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Janus dichalcogenide multilayers provide a paradigmatic platform to engineer electronic phenomena dominated by spin–orbit coupling. Their unique spin–orbit effects stem from the mirror symmetry breaking in each layer, which induces a colossal Rashba spin–orbit effect in comparison with the conventional dichalcogenide counterparts. Here we put forward twisted Janus dichalcogenide bilayers as a simple platform to realize spin–orbit correlated states. We demonstrate the emergence of flat bands featuring strong spin-momentum locking and the emergence of symmetry broken states with associated non-coplanar magnetization when interactions are included. We further show that the symmetry broken states can be controlled by means of a magnetic substrate, strongly impacting the non-coplanar magnetic texture of the moire unit cell. Our results put forward twisted Janus multilayers as a powerful platform to explore spin–orbit correlated physics, and highlighting the versatility of magnetic substrates to control unconventional moire magnetism. [ABSTRACT FROM AUTHOR]

We study the effect of the Rashba spin–orbit coupling on the Fermi arcs of topological Dirac semimetals. The Rashba coupling is induced by breaking the inversion symmetry at the surface. Remarkably, this coupling could be enhanced by the interaction with the substrate and controlled by an external electric field. We study analytically and numerically the rotation of the spin of the surface states as a function of the electron's momentum and the coupling strength. Furthermore, a detailed analysis of the spin-dependent two-terminal conductance is presented in the clean limit and with the addition of a random distribution of impurities. Depending on the magnitude of the quadratic terms in the Hamiltonian, the spin-flip conductance may become dominant, thus showing the potential of the system for spintronic applications, since the effect is robust even in the presence of disorder. [ABSTRACT FROM AUTHOR]

We theoretically study the inverse Faraday effect, i.e., the optical induction of spin polarization with circularly polarized light, by particularly focusing on effects of band dispersions and Fermi surfaces in crystal systems with the spin–orbit interaction (SOI). By numerically solving the time-dependent Schrödinger equation of a tight-binding model with the Rashba-type SOI, we reproduce the light-induced spin polarization proportional to where E0 and ω are the electric-field amplitude and the angular frequency of light, respectively. This optical spin induction is attributed to dynamical magnetoelectric coupling between the light electric field and the electron spins mediated by the SOI. We elucidate that the magnitude and sign of the induced spin polarization sensitively depend on the electron filling. To understand these results, we construct an analytical theory based on the Floquet theorem. The theory successfully explains the dependencies on E0 and ω and ascribes the electron-filling dependence to a momentum-dependent effective magnetic field governed by the Fermi-surface geometry. Several candidate materials and experimental conditions relevant to our theory and model parameters are also discussed. Our findings will enable us to engineer the magneto-optical responses of matters via tuning the material parameters. [ABSTRACT FROM AUTHOR]

Dirac semimetals (DSMs) are three-dimensional analogue to graphene with symmetry enforced bulk Dirac nodes. Among various DSMs, ZrSiS has attracted great interests recently, due to its three dimensional Dirac nodal line protected by the nonsymmorphic symmetry. It belongs to a large family of isostructural compounds with rich quantum phenomenon. Here we present a comprehensive study of the first principle calculation, angle-resolved photoemission spectroscopy measurements, and scanning tunneling microscope experiments on ZrGeTe, a member of the ZrSiS family with stronger spin–orbit coupling (SOC). Our band structure calculation shows Dirac line nodes along $\bar{AM}$ and $\bar{XR}$ , the signature of linearly dispersive diamond-shaped band around $\bar{{\Gamma}}$ , and the existence of floating gapless surface states at $\bar{X}$ with Rashba spin-split helical spin texture. Furthermore, characteristic q -vectors including two Umklapp scattering vectors revealed by our quasiparticle scattering interference imaging can be identified with joint density of states simulation based on our calculated band structure. Our results demonstrate the effects of large SOC on the electronic structure of ZrGeTe, which may benefit the potential application by utilizing its exotic quantum states in the future.

The layered polar semiconductor BiTeI exhibits large Rashba-type spin–orbit splittings in its bulk and surface electronic structure. Here we report an artificial structural modification near the surface of BiTeI(0001) induced by annealing in vacuum. Using scanning tunneling microscopy we show that the annealing-induced change in the near-surface stoichiometry results in a structural change from a non-centrosymmetric triple-layered to a quintuple-layered structure. The structural change gives rise to the emergence of topological surface states with helical spin texture as demonstrated by angle-resolved photoemission experiments and relativistic first-principles calculations. The results provide a way to modify the electronic structure of layered materials by a controlled manipulation of the atomic stacking sequences.

