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 window can be tuned by varying these parameters. This study shows that monolayer MoS2 can be a promising tunable optical and optoelectronic material that is active in the infrared to terahertz spectral range.
The spin-dependent density of states and the density of spin polarization of an InAs-based two-dimensional electron gas with the Rashba spin-orbit coupling under an intense terahertz laser field are investigated by utilizing the Floquet states to solve the time-dependent Schrödinger equation. It is found that both densities are strongly affected by the terahertz laser field. Especially a terahertz magnetic moment perpendicular to the external terahertz laser field in the electron gas is induced. This effect can be used to convert terahertz electric signals into terahertz magnetic ones efficien…
Persistent, oscillatory charge and spin currents are shown to be driven by a two-component terahertz laser pulse in a one-dimensional mesoscopic ring with Rashba-Dresselhaus spin orbit interactions (SOI) linear in the electron momentum. The characteristic interference effects result from the opposite precession directions imposed on the electron spin by the two SOI couplings. The time dependence of the currents is obtained by solving numerically the equation of motion for the density operator, which is later employed in calculating statistical averages of quantum operators on few electron eige…
We investigate the effects of the intense terahertz laser field and the spin-orbit coupling on single electron spin in a quantum dot. The laser field and the spin-orbit coupling can strongly affect the electron density of states and can excite a magnetic moment. The direction of the magnetic moment depends on the symmetries of the system, and its amplitude can be tuned by the strength and frequency of the laser field as well as the spin-orbit coupling.
The spin texture in a gate-controlled superlattice with Rashba spin-orbit coupling is studied in the presence of external terahertz radiation causing the superlattice miniband transitions. It is shown that the local distribution of spin density can be flipped by tuning the radiation intensity, allowing the controlled coupling of spins and photons with different polarizations.
The spin-galvanic effect and the circular photogalvanic effect induced by terahertz radiation are applied to determine the relative strengths of Rashba and Dresselhaus band spin-splitting in (001)-grown GaAs and InAs based two dimensional electron systems. We observed that shifting the $δ$-doping plane from one side of the quantum well to the other results in a change of sign of the photocurrent caused by Rashba spin-splitting while the sign of the Dresselhaus term induced photocurrent remains. The measurements give the necessary feedback for technologists looking for structures with equal Ras…
We theoretically demonstrate that a rotating electric-field component of circularly polarized microwave or terahertz light can induce electron-spin polarization within a few picoseconds in a two-dimensional electron system with the Rashba spin-orbit interaction by taking advantage of the magnetoelectric coupling. The efficiency turns out to be several orders of magnitude greater than that of conventional methods, indicating high potential of this technique for future spintronics.
When subjected to a linearly polarized terahertz pulse, a mesoscopic ring endowed with spin-orbit interaction (SOI) of the Rashba-Dresselhaus type exhibits nonuniform azimuthal charge and spin distributions. Both types of SOI couplings are considered linear in the electron momentum. Our results are obtained within a formalism based on the equation of motion satisfied by the density operator which is solved numerically for different values of the angle $ϕ$, the angle determining the polarization direction of the laser pulse. Solutions thus obtained are later employed in determining the time-dep…
The spin relaxation in a 1D InAs quantum dot with the Rashba spin-orbit coupling under driving THz magnetic fields is investigated by developing the kinetic equation with the help of the Floquet-Markov theory, which is generalized to the system with the spin-orbit coupling, to include both the strong driving field and the electron-phonon scattering. The spin relaxation time can be effectively prolonged or shortened by the terahertz magnetic field depending on the frequency and strength of the terahertz magnetic field. The effect can be understood as the sideband-modulated spin-phonon scatterin…
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. This can be exploited in a spin-based field-effect transistor (spin- FET), where the Rashba system forms a 2D channel between ferromagnetic (FM) source and drain electrodes. The electron spin precesses when propagating through the Rashba channel and spin orientations (anti)paralle…
A microscopic kinetic theory is developed which allows to investigate non-Abelian SU(2) systems interacting with meanfields and spin-orbit coupling under magnetic fields in one, two, and three dimensions. The coupled kinetic equations for the scalar and spin components are presented and linearized with respect to an external electric field. The dynamical classical and quantum Hall effect are described in this way as well as the anomalous Hall effect where a new symmetric dynamical contribution to the conductivity is presented. The coupled density and spin response functions to an electric fiel…
We report on the observation of the circular (helicity-dependent) and linear photogalvanic effects in Si-MOSFETs with inversion channels. The developed microscopic theory demonstrates that the circular photogalvanic effect in Si structures it is of pure orbital nature originating from the quantum interference of different pathways contributing to the light absorption.
