In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain certain peculiarities in the electron spin resonance of two-dimensional semiconductors. Over the past thirty years, similar ideas have been leading to a vast number of predictions, discoveries, and innovative concepts far beyond semiconductors. The past decade has been particularly creative with the realizations of means to manipulate spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and with the discovery of new topological classes of materials. These developments reinvigorated the interest of physicists and materials scientists in the development of inversion asymmetric structures ranging from layered graphene-like materials to cold atoms. This review presents the most remarkable recent and ongoing realizations of Rashba physics in condensed matter and beyond.
When the inversion symmetry is broken at a surface, spin-orbit interaction gives rise to spin-dependent energy shifts - a phenomenon which is known as the spin Rashba effect. Recently, it has been recognized that an orbital counterpart of the spin Rashba effect - the orbital Rashba effect - can be realized at surfaces even without spin- orbit coupling. Here, we propose a mechanism for the orbital Rashba effect based on sp orbital hybridization, which ultimately leads to the electric polarization of surface states. As a proof of principle, we show from first principles that this effect leads to…
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.
We have studied spin-depend electron tunnelling through the Rashba barrier in a monolayer graphene lattice. The transfer matrix method, have been employed to obtain the spin dependent transport properties of the chiral particles. It is shown that graphene sheets in presence of Rashba spin-orbit barrier will act as an electron spin- inverter.
We show that a finite magnetic flux threading a multichannel semiconductor ring induces spin accumulation at the borders of the sample when the Rashba spin-orbit interaction is taken into account even in the absence of external electric fields.
Theory of Rashba spin-orbit coupling in magnetic metals is worked out from microscopic Hamiltonian describing d-orbitals. When structural inversion symmetry is broken, electron hopping between $d$-orbitals generates chiral ordering of orbital angular momentum, which combines with atomic spin-orbit coupling to result in the Rashba interaction. Rashba parameter characterizing the interaction is band-specific, even reversing its sign from band to band. Large enhancement of the Rashba parameter found in recent experiments is attributed to the orbital mixing of 3d magnetic atoms with non-magnetic h…
We derive the effective dimensionally reduced Schrödinger equation with spin-orbit interaction in low-dimensional electronic strain driven nanostructures. A method of adiabatic separation among fast normal quantum degrees of freedom and slow tangential quantum degrees of freedom is used to show the emergence of a strain-induced Rashba-like spin-orbit interaction (SOI). By applying this analysis to one-dimensional curved quantum wires we demonstrate that the curvature-induced Rashba SOI leads to enhanced spin-orbit effects.
We study the effect of anisotropy of the Rashba coupling on the extrinsic spin Hall effect due to spin-orbit active adatoms on graphene. In addition to the intrinsic spin-orbit coupling, a generalized anisotropic Rashba coupling arising from the breakdown of both mirror and hexagonal symmetries of pristine graphene is considered. We find that Rashba anisotropy can strongly modify the dependence of the spin Hall angle on carrier concentration. Our model provides a simple and general description of the skew scattering mechanism due to the spin-orbit coupling that is induced by proximity to large…
The Rashba and Dresselhaus types of spin-orbit coupling are two typical linear coupling forms. We establish the fundamental physics of a model which can be viewed as the double version of the Rashba and Dresselhaus spin-orbit coupling. This model describes the low energy physics of a class of massless Dirac fermions in spin-orbit systems. The physical properties of the massless Dirac fermions are determined by the mathematical relations of spin-orbit coefficients. For equal Rashba and Dresselhauss coupling constants, k-independent eigenspinors and a persistent spin helix combined with massless…
Domain wall in bilayer graphene with Rashba spin-orbital coupling and staggered sublattice potentials, at the interface between two domains with different gated voltages, is studied. Varying type of zero-line modes are identified, including zero-line mode with pure spin filtering effect. The Y-shape current partition at the junction among three different domains are proposed.
Determination of Rashba and Dresselhaus spin-orbit interaction strengths in a particular sample remains a challenge even today. In this article we investigate the possibilities of measuring the absolute values of these interaction strengths by calculating persistent charge and spin currents in a mesoscopic ring. Our numerical results can be verified experimentally.