Using the physisorption and chemisorption of inorganic molecules on BiAg _2 /Ag(111) we demonstrate from first principles that the spin–orbit splitting and the spin direction of surface Rashba-split states can be manipulated selectively. Although NH _3 is physisorbed, it nevertheless leads to a slight enhancement of the outward buckling of the surface Bi that increases the magnitude of the Rashba splitting. On the other hand, the weakly chemisorbed BH _3 determines a strong inward relaxation of the surface Bi such that the occupied Rashba state shifts into Ag bulk states while a new unoccupied one is induced. Importantly, for the BH _3 –BiAg _2 /Ag(111) system the size of the out-of-plane spin polarization is significantly larger than the in-plane one at variance with the clean surface case.

The spin splitting of conduction band electrons in inversion-asymmetric InGaAs/InP quantum wells (QWs) is studied by Shubnikov-de Haas measurements combining the analysis of beating patterns and coincidence measurements in doubly tilted magnetic fields. The method allows us to determine the absolute values of the Rashba and linear Dresselhaus spin–orbit interaction (SOI) coefficients, their relative sign and the full Landé g-tensor. This is achieved by analyzing the anisotropy of the beat node positions with respect to both polar and azimuthal angles between the magnetic field direction and the QW normal. We show that the SOI is dominated by a large Rashba coefficient together with a linear Dresselhaus coefficient that is 10% of the Rashba coefficient. Their relative sign is found to be positive. The g-tensor is found to have a marked out-of-plane anisotropy and a smaller but distinct in-plane anisotropy due to SOI.

We report on a combined low-temperature scanning tunneling spectroscopy (STS), angle-resolved photoemission spectroscopy (ARPES), and density functional theory (DFT) investigation of the R30�Pb/Ag(111) surface alloy which provides a giant Rashba-type spin splitting. With STS we observed spectroscopic features that are assigned to two hole-like Rashba-split bands in the unoccupied energy range. By means of STS and quantum interference mapping we determine the band onsets, splitting strengths, and dispersions for both bands. The unambiguous assignment of scattering vectors is achieved by comparison to ARPES measurements. While intra-band scattering is found for both Rashba bands, inter-band scattering is only observed in the occupied energy range. Spin- and orbitally-resolved band structures were obtained by DFT calculations. Considering the scattering between states of different spin- and orbital character, the apparent deviation between experimentally observed scattering events and the theoretically predicted spin polarization could be resolved. [ABSTRACT FROM AUTHOR]

We study the electron spin relaxation in both symmetric and asymmetric GaAs/AlGaAs quantum wells (QWs) grown on (110) substrates in an external magnetic field B applied along the QW normal. The spin polarization is induced by circularly polarized light and is detected using the time-resolved Kerr rotation technique. In the asymmetric structure, where a δ-doped layer on one side of the QW produces the Rashba contribution to the conduction-band spin–orbit splitting, the lifetime of electron spins aligned along the growth axis exhibits an anomalous dependence on B in the range 0�<�B�<�0.5 T; this results from the interplay between the Dresselhaus and Rashba effective fields which are perpendicular to each other. For larger magnetic fields, the spin lifetime increases, which is a consequence of the cyclotron motion of the electrons and is also observed in (001)-grown quantum wells. The experimental results are in agreement with the calculation of the spin lifetimes in (110)-grown asymmetric quantum wells described by the point group Cs, where the growth direction is not the principal axis of the spin-relaxation-rate tensor. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We show that dynamics in the spin–orbit coupling field simulate the von Neumann measurement of a particle spin. We demonstrate how the measurement influences the spin and coordinate evolution of a particle by comparing two examples of such a procedure. The first example is a simultaneous measurement of spin components, σx and σy, corresponding to non-commuting operators, which cannot be accurately obtained together at a given time instant due to the Heisenberg uncertainty ratio. By mapping spin dynamics onto a spatial walk, such a procedure determines measurement-time averages of σx and σy, which can already be precisely evaluated in a single short-time measurement. The other, qualitatively different, example is the spin of a one-dimensional particle in a magnetic field. Here, the measurement outcome depends on the angle between the spin–orbit coupling and magnetic fields. These results can be applied to studies of spin–orbit coupled cold atoms and electrons in solids. [ABSTRACT FROM AUTHOR]