Here, we report first principles calculations and analysis of laser-induced photocurrents at the surface of a prototype Rashba system. By referring to Keldysh non-equilibrium formalism combined with the Wannier interpolation scheme we perform first-principles electronic structure calculations of a prototype BiAg$_2$ surface alloy, which is a well-known material realization of the Rashba model. In addition to non-magnetic ground state situation we also study the case of in-plane magnetized BiAg$_2$. We calculate the laser-induced charge photocurrents for the ferromagnetic case and the laser-ind…
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 demonstrate the theoretical possibility of obtaining a pure spin current in a 1D ring with spin-orbit interaction by irradiation with a non-adiabatic, two-component terahertz laser pulse, whose spatial asymmetry is reflected by an internal dephasing angle $ϕ$. The stationary solutions of the equation of motion for the density operator are obtained for a spin-orbit coupling linear in the electron momentum (Rashba) and used to calculate the time-dependent charge and spin currents. We find that there are critical values of $ϕ$ at which the charge current disappears, while the spin current reac…
Motivated by recent experimental studies of thin-film devices containing a single ferromagnetic layer, we develop a quantum kinetic theory of current-induced magnetic torques in Rashba-model ferromagnets. We find that current-induced spin-densities that are responsible for the switching behavior are due most essentially to spin-dependent quasiparticle lifetimes and derive analytic expressions for relevant limits of a simple model. Quantitative model parameter estimates suggest that spin-orbit coupling in the adjacent metal normal magnetic layer plays an essential role in the strength of the sw…
Using the Kubo formalism, the magnetic properties of the system in the linear regime have been investigated. Mainly the effect of non-magnetic substrate on the spin susceptibility is calculated. Results show that the Rashba coupling interaction has a central role in the magnetic response function of the system and it is really remarkable since this type of spin orbit coupling can be effectively controlled by an external gate voltage. Most importantly it was shown that, in the presence of the Rashba interaction a magnetic phase transition could be observed. This magnetic phase corresponds to a …
The orientation of the local electron spin quantization axis in momentum space is identified as the most significant physical variable in determining the states of a two-dimensional electron liquid in the presence of Rashba spin-orbit coupling. Within mean field theory several phases can be identified that are characterized by a simple symmetric momentum space occupation. The problem admits uniform paramagnetic as well as spin polarized chiral solutions. The latter have a nontrivial spin texture in momentum space and are constructed out of states that are not solutions of the non interacting H…
We investigate the transport properties of ballistic quantum wires in the presence of Zeeman spin splittings and a spatially inhomogeneous Rashba interaction. The Zeeman interaction is extended along the wire and produces gaps in the energy spectrum which allow electron propagation only for spinors lying along a certain direction. For spins in the opposite direction the waves are evanescent far away from the Rashba region, which plays the role of the scattering center. The most interesting case occurs when the magnetic field is perpendicular to the Rashba field. Then, the spins of the asymptot…
High-order terahertz (THz) sideband generation (HSG) in semiconductors is a phenomenon with physics similar to high-order harmonic generation but in a much lower frequency regime. It was found that the electron-hole pairs excited by a weak optical laser can accumulate Berry phases along a cyclic path under the driving of a strong THz field. The Berry phases appear as the Faraday rotation angles of the emission signal under short-pulse excitation in monolayer MoS$_2$. In this paper, the theory of Berry phase in THz extreme nonlinear optics is applied to biased bilayer graphene with Bernal stack…
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.…
We study the band structure modulation and spin-Hall effect of a two-dimensional heavy-hole system with $k^3$-Rashba spin-orbit coupling (RSOC), irradiated by linearly polarized light. We find that the band structure becomes anisotropic under the illumination by the light. Most remarkably, a pair of additional spin-degeneracy points (apart from $Γ$ point) emerge in the energy dispersion, the locations of which are solely determined by the strength of the amplitude of the incident light. If this degeneracy occurs around the Fermi level, the spin-Hall conductivity (SHC) exhibits a resonance. Awa…