We consider a disordered graphene layer with anisotropic Rashba spin-orbit coupling subjected to a longitudinal electric field. Using the linear response theory we calculate current-induced spin polarization including in-plane normal and parallel components with respect to the electric field direction. Unlike the case of isotropic Rashba spin-orbit where the normal component of spin polarization is linear in terms of Fermi energy around the Dirac point, anisotropic Rashba spin-orbit can result in non-linear dependence of this component at such energies within the Lifshitz points. Furthermore, …
We have investigated the electronic properties of elliptical quantum dots in a perpendicular external magnetic field, and in the presence of the Rashba spin-orbit interaction. Our work indicates that the Fock-Darwin spectra display strong signature of Rashba spin-orbit coupling even for a low magnetic field, as the anisotropy of the quantum dot is increased. An explanation of this pronounced effect with respect to the anisotropy is presented. The strong spin-orbit coupling effect manifests itself prominently in the corresponding dipole-allowed optical transitions, and hence is susceptible to d…
A key concept in the emerging field of spintronics is the gate voltage or electric field control of spin precession via the effective magnetic field generated by the Rashba spin orbit interaction. Here, we demonstrate the generation and tuning of electric field induced Rashba spin orbit interaction in InAs nanowires where a strong electric field is created either by a double gate or a solid electrolyte surrounding gate. In particular, the electrolyte gating enables six-fold tuning of Rashba coefficient and nearly three orders of magnitude tuning of spin relaxation time within only 1 V of gate …
The Harper-Hofstadter problem for two-dimensional electron gas with Rashba spin-orbit coupling subject to periodic potential and perpendicular magnetic field is studied analytically and numerically. The butterfly-like energy spectrum, spinor wave functions as well as the spin density and average spin polarization are calculated for actual parameters of semiconductor structure. Our calculations show that in two-dimensional electron gas subject to periodic potential and uniform magnetic field the effects of energy spectrum splitting caused by large spin-orbit Rashba coupling can be observed expe…
We consider a finite range ac-biased front gate acting upon a quantum channel with Rashba and Dresselhaus spin-orbit interaction effects. The ac-biased gate, giving rise to a dynamical Rashba coupling, causes spin-resolved coherent resonant inelastic scattering. A pure dc spin current is subsequently generated without accompanying charge current. In the presence of Dresselhaus effect, the dc spin current is suppressed in the low kinetic energy regime but is assisted in the high kinetic energy regime.
In this work we study the effects of a longitudinal periodic potential on a parabolic quantum wire defined in a two-dimensional electron gas with Rashba spin-orbit interaction. For an infinite wire superlattice we find, by direct diagonalization, that the energy gaps are shifted away from the usual Bragg planes due to the Rashba spin-orbit interaction. Interestingly, our results show that the location of the band gaps in energy can be controlled via the strength of the Rashba spin-orbit interaction. We have also calculated the charge conductance through a periodic potential of a finite length …
We show theoretically that conversion between spin and charge by spin-orbit interaction in metals occurs even in a non-local setup where magnetization and spin-orbit interaction are spatially separated if electron diffusion is taken into account. Calculation is carried out for the Rashba spin-orbit interaction treating the coupling with a ferromagnet perturbatively. The results indicate the validity of the concept of effective spin gauge field (spin motive force) in the non-local configuration. The inverse Rashba-Edelstein effect observed for a trilayer of a ferromagnet, a normal metal and a h…
We theoretically study phonon-drag contribution to the thermoelectric power and hot-electron energy-loss rate in a Rashba spin-orbit coupled two-dimensional electron system (2DES) in the Bloch-Gruneisen (BG) regime. We assume that electrons interact with longitudinal acoustic phonons through deformation potential and with both longitudinal and transverse acoustic phonons through piezoelectric potential. Effect of the Rashba spin-orbit interaction on magnitude and temperature dependence of the phonon-drag thermoelectric power and hot-electron energy-loss rate are discussed. We numerically extra…
We report on $\vec{k}\cdot\vec{p}$ calculations of Rashba spin-orbit coupling controlled by external gates in InAs/InAsP core-shell nanowires. We show that charge spilling in the barrier material allows for a stronger symmetry breaking than in homoegenous nano-materials, inducing a specific interface-related contribution to spin-orbit coupling. Our results qualitatively agree with recent experiments [S. Futhemeier \textit{et al.}, Nat. Commun. \textbf{7}, 12413 (2016)] and suggest additional wavefunction engineering strategies to enhance and control spin-orbit coupling.
Using canonical transformations we diagonalize approximately the Hamiltonian of a gaussian wire with Rashba spin-orbit interaction. This proceedure allows us to obtain the energy dispersion relations and the wavefunctions with good accuracy, even in systems with relatively strong Rashba coupling. With these eigenstates one can calculate the non-equilibrium spin densities induced by applying bias voltages across the sample. We focus on the $z$-component of the spin density, which is related to the spin Hall effect.