Spin electromagnetic fields driven by the Rashba spin–orbit interaction, or Rashba-induced spin Berry's phase, in ferromagnetic metals are theoretically studied using the Keldysh Green's function method. Considering the limit of strong sd coupling without spin relaxation (adiabatic limit), the spin electric and magnetic fields are determined by calculating transport properties. The spin electromagnetic fields can be expressed in terms of a Rashba-induced effective vector potential, and thus they satisfy Maxwell's equation. In contrast to the conventional spin Berry's phase, the Rashba-induced one is linear in the gradient of magnetization profile, and thus can be extremely large even for slowly varying structures. We show that the Rashba-induced spin Berry's phase exerts a Lorentz force on spin resulting in a giant spin Hall effect in magnetic thin films in the presence of magnetization structures. A Rashba-induced spin magnetic field would be useful to distinguish between topologically equivalent magnetic structures. We propose experimental setups where a Rashba-induced spin magnetic field is identified. [ABSTRACT FROM AUTHOR]

Using spin and angle-resolved photoemission spectroscopy we investigate a momentum region in Pb quantum well states on Si(111) where hybridization between Rashba-split bands alters the band structure significantly. Starting from the Rashba regime where the dispersion of the quasi-free two-dimensional electron gas is well described by two spin-polarized parabolas, we find a breakdown of the Rashba behavior which manifests itself (i) in a spin splitting that is no longer proportional to the in-plane momentum and (ii) in a reversal of the sign of the momentum splitting. Our experimental findings are well explained by including interband spin–orbit coupling that mixes Rashba-split states with anti-parallel rather than parallel spins. Similar results for Pb/Cu(111) reveal that the proposed hybridization scenario is independent on the supporting substrate. [ABSTRACT FROM AUTHOR]

The quantum oscillatory magnetization M of a two-dimensional electron system in a magnetic field B is found to provide quantitative information on both the Rashba- and Dresselhaus spin–orbit interaction (SOI). This is shown by first numerically solving the model Hamiltonian including the linear Rashba- and Dresselhaus SOI and the Zeeman term in particular in a doubly tilted magnetic field and second evaluating the intrinsically anisotropic magnetization for different directions of the in-plane magnetic field component. The amplitude of specific magnetic quantum oscillations in M(B) is found to be a direct measure of the SOI strength at fields B where SOI-induced Landau level anticrossings occur. The anisotropic M allows one to quantify the magnitude of both contributions as well as their relative sign. The influence of cubic Dresselhaus SOI on the results is discussed. We use realistic sample parameters and show that recently reported experimental techniques provide a sensitivity which allows for the detection of the predicted phenomena. [ABSTRACT FROM AUTHOR]

The surface alloy Bi/Cu(111) shows a paradigmatic free-electron-like surface state with a very large Rashba-type spin–orbit splitting. Using angle-resolved photoemission we investigate how adsorbates of different chemical nature influence the size of the spin splitting in this system. We find that the adsorption of small amounts of monovalent Na atoms leads to an enhancement of the spin splitting while an overlayer of the closed-shell rare gas Xe causes a reduction. The latter result is in contrast to the Au(111) surface for which an increased splitting size after Xe-adsorption was observed. We discuss these experimental findings in terms of the characteristic differences of the surface state wave functions and their spatial deformation in the presence of different types of adsorbates. Our results provide insight into the complex interplay of atomic and interface potential gradients governing the Rashba effect. [ABSTRACT FROM AUTHOR]

The Ir(111) surface is known to host a surface state with a giant spin–orbit splitting due to the Rashba effect. This surface state is stable even in air when Ir is protected with an epitaxial graphene overlayer. In the present paper, we reveal an effect allowing one to tune the binding energy of this spin-split surface state up and down and demonstrate the practical application of this effect by two different approaches. The first approach is related to a decoration of the moiré pattern of single-layer graphene on Ir(111) by self-assembled nanoclusters of different compositions. The clusters locally pin graphene to the Ir substrate and enhance the amplitude of its structural corrugation, which, in turn, leads to an increase in the surface state binding energy. The second approach is related to the synthesis of few-layer graphene on Ir(111) by segregation of carbon. Additional graphene layers induce a shift of the Ir surface state towards lower binding energies and bring it almost to the Fermi level. Based on density functional calculations performed for the graphene/Ir(111) system, we show that in both cases the effect causing the binding energy shifts is intimately related to the distance between graphene and the Ir surface, which is subject to change due to deposition of clusters or by increasing the amount of graphene overlayers. In contrast, the observed spin–orbit splitting of the Ir(111) surface state remains remarkably robust and constant in all cases. Our theoretical analysis reveals that such stability can be explained by the localization properties of the Ir surface state that is a deep surface resonance. [ABSTRACT FROM AUTHOR]