We propose and discuss terahertz electro-absorption modulators based on graphene plasmonic structures. The active device consists of a self-gated pair of graphene layers, which are patterned to structures supporting THz plasmonic resonances. These structures allow for efficient control of the effective THz optical conductivity, thus absorption, even at frequencies much higher than the Drude roll-off in graphene where most previously proposed graphene-based devices become inefficient. Our analysis shows that reflectance-based device configurations, engineered so that the electric field is enhan…
A tight-binding model of bcc tungsten that includes spin-orbit coupling is developed and applied to the surface states of (110) tungsten thin films. The model describes accurately the anisotropic Dirac cone-like dispersion and Rashba-like spin polarization of the surface states, including the crucial effect of the relaxation of the surface atomic layer of the tungsten towards the bulk. It is shown that the surface relaxation affects the tungsten surface states because it results in increased overlaps between atomic orbitals of the surface atomic layer and nearby layers whereas electric fields …
We use an exact solution of the relaxation-time Boltzmann equation in a uniform AC electric field to describe the nonlinear optical response of graphene in the terahertz (THz). The cases of monolayer, bilayer and ABA-stacked trilayer graphene are considered, and the monolayer species is shown to be the most appropriate one to exploit the nonlinear free electron response. We find that a single layer of monolayer graphene shows an optical bistability in the THz range, within the electromagnetic power range attainable in practice. The current associated with the third harmonic generation is also …
Electric weak links, the term used for those parts of an electrical circuit that provide most of the resistance against the flow of an electrical current, are important elements of many nanodevices. Quantum dots, nanowires and nano-constrictions that bridge two bulk conductors (or superconductors) are examples of such weak links. Here we consider nanostructures where the electronic spin-orbit interaction is strong in the weak link but is unimportant in the bulk conductors, and explore theoretically the role of the spin-orbit active weak link (which we call a "Rashba spin splitter") as a source…
Spin current plays a central role in spintronics. In particular, finding more efficient ways to generate spin current has been an important issue and studied actively. For example, representative methods of spin current generation include spin polarized current injections from ferromagnetic metals, spin Hall effect, and spin battery. Here we theoretically propose a new mechanism of spin current generation based on nonlinear phenomena. By using Boltzmann transport theory, we show that a simple application of the electric field $\bf{E}$ induces spin current proportional to $\bf{E^2}$ in noncentr…
We study analytically and numerically spin effects in MoS_2 monolayer armchair quantum wires and quantum dots. The interplay between intrinsic and Rashba spin orbit interactions induced by an electric field leads to helical modes, giving rise to spin filtering in time-reversal invariant systems. The Rashba spin orbit interaction can also be generated by spatially varying magnetic fields. In this case, the system can be in a helical regime with nearly perfect spin polarization. If such a quantum wire is brought into proximity to an s-wave superconductor, the system can be tuned into a topologic…
In this study, terahertz (THz) absorption and transmission of monolayer MoS$_{2}$ was calculated under different carrier concentrations. Results showed that the THz absorption of monolayer MoS$_{2}$ is very small even under high carrier concentrations and large incident angle. Equivalent loss of the THz absorption is the total sum of reflection and absorption that is one to three grades lower than that of graphene. The monolayer MoS$_{2}$ transmission is much larger than that of the traditional GaAs and InAs two-dimensional electron gas. The field-effect tubular structure formed by the monolay…
The magnetic circular dichroism and the Faraday rotation are the fundamental phenomena of great practical importance arising from the breaking of the time reversal symmetry by a magnetic field. In most materials the strength and the sign of these effects can be only controlled by the field value and its orientation. Furthermore, the terahertz range is lacking materials having the ability to affect the polarisation state of the light in a non-reciprocal manner. Here we demonstrate, using broadband terahertz magneto-electro-optical spectroscopy, that in graphene both the magnetic circular dichro…