We consider the magnetic response of a two-dimensional electron gas (2DEG) with both Rashba and Dresselhaus spin-orbit coupling to a microwave excitation. We generalize the results of [A. Shnirman and I. Martin, Europhys. Lett. 78, 27001 (2007).], where pure Rashba coupling was studied. We observe that the microwave with the in-plane electric field and the out-of-plane magnetic field creates an out-of-plane spin polarization. The effect is more prominent in clean systems with resolved spin-orbit-split subbands. Considered as response to the microwave magnetic field, the spin-orbit contribution…
Following the early theoretical descriptions of the spin-orbit-induced spin torque [S.G. Tan et al., arXiv:0705.3502 (2007); S.G.Tan et al., Ann. Phys.326, 207 (2011)], the first experimental observation of such effect was reported by L. M. Miron et al., Nature Mater, 9, 230 (2010). We present in this article three additional spin torque terms that arise from the non-uniformity in magnetization space of the Rashba spin-orbit effect. We propose a simple Rashba gradient device which could potentially lower switching current by n orders of magnitude, where large n measures a small magnetization c…
We consider a single-level quantum dot coupled to two leads which are ferromagnetic in general. Apart from tunneling processes conserving electron spin, we also include processes associated with spin-flip of tunneling electrons, which appear due to Rashba spin-orbit coupling. Charge and heat currents are calculated within the non-equilibrium Green's function technique. When the electrodes are half-metallic (fully spin polarized), the Rashba spin-orbit coupling leads to Fano-like interference effects, which result in an enhanced thermoelectric response. It is also shown that such a system can o…
We present calculations of the frequency-dependent spin susceptibility tensor of a two-dimensional electron gas with competing Rashba and Dresselhaus spin-orbit interaction. It is shown that the interplay between both types of spin-orbit coupling gives rise to an anisotropic spectral behavior of the spin density response function which is significantly different from that of vanishing Rashba or Dresselhaus case. Strong resonances are developed in the spin susceptibility as a consequence of the angular anisotropy of the energy spin-splitting. This characteristic optical modulable response may b…
In this article, the modified Kane-Mele Hamiltonian is derived for graphene with wedge disclination and spin orbit couplings (intrinsic and Rashba). The wedge disclination changes the flat lattice into the conical lattice and hence modifies the spin orbit couplings. The Hamiltonian is exactly solved for the intrinsic spin orbit interaction and perturbatively for the Rashba spin orbit interaction. It is shown that there exists the Kramer's degenerate midgap localized spin separated fluxon states around the defect. These zero energy spin separated states occur at the external magnetic flux value…
Magnetization dynamics in a ferromagnet can induce a spin-dependent electric field through spin motive force. Spin current generated by the spin-dependent electric field can in turn modify the magnetization dynamics through spin-transfer torque. While this feedback effect is usually weak and thus ignored, we predict that in Rashba spin-orbit coupling systems with large Rashba parameter $α_{\rm R}$, the coupling generates the spin-dependent electric field [$\pm(α_{\rm R}m_e/e\hbar) (\vhat{z}\times \partial \vec{m}/\partial t)]$, which can be large enough to modify the magnetization dynamics sig…
We search for the uniform Hartree-Fock ground state of the two-dimensional electron gas formed in semiconductor heterostructures including the Rashba spin-orbit interaction. We identify two competing quantum phases: a ferromagnetic one with partial spin polarization in the perpendicular direction and a paramagnetic one with in-plane spin. We present a phase diagram in terms of the relative strengths of the Rashba to the Coulomb interaction and the electron density. We compare our theoretical description with existing experimental results obtained in GaAs-AlGaAs heterostructures.
By using the momentum-space Lanczos recursive method which considers rigorously all multiple-scattering events, we unveil that the non-perturbative disorder effect has dramatic impact on the charge transport of a two-dimensional electron system with Rashba spin-orbit coupling in the low-density region. Our simulations find a power-law dependence of the dc longitudinal conductivity on the carrier density, with the exponent linearly dependent on the Rashba spin-orbit strength but independent of the disorder strength. Therefore, the classical charge transport influenced by complicated multiple-sc…
We analyze theoretically optical generation of a spin-polarized charge current (photogalvanic effect) and spin polarization in graphene with Rashba spin-orbit coupling. An external magnetic field is applied in the graphene plane, which plays a crucial role in the mechanism of current generation. We predict a highly efficient resonant-like photogalvanic effect in a narrow frequency range which is determined by the magnetic field. A relatively less efficient photogalvanic effect appears in a broader frequency range, determined by the electron concentration and spin-orbit coupling strength.