I perform a complete classification of two-dimensional, quasi-one-dimensional (1D) and 1D topological superconductors which originate from the suitable combination of inhomogeneous Rashba spin–orbit coupling, magnetism and superconductivity. My analysis reveals alternative types of topological superconducting platforms for which Majorana fermions are accessible. Specifically, I observe that for quasi-1D systems with Rashba spin–orbit coupling and time-reversal violating superconductivity, such as for instance due to a finite Josephson current flow, Majorana fermions can emerge even in the absence of magnetism. Furthermore, for the classification I also consider situations where additional ‘hidden’ symmetries emerge, with a significant impact on the topological properties of the system. The latter generally originate from a combination of space group and complex conjugation operations that separately do not leave the Hamiltonian invariant. Finally, I suggest alternative directions in topological quantum computing for systems with additional unitary symmetries. [ABSTRACT FROM AUTHOR]

We performed in situ transport measurements of ultrathin Bi(111) films grown on Si(111) surface, with a four-tip scanning tunneling microscope using metal-coated carbon nanotube (CNT) tips. When the distance between the current injection tip (nonmagnetic Pt-coated CNT tip) and voltage tip (magnetic CoFe-coated CNT tip) was smaller than 1 μm, we found a violation of Green's reciprocity theorem which should hold with no spin transport. This was interpreted as a signal of the current-induced spin polarization (CISP) that occurs due to the Rashba spin-splitting surface-state bands of the Bi(111). The result was reasonably in accord with quantitative analyses based on the CISP theory of Rashba systems. [ABSTRACT FROM AUTHOR]

We present a combined experimental and theoretical study of spin–orbit-induced spin splittings in the unoccupied surface electronic structure of the prototypical Rashba system Au(111). Spin- and angle-resolved inverse-photoemission measurements reveal a Rashba-type spin splitting in the unoccupied part of the L-gap surface state. With increasing momentum parallel to the surface, the spectral intensity is lowered and the spin splitting vanishes as the surface state approaches the band-gap boundary. Furthermore, we observe significantly spin-dependent peak positions and intensities for transitions between unoccupied sp-like bulk bands. Possible reasons for this behavior are considered: initial and final-state effects as well as the transition itself, which is controlled by selection rules depending on the symmetry of the involved states. Based on model calculations, we identify the initial states as origin of the observed Rashba-type spin effects in bulk transitions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Rashba spin-orbit coupling together with electron correlations in the metallic interface between SrTiO3 and LaAlO3 can lead to an unusual combination of magnetic and orbital ordering. We consider such phenomena in the context of the recent observation of anisotropic magnetism. Firstly, we show that Rashba spin-orbit coupling can account for the observed magnetic anisotropy, assuming a correlation driven (Stoner type) instability toward ferromagnetism. Secondly, we investigate nematicity in the form of an orbital imbalance between dxz/dyz orbitals. We find an enhanced susceptibility toward nematicity due to the van Hove singularity in the low-electron-density regime. In addition, the coupling between in-plane magnetization anisotropy and nematic order provides an effective symmetry breaking field in the magnetic phase. We estimate this coupling to be substantial in the low-electron-density regime. The resulting orbital ordering can affect magneto transport. [ABSTRACT FROM AUTHOR]

By all-electron ab initio calculations, the layered polar semiconductor BiTeCl is shown to host giant bulk Rashba spin splitting, similar to the recently reported compound BiTeI. In both materials, the standard Rashba-Bychkov model is no longer applicable, because of huge band extrema shifts even in the absence of spin-orbit coupling and a strong momentum dependence of the Rashba coupling constant (αR). By assuming αR to be orbital dependent, a phenomenological extension of the Rashba-Bychkov model is proposed which explains the splitting behavior of states with small in-plane momentum. [ABSTRACT FROM AUTHOR]