Optical control of Dirac surface states (SS) in topological insulators (TI) remains one of the most challenging problems governing their potential applications in novel electronic and spintronic devices. Here, using visible-range transient absorption spectroscopy exploiting ~340 nm (~3.65 eV) pumping, we provide evidence for dynamic opening of a gap in Dirac SS of the thin-film 3D TI Bi2Se3, which has been induced by the dynamic Rashba effect occurring in the film bulk with increasing optical pumping power (photoexcited carrier density). The observed effect appears through the transient absorp…
We use first-principles calculations to show that van der Waals (vdW) heterostructures consisting of few-layer Bi$_2$Se$_3$ and PtSe$_2$ exhibit electronic and spintronics properties that can be tuned by varying the constituent layers. Type-II band alignment with layer-tunable band gaps and type-III band alignment with spin-splittings have been found. Most noticeably, we reveal the coexistence of Rashba-type spin-splittings (with large $α_{\rm R}$ parameters) in both the conduction and valence band stemming from few-layer Bi$_2$Se$_3$ and PtSe$_2$, respectively, which has been confirmed by spi…
We study electron transport through waveguides (WGs) in which the strengths of the Rashba ($α$) and Dresselhaus ($β$) terms of the spin-orbit interaction (SOI) vary in space. Subband mixing, due to lateral confinement, is taken into account only between the two first subbands. For sufficiently narrow WGs the transmission $T$ exhibits a square-like shape as a function of $α$ or $β$. Particular attention is paid to the case of equal SOI strengths, $α=β$, for which spin-flip processes are expected to decrease. The transmission exhibits resonances as a function of the length of a SOI-free region s…
We use a mean field approach to study the conductance modulation of gate controlled semiconductor spin interferometers based on the Rashba spin-orbit coupling effect. The conductance modulation is found to be mostly due to Ramsauer type transmission resonances rather than the Rashba effect in typical structures. This is because of significant reflections at the interferometer's contacts due to large potential barriers and effective mass mismatch between the contact material and the semiconductor. Thus, unless particular care is taken to eliminate these reflections, any observed conductance mod…
The ability of spin-orbit interactions to convert charge current into spin current, most often in the bulk of heavy metal thin films, has been the hallmark of spintronics in the last decade. In this study, we demonstrate how the insertion of light metal element interface profoundly affects both the nature of spin-orbit torque and its efficiency in terms of damping-like ($H_{\text{DL}}$) and field-like ($H_{\text{FL}}$) effective fields in ultrathin Co ferromagnet. Indeed, we measure unexpectedly large $H_{\text{FL}}$/$H_{\text{DL}}$ ratio ($\sim$2.5) upon inserting a 1.4 nm thin Al layer in Pt…
Traditionally, strong-field physics explores phenomena in matter (atoms, molecules, and solids) driven by an extremely strong laser field nonperturbatively. However, even in the complete absence of an external electromagnetic field, strong-field phenomena can arise when matter strongly couples with the zero-point field of the quantum vacuum state, i.e., fluctuating electromagnetic waves whose expectation value is zero. Some of the most striking examples of this occur in a cavity setting, in which an ensemble of two-level atoms resonantly interacts with a single photonic mode of vacuum fields, …
Despite its extremely weak intrinsic spin-orbit coupling (SOC), graphene has been shown to acquire considerable SOC by proximity coupling with exfoliated transition metal dichalcogenides (TMDs). Here we demonstrate strong induced Rashba SOC in graphene that is proximity coupled to a monolayer TMD film, MoS2 or WSe2, grown by chemical vapor deposition with drastically different Fermi level positions. Graphene/TMD heterostructures are fabricated with a pickup-transfer technique utilizing hexagonal boron nitride, which serves as a flat template to promote intimate contact and therefore a strong i…
Skew scattering on rare impurity configurations is shown to dominate the anomalous Hall effect in a 2D Rashba ferromagnet. The mechanism originates in scattering on rare impurity pairs separated by distances of the order of the Fermi wave length. Corresponding theoretical description goes beyond the conventional non-crossing approximation. The mechanism provides the only contribution to the anomalous Hall conductivity in the most relevant metallic regime and strongly modifies previously obtained results for lower energies in the leading order with respect to impurity strength.