We study a two-dimensional electron system in the presence of both Rashba and Dresselhaus spin-orbit interactions in a perpendicular magnetic field. Defining two suitable boson operators and using the unitary transformations we are able to obtain the exact Landau levels in the range of all the parameters. When the strengths of the Rashba and Dresselhaus spin-orbit interactions are equal, a new analytical solution for the vanishing Zeeman energy is found, where the orbital and spin wave functions of electron are separated. It is also shown that in this case the Zeeman and spin-orbit splittings …
Electronic bound states around charged impurities in two-dimensional systems with structural inversion asymmetry can be described in terms of a two-dimensional hydrogen atom in the presence of a Rashba spin-orbit interaction. Here, the energy levels of the bound electron are evaluated numerically as a function of the spin-orbit interaction, and analytic expressions for the weak and strong spin-orbit coupling limits are compared with the numerical results. It is found that, besides the level splitting due to the lack of inversion symmetry, the energy levels are lowered for sufficiently strong s…
The effect of Rashba spin-orbital interaction upon supercurrent in S-2DEG-S proximity junctions is investigated in the clean limit. Generalization of Beenakker's formula for Andreev levels to the case of spin-orbital scattering is presented. Spin-orbit - induced splitting of Andreev bound-states is predicted for a junction of infinite width, and with non-vanishing normal backscattering at S/N interfaces. Semiclassical average of the Josephson current is however insensitive to the Rashba coupling as long as electron-electron interaction in 2DEG is neglected.
We have identified two useful exact properties of the perturbative expansion for the case of a two-dimensional electron liquid with Rashba or Dresselhaus spin-orbit interaction and in the absence of magnetic field. The results allow us to draw interesting conclusions regarding the dependence of the exchange and correlation energy and of the quasiparticle properties on the strength of the spin-orbit coupling which are valid to all orders in the electron-electron interaction.
We investigate mesoscopic fluctuations in the spin polarization generated by a static electric field and by Rashba spin-orbit interaction in a disordered 2D electron gas. In a diagrammatic approach we find that the out-of-plane polarization -- while being zero for self-averaging systems -- exhibits large sample-to-sample fluctuations which are shown to be well within experimental reach. We evaluate the disorder-averaged variance of the susceptibility and find its dependence on magnetic field, spin-orbit interaction, dephasing, and chemical potential difference.
The spin-orbit splitting of the electron levels in a two-dimensional quantum dot in a perpendicular magnetic field is studied. It is shown that at the point of an accidental degeneracy of the two lowest levels above the ground state the Rashba spin-orbit coupling leads to a level anticrossing and to mixing of spin-up and spin-down states, whereas there is no mixing of these levels due to the Dresselhaus term. We calculate the relaxation and decoherence times of the three lowest levels due to phonons. We find that the spin relaxation rate as a function of a magnetic field exhibits a cusp-like s…
Linear conductance of graphene-based p-n junctions with Rashba spin-orbit coupling is considered theoretically. A square potential step is used to model the junctions, while the coupling is introduced in terms of the Kane-Mele model (C.L. Kane and E.J. Mele, Phys.Rev.Lett. 95, 226801(2005)). The main objective is a description of electronic transport in junctions where Rashba parameter is nonuniform. Such a nonuniformity can appear when graphene is asymmetrically covered with atomic layers, or when Rashba coupling is strongly dependent on electric field. It is shown that conductance is signifi…
We establish an exact analytical treatment for the determination of the strengths of the Rashba and Dresselhaus spin-orbit interactions in a single sample by measuring persistent spin current. A hidden symmetry is exploited in the Hamiltonian to show that the spin current vanishes when the strength of the Dresselhaus interaction becomes equal to the strength of the Rashba term. The results are sustained even in the presence of disorder and thus an experiment in this regard will be challenging.