The spin-resolved electronic band structure of Au-induced metallic atomic wires on a vicinal silicon surface, Si(553), was investigated using spin- and angle-resolved photoelectron spectroscopy. We directly measured the spin polarization of three partially filled one-dimensional metallic bands, a one-third-filled band, and the doublet of nearly half-filled bands. For the half-filled doublet, the strong apparent spin polarization was observed near the Fermi energy with a minor out-of-plane spin component. This observation is consistent with the Rashba-type spin-orbit splitting and with a recent experiment on a similar doublet of Si(557)-Au. In contrast, the one-third-filled band does not show a substantial spin polarization within the experimental accuracy, indicating a much smaller spin splitting, if any. These results are discussed for the origin of the partially filled bands and for the intriguing broken-symmetry ground state observed at low temperature.

We have performed spin- and angle-resolved photoemission spectroscopy of antimony (Sb) and bismuth (Bi) thin films grown on Si(111) to elucidate the nature of the Rashba effect in the spin-split surface bands. In Sb, we revealed spin polarization with the in-plane vortical texture on an elongated hole-like Fermi surface. The spin polarization is strongly momentum-dependent, almost vanishing at the region away from the Brillouin zone center. Such unusual suppression of the spin polarization is not observed in Bi, pointing to a strong influence from the quantized bulk bands on the surface spin polarization in Sb. The present result strongly suggests that bulk-surface interband scattering should be properly taken into account to understand the Rashba surface states in group-V semimetals.

We report on a combined low-temperature scanning tunneling spectroscopy (STS), angle-resolved photoemission spectroscopy (ARPES), and density functional theory (DFT) investigation of the $(\sqrt{3}\times \sqrt{3})$ R 30°Pb/Ag(111) surface alloy which provides a giant Rashba-type spin splitting. With STS we observed spectroscopic features that are assigned to two hole-like Rashba-split bands in the unoccupied energy range. By means of STS and quantum interference mapping we determine the band onsets, splitting strengths, and dispersions for both bands. The unambiguous assignment of scattering vectors is achieved by comparison to ARPES measurements. While intra-band scattering is found for both Rashba bands, inter-band scattering is only observed in the occupied energy range. Spin- and orbitally-resolved band structures were obtained by DFT calculations. Considering the scattering between states of different spin- and orbital character, the apparent deviation between experimentally observed scattering events and the theoretically predicted spin polarization could be resolved.

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)- $\sqrt{3}\times \sqrt{3}$ 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.

The magnetoresistance of a three-dimensional Rashba metal placed on top of a ferromagnetic insulator is theoretically investigated. In addition to the intrinsic Rashba spin–orbit interaction, we consider extrinsic spin–orbit coupling via side-jump and skew scattering, as well as Elliott–Yafet spin relaxation. The latter is anisotropic due to the mass anisotropy which reflects the noncentrosymmetric crystal structure. A quasiclassical approach is employed to derive coupled spin-diffusion equations, which are supplemented by boundary conditions that account for the spin-transfer torque at the interface of the bilayer. The magnetoresistance is fully determined by the current-induced spin polarization, i.e., it cannot in general be ascribed to a single (bulk) spin Hall angle. Our theory reproduces several features of the experiments, at least qualitatively, and contains established phenomenological results in the relevant limiting cases. In particular, the anisotropy of the Elliott–Yafet spin relaxation mechanism plays a major role for the interpretation of the observed magnetoresistance. [ABSTRACT FROM AUTHOR]

We investigate long-range chiral magnetic interactions among adatoms mediated by surface states spin-splitted by spin–orbit coupling. Using the Rashba model, the tensor of exchange interactions is extracted wherein a thepseudo-dipolar interaction is found, in addition to the usual isotropic exchange interaction and the Dzyaloshinskii–Moriya interaction. We find that, despite the latter interaction, collinear magnetic states can still be stabilized by the pseudo-dipolar interaction. The interadatom distance controls the strength of these terms, which we exploit to design chiral magnetism in Fe nanostructures deposited on a Au(111) surface. We demonstrate that these magnetic interactions are related to superpositions of the out-of-plane and in-plane components of the skyrmionic magnetic waves induced by the adatoms in the surrounding electron gas. We show that, even if the interatomic distance is large, the size and shape of the nanostructures dramatically impacts on the strength of the magnetic interactions, thereby affecting the magnetic ground state. We also derive an appealing connection between the isotropic exchange interaction and the Dzyaloshinskii–Moriya interaction, which relates the latter to the first-order change of the former with respect to spin–orbit coupling. This implies that the chirality defined by the direction of the Dzyaloshinskii–Moriya vector is driven by the variation of the isotropic exchange interaction due to the spin–orbit interaction. [ABSTRACT FROM AUTHOR]