Spin-charge interconversion is a very active direction in spintronics. Yet, the complex behaviour of some of the most promising systems such as SrTiO$_3$ (STO) interfaces is not fully understood. Here, on the basis of a 6-band $\boldsymbol{k.p}$ method combined with spin-resolved scattering theory, we give a theoretical demonstration of transverse spin-charge interconversion physics in STO Rashba interfaces. Calculations involve injection of spin current from a ferromagnetic contact by resonant tunneling into the native Rashba-split resonant levels of the STO triangular quantum well. We comput…
Although most theoretical calculations of quantum wells with non-square profiles assume that material composition is varied continuously, it is more common in experiment to grow digital alloys. We compare the Rashba spin-orbit interaction of triangular wells using continuous, discrete, and digital alloying profiles in (001)-grown triangular InSb/Al_f(z)In_(1-f(z))Sb, finding a very large difference between digital alloying and the others, including a sign change in the Rashba spin-orbit coupling. We find that the interface contribution to the Rashba spin-orbit coupling is much larger in the co…
The Rashba effect is one of the most striking manifestations of spin-orbit coupling in solids, and provides a cornerstone for the burgeoning field of semiconductor spintronics. It is typically assumed to manifest as a momentum-dependent splitting of a single initially spin-degenerate band into two branches with opposite spin polarisation. Here, combining polarisation-dependent and resonant angle-resolved photoemission measurements with density-functional theory calculations, we show that the two "spin-split" branches of the model giant Rashba system BiTeI additionally develop disparate orbital…
We study Aharonov-Bohm effect in a two-terminal helical ring with long-range hopping in presence of Rashba spin-orbit interaction. We explore how the spin polarization behavior changes depending on the applied magnetic flux and the incoming electron energy. The most interesting feature that we articulate in this system is that zero-energy crossings appear in the energy spectra at $Φ=0$ and also at integer multiples of half-flux quantum values ($n Φ_0/2$, $n$ being an integer) of the applied magnetic flux. We investigate the transport properties of the ring using Green's function formalism and …
Optical properties of metallic nanoparticles are most often considered in terms of plasmons, the coupled states of light and quasi-free electrons. Here we predict that confinement of electrons inside the nanostructure leads to another, very different, type of resonance, which determines the optical properties in the frequency range significantly below the plasmonic resonance. We demonstrate that closely placed confinement-induces resonances typically join into a single composite "super-resonance" which produces giant nonlinearity at low frequencies. Our simulations show how such nonlinearities…
The electronic and optoelectronic properties of two dimensional materials have been extensively explored in graphene and layered transition metal dichalcogenides (TMDs). Spintronics in these two-dimensional materials could provide novel opportunities for future electronics, for example, efficient generation of spin current, which should enable the efficient manipulation of magnetic elements. So far, the quantitative determination of charge current induced spin current and spin-orbit torques (SOTs) on the magnetic layer adjacent to two-dimensional materials is still lacking. Here, we report a l…
It was recently shown that a spatially modulated Rashba spin-orbit coupling in a quantum wire drives a transition from a metallic to an insulating state when the wave number of the modulation becomes commensurate with the Fermi wave length of the electrons in the wire. It was suggested that the effect may be put to practical use in a future spin transistor design. In the present article we revisit the problem and present a detailed analysis of the underlying physics. First, we explore how the build-up of charge density wave correlations in the quantum wire due to the periodic gate configuratio…
Nonlinear couplings between photons and electrons in new materials give rise to a wealth of interesting nonlinear phenomena. This includes frequency mixing, optical rectification or nonlinear current generation, which are of particular interest for generating radiation in spectral regions that are difficult to access, such as the terahertz gap. Owing to its specific linear dispersion and high electron mobility at room temperature, graphene is particularly attractive for realizing strong nonlinear effects. However, since graphene is a centrosymmetric material, second-order nonlinearities a prio…
It is commonly believed that weak light-matter interactions in low-mobility graphene dramatically limits tunability of graphene-based optoelectronic devices, such as tunable absorbers or switches. In this paper, we develop and use a simple circuit model to understand absorption in graphene sheets. In particular, we show that light interacts weakly also with very high-mobility graphene sheets and propose systematic design means to overcome these problems. The results have allowed us to demonstrate in the terahertz band that perfect absorption with excellent electrical tunability can be achieved…