New exact and asymptotical results for the one particle Green's function of 2D electrons with combined Rashba - Dresselhaus spin - orbit interaction in the presence of in-plane uniform magnetic field are presented. A special case that allows an exact analytical solution is also highlighted. To demonstrate the advantages of our approach we apply the obtained Green's function to calculation of electron density and magnetization
We present a proposal for an adiabatic quantum pump based on a graphene monolayer patterned by electrostatic gates and operated in the low-energy Dirac regime. The setup under investigation works in the presence of inhomogeneous spin-orbit interactions of intrinsic- and Rashba-type and allows to generate spin polarized coherent current. A local spin polarized current is induced by the pumping mechanism assisted by the spin-double refraction phenomenon.
The Rashba spin-orbit coupling in carbon nanotubes and its effect on spin-dependent transport properties are analyzed theoretically. We focus on clean non-interacting nanotubes with tunable number of subbands $N$. The peculiar band structure is shown to allow in principle for Datta-Das oscillatory behavior in the tunneling magnetoresistance as a function of gate voltage, despite the presence of multiple bands. We discuss the conditions for observing Datta-Das oscillations in carbon nanotubes.
We study a one-dimensional helical system with random Rashba spin-orbit coupling. Using renor- malization group methods, we derive a consistent set of flow equations governing the important con- trol parameters of the backscattering process. Thereby, we prove the existence of disorder-induced two-particle backscattering that can even be non-local in space. This analysis allows us to derive the scaling form of the conductance at low temperatures. We find that two-particle backscattering due to random spin-orbit coupling differs from the one off a single Rashba impurity by both the scaling of th…
The spin-orbit interaction (SOI) of the two-dimensional hole gas in the inversion symmetric semiconductor Ge is studied in a strained-Ge/SiGe quantum well structure. We observed weak anti-localization (WAL) in the magnetoconductivity measurement, revealing that the WAL feature can be fully described by the k-cubic Rashba SOI theory. Furthermore, we demonstrated electric field control of the Rashba SOI. Our findings reveal that the heavy hole (HH) in strained-Ge is a purely cubic-Rashba-system, which is consistent with the spin angular momentum mj = +-3/2 nature of the HH wave function.
Thermoelectric transport phenomena in a single-level quantum dot coupled to ferromagnetic leads are considered theoretically in the Kondo regime. The dot is described by the Anderson model with Rashba type spin-orbit interaction. The finite-U mean field slave boson technique is used to describe the transport characteristics, like heat conductance, thermopower, thermoelectric efficiency (figure of merit). The role of quantum interference effects in thermoelectric parameters is also analyzed.
Spin polarization induced by an external electric field in graphene is considered theoretically in the linear response regime. The graphene is assumed to be deposited on a substrate which leads to the spin-orbit interaction of Rashba type. The induced spin polarization is shown to be in the graphene plane and perpendicular to the electric field. However, the spin polarization changes sign when the Fermi level, whose position can be controlled by an external gate voltage, crosses the Dirac points.
Pumping of charge current by spin dynamics in the presence of the Rashba spin-orbit interaction is theoretically studied. Considering disordered electron, the exchange coupling and spin-orbit interactions are treated perturbatively. It is found that dominant current induced by the spin dynamics is interpreted as a consequence of the conversion from spin current via the inverse spin Hall effect. We also found that the current has an additional component from a fictitious conservative field. Results are applied to the case of moving domain wall.
We study the electronic band structure of monolayer graphene when Rashba spin-orbit coupling is present. We show that if the Rashba spin-orbit coupling is stronger than the intrinsic spin-orbit coupling, the low energy bands undergo trigonal-warping deformation and that for energies smaller than the Lifshitz energy, the Fermi circle breaks up into separate parts. The effect is very similar to what happens in bilayer graphene at low energies. We discuss the possible experimental implications, such as threefold increase of the minimal conductivity for low electron densities, the wavenumber depen…
We study the spin dynamics of two dimensional electron gases (2DEGs) with Rashba spin-orbit coupling by taking account of electron-electron interactions. The diffusion equations for charge and spin densities are derived by making use of the path-integral approach and the quasiclassical Green's function. Analyzing the effect of the interactions, we show that the spin-relaxation time can be enhanced by the electron-electron interaction in the ballistic regime.
We calculate the current-voltage characteristic of a one-dimensional band insulator with magnetic field and Rashba spin-orbit coupling which is connected to nonmagnetic leads. Without spin-orbit coupling we find a complete spin-filtering effect, meaning that the electric transport occurs in one spin channel only. For a large magnetic field which closes the band gap, we show that spin-orbit coupling leads to a transition from metallic to insulating behavior. The oscillations of the different spin-components of the current with the length of the transport channel are studied as well.