Spin-split heavy-hole gases in strained germanium quantum wells were characterized by polarisation-resolved terahertz time-domain spectroscopy. Effective masses, carrier densities, g-factors, transport lifetimes, mobilities and Rashba spin-splitting energies were evaluated, giving quantitative insights into the influence of strain. The Rashba coefficient was found to lower for samples with higher biaxial compressive strain, while heavy-hole mobilities were enhanced to over cm2 V−1 s−1 at 3 K. This high mobility enabled the observation of the optical quantum Hall effect at terahertz frequencies for spin-split two-dimensional heavy-holes, evidenced as plateaux in the transverse magnetoconductivity at even and odd filling factors. [ABSTRACT FROM AUTHOR]

We theoretically explore a Rashba spin–orbit coupling scheme which operates entirely in the absolute ground state manifold of an alkali atom, thereby minimizing all inelastic processes. An energy gap between ground eigenstates of the proposed coupling can be continuously opened or closed by modifying laser polarizations. Our technique uses far-detuned ‘Raman’ laser coupling to create the Rashba potential, which has the benefit of low spontaneous emission rates. At these detunings, the Raman matrix elements that link mF magnetic sublevel quantum numbers separated by two are also suppressed. These matrix elements are necessary to produce the Rashba Hamiltonian within a single total angular momentum f manifold. However, the far-detuned Raman couplings can link the three XYZ states familiar to quantum chemistry, which possess the necessary connectivity to realize the Rashba potential. We show that these XYZ states are essentially the hyperfine spin eigenstates of dressed by a strong radio-frequency magnetic field. [ABSTRACT FROM AUTHOR]

Many researchers have reported on spin filters using linear Rashba spin–orbit interactions (SOI). However, spin filters using square and cubic Rashba SOIs have not yet been reported. We consider that this is because the Aharonov–Casher (AC) phases acquired under square and cubic Rashba SOIs are ambiguous. In this study, we try to derive the AC phases acquired under square and cubic Rashba SOIs from the viewpoint of non-Abelian SU(2) gauge theory. These AC phases can be derived successfully from the non-Abelian SU(2) gauge theory without the completing square methods. Using the results, we investigate the spin filtering in a double quantum dot (QD) Aharonov–Bohm (AB) ring under linear, square, and cubic Rashba SOIs. This AB ring consists of elongated QDs and quasi-one-dimensional quantum nanowires under an external magnetic field. The spin transport is investigated from the left nanowire to the right nanowire in the above structure within the tight-binding approximation. In particular, we focus on the difference of spin filtering among linear, square, and cubic Rashba SOIs. The calculation is performed for the spin polarization by changing the penetrating magnetic flux for the AB ring subject to linear, square, and cubic Rashba SOIs. It is found that perfect spin filtering is achieved for all of the Rashba SOIs. This result indicates that this AB ring under general Rashba SOIs can be a promising device for spin current generation. Moreover, the AB rings under general Rashba SOIs behave in totally different ways in response to penetrating magnetic flux, which is attributed to linear, square, and cubic behaviors in the in-plane momentum. This result enables us to make a clear distinction between linear, square, and cubic Rashba SOIs according to the peak position of the perfect spin filtering. [ABSTRACT FROM AUTHOR]

A correction to an article on enhanced giant Rashba splitting is presented.

The Rashba effect, discovered in 1959, continues to supply fertile ground for fundamental research and applications. It provided the basis for the proposal of the spin transistor by Datta and Das in 1990, which has largely inspired the broad and dynamic field of spintronics. More recent developments include new materials for the Rashba effect such as metal surfaces, interfaces and bulk materials. It has also given rise to new phenomena such as spin currents and the spin Hall effect, including its quantized version, which has led to the very active field of topological insulators. The Rashba effect plays a crucial role in yet more exotic fields of physics such as the search for Majorana fermions at semiconductor-superconductor interfaces and the interaction of ultracold atomic Bose and Fermi gases. Advances in our understanding of Rashba-type spin-orbit couplings, both qualitatively and quantitatively, can be obtained in many different ways. This focus issue brings together the wide range of research activities on Rashba physics to further promote the development of our physical pictures and concepts in this field. The present Editorial gives a brief account on the history of the Rashba effect including material that was previously not easily accessible before summarizing the key results of the present focus issue as a guidance to the reader. [ABSTRACT FROM AUTHOR]

