splitting and persists when the Rashba splitting is about zero. The WAL amplitude in wires with normal band ordering is an order of magnitude smaller than for wires with an inverted band structure. These observations are attributed to the Dirac-like dispersion of the energy bands in HgTe quantum wells. From the magnetic-field and temperature dependencies we extract the dephasing lengths and band Berry phases. The weaker WAL for samples with a normal band structure can be explained by a nonuniversal Berry phase which always exceeds π, the characteristic value for gapless Dirac fermions.