We theoretically investigate the spin-dependent Seebeck effect in an Aharonov-Bohm mesoscopic ring in the presence of both Rashba and Dresselhaus spin-orbit interactions under magnetic flux perpendicular to the ring. We apply the Green's function method to calculate the spin Seebeck coefficient employing the tight-binding Hamiltonian. It is found that the spin Seebeck coefficient is proportional to the slope of the energy-dependent transmission coefficients. We study the strong dependence of spin Seebeck coefficient on the Fermi energy, magnetic flux, strength of spin-orbit coupling, and tempe…
We investigate the spin accumulation effect in eccentric semiconductor multichannel rings with Rashba spin-orbit interaction and threaded by a magnetic flux. Due to the finite eccentricity, the spin polarization induced at the borders of the sample is anisotropic and exhibits different patterns and intensities at specific angular directions. This effect, reminiscent of the spin polarization drift induced by the application of an in plane electric field, could be used to manipulate and functionalize the spin polarization in electronic nanorings.
We study the edge states in a two dimensional electron gas with a transverse magnetic field and Rashba spin-orbit coupling. In the bulk, the interplay between the external field perpendicular to the gas plane and the spin-orbit coupling leads to two branches of states that, within the same energy window, have different cyclotron radii. For the edge states, surface reflection generates hybrid states with the two cyclotron radii. We analyze the spectrum and spin structure of these states and present a semiclassical picture of them.
We present low temperature magnetoconductivity measurements of a density-tunable and high mobility two-dimensional electron gas confined in the wide bandgap GaN/AlGaN system. We observed pronounced anti-localization minima in the low-field conductivity, indicating the presence of strong spin-orbit coupling. Density dependent measurements of magnetoconductivity indicate that the coupling is mainly due to the Bychkov-Rashba mechanism. In addition, we have derived a closed-form expression for the magnetoconductivity, allowing us to extract reliable transport parameters for our devices. The Rashba…
We investigate the effect of Rashba spin-orbit coupling (SOC) on the optoelectronic properties of n- and p-type monolayer MoS2. The optical conductivity is calculated within the Kubo formalism. We find that the spin-flip transitions enabled by the Rashba SOC result in a wide absorption window in the optical spectrum. Furthermore, we evaluate the effects of the polarization direction of the radiation, temperature, carrier density, and the strength of the Rashba spin-orbit parameter on the optical conductivity. We find that the position, width, and shape of the absorption peak or absorption wind…
Starting from a microscopic tight-binding model and using second order perturbation theory, we derive explicit expressions for the intrinsic and Rashba spin-orbit interaction induced gaps in the Dirac-like low-energy band structure of an isolated graphene sheet. The Rashba interaction parameter is first order in the atomic carbon spin-orbit coupling strength $ξ$ and first order in the external electric field $E$ perpendicular to the graphene plane, whereas the intrinsic spin-orbit interaction which survives at E=0 is second order in $ξ$. The spin-orbit terms in the low-energy effective Hamilto…
Electron optics exploits the analogies between rays in geometrical optics and electron trajectories, leading to interesting insights and potential applications. Graphene, with its two-dimensionality and photon-like behavior of its charge carriers, is the perfect candidate for the exploitation of electron optics. We show that a circular gate-controlled region in the presence of Rashba spin-orbit interaction in graphene may indeed behave as a Veselago electronic lens but with two different indices of refraction. We demonstrate that this birefringence results in complex caustics patterns for a ci…
We developed the theory of electronic properties of semiconductor quantum rings with the Rashba spin-orbit interaction irradiated by an off-resonant high-frequency electromagnetic field (dressing field). Within the Floquet theory of periodically driven quantum systems, it is demonstrated that the dressing field drastically modifies all electronic characteristics of the rings, including spin-orbit coupling, effective electron mass and optical response. Particularly, the present effect paves the way to controlling the spin polarization of electrons with light in prospective ring-shaped spintroni…
The effect of Rashba spin-orbit (SO) interaction on the hole states in a quantum dot is studied in the presence of an external magnetic field. We demonstrate here that the Rashba SO coupling has a profound effect on the energy spectrum of the holes revealing level repulsions between the states with the same total momentum. We also show that the resulting spin-orbit gap is much larger than the corresponding one for the electron energy levels in a quantum dot. Inter-hole interactions only marginally reduce the spin-orbit gap. This enhanced Rashba effect would manifest itself in the tuneling curr…