We investigate the topological properties and the accessible Majorana fermion (MF) phases arising in a hybrid device consisting of a chain of magnetic adatoms placed on the surface of a conventional superconductor with Rashba spin–orbit coupling (SOC). By identifying the favored classical magnetic ground state of the adatom chain, we extract the corresponding phase diagram which exhibits an interplay of ferromagnetic (FM), antiferromagnetic (AFM) and spiral orders. We determine the parameter regime for which the FM or AFM phases dominate over the spiral and additionally become stable against thermal and quantum fluctuations. For the topological analysis we focus on the FM and AFM cases and employ a low-energy effective model relying on Shiba bound states. We find that for both magnetic patterns the hybrid system behaves as a topological superconductor which can harbor one or even two MFs per edge, due to chiral symmetry. As we show, the two magnetic orderings lead to qualitatively and quantitatively distinct topological features that are reflected in the spatial profile of the MF wavefunctions. Finally, we propose directions on how to experimentally access the diverse MF phases by varying the adatom spacing, the SOC strength, or the magnetic moment of the adatoms in consideration. [ABSTRACT FROM AUTHOR]

We investigate the influence of different spin–orbit couplings on topological phase transitions in the bilayer Kane–Mele model. We find that the competition between intrinsic spin–orbit coupling and Rashba spin–orbit coupling can lead to two dimensional topological metallic states with nontrivial topology. Such phases, although having a metallic bulk, still possess edge states with well defined topological invariants. Specifically, we show that with preserved time reversal symmetry the system can exhibit a -metallic phase with spin helical edge states and a nontrivial invariant. When time reversal symmetry is broken, a Chern metallic phase could appear with chiral edge states and a nontrivial Chern invariant. [ABSTRACT FROM AUTHOR]

We investigate the two-dimensional Fermi surface of high-mobility LaAlO3/SrTiO3 interfaces using Shubnikov-de Haas oscillations. Our analysis of the oscillation pattern underscores the key role played by the Rashba spin–orbit interaction brought about by the breaking of inversion symmetry, as well as the dominant contribution of the heavy dxz/dyz orbitals on electrical transport. We furthermore bring into light the complex evolution of the oscillations with the carrier density, which is tuned by the field effect. [ABSTRACT FROM AUTHOR]

The surface electronic structure of the narrow-gap seminconductor BiTeI exhibits a large Rashba-splitting which strongly depends on the surface termination. Here we report on a detailed investigation of the surface morphology and electronic properties of cleaved BiTeI single crystals by scanning tunneling microscopy, photoelectron spectroscopy (ARPES, XPS), electron diffraction (SPA-LEED) and density functional theory calculations. Our measurements confirm a previously reported coexistence of Te- and I-terminated surface areas originating from bulk stacking faults and find a characteristic length scale of ∼100 nm for these areas. We show that the two terminations exhibit distinct types of atomic defects in the surface and subsurface layers. For electronic states resided on the I terminations we observe an energy shift depending on the time after cleavage. This aging effect is successfully mimicked by depositon of Cs adatoms found to accumulate on top of the I terminations. As shown theoretically on a microscopic scale, this preferential adsorbing behaviour results from considerably different energetics and surface diffusion lengths at the two terminations. Our investigations provide insight into the importance of structural imperfections as well as intrinsic and extrinsic defects on the electronic properties of BiTeI surfaces and their temporal stability. [ABSTRACT FROM AUTHOR]

We have performed spin- and angle-resolved photoemission spectroscopy of antimony (Sb) and bismuth (Bi) thin films grown on Si(111) to elucidate the nature of the Rashba effect in the spin-split surface bands. In Sb, we revealed spin polarization with the in-plane vortical texture on an elongated hole-like Fermi surface. The spin polarization is strongly momentum-dependent, almost vanishing at the region away from the Brillouin zone center. Such unusual suppression of the spin polarization is not observed in Bi, pointing to a strong influence from the quantized bulk bands on the surface spin polarization in Sb. The present result strongly suggests that bulk-surface interband scattering should be properly taken into account to understand the Rashba surface states in group-V semimetals. [ABSTRACT FROM AUTHOR]