We present the effective low-energy theory for interacting 1D quantum wires subject to Rashba spin-orbit coupling. Under a one-loop renormalization group scheme including all allowed interaction processes for not too weak Rashba coupling, we show that electron-electron backscattering is an irrelevant perturbation. Therefore no gap arises and electronic transport is described by a modified Luttinger liquid theory. As an application of the theory, we discuss the RKKY interaction between two magnetic impurities. Interactions are shown to induce a slower power-law decay of the RKKY range function than the usual 1D noninteracting $\cos(2k_F x)/|x|$ law. Moreover, in the noninteracting Rashba wire, the spin-orbit coupling causes a twisted (anisotropic) range function with several different spatial oscillation periods. In the interacting case, we show that one special oscillation period leads to the slowest decay, and therefore dominates the RKKY interaction for large separation.
We study the RKKY interaction mediated by the helical edge states of a quantum spin Hall insulator in the presence of the Rashba spin-orbital coupling induced by an external electric field and the electron-electron interaction. We show that in the presence of the Rashba coupling, the RKKY interaction induced by the helical edge states contains not only the Heisenberg-like and the Dzyaloshinskii-Moria terms but also the nematic-type term that is not present originally, with the range functions depending on the strength of the Rashba coupling. We also show that the electron-electron interaction …
We study theoretically the statistical properties of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between localized magnetic moments in a disordered two-dimensional electron gas with both Rashba and Dresselhaus spin-orbit couplings. Averaging over disorder, the static spin susceptibility tensor is evaluated diagrammatically in the mesoscopic (phase-coherent) regime. The disorder-averaged susceptibility leads to a twisted exchange interaction suppressed exponentially with distance, whereas the second-order correlations, which determine the fluctuations (variance) of the RKKY energy, dec…
In this work we have investigated the effect of Rashba splitting on the RKKY interaction in TI thin film both at finite and zero chemical potential. We find that the spin susceptibility of Rashba materials including TI thin film is strongly dependent on the direction of distance vector. Moreover, we find another term in the off-diagonal terms of the spin-susceptibility tensor which in contrast to the well-known DM-like term is symmetric. We show how one can tune the RKKY interaction by using electric field applied perpendicularly to the surface plane and by small chemical doping giving rise to…
We study theoretically the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in one- and two-dimensions in presence of a Rashba spin-orbit (SO) coupling. We show that rotation of the spin of conduction electrons due to SO coupling causes a twisted RKKY interaction between localized spins which consists of three different terms: Heisenberg, Dzyaloshinsky-Moriya, and Ising interactions. We also show that the effective spin Hamiltonian reduces to the usual RKKY interaction Hamiltonian in the twisted spin space where the spin quantization axis of one localized spin is rotated.
In this letter, we have studied the spin torque based magnetization oscillations and switching in presence of Rashba - Zeeman (RZ), Ruderman - Kittel - Kasuya - Yoside (RKKY) and Dzyaloshinskii - Moriya (DM) interactions in a double barrier RZ$|$Heavy Metal (HM)$|$RZ magnetic tunnel junction (MTJ). The system has stable magnetization oscillations and can work as an oscillator or a switcher for a significant difference in the strength of RKKY and DM interaction under suitable spin transfer torque (STT). For the proposed system with same order of RKKY and DM interaction, a nonlinear characterist…
The bulk Rashba semiconductors BiTeX (X=I, Cl and Br) with intrinsically enhanced Rashba spin-orbit coupling provide a new platform for investigation of spintronic and magnetic phenomena in materials. We theoretically investigate the interlayer exchange interaction between two ferromagnets deposited on opposite surfaces of a bulk Rashba semiconductor BiTeI in its trivial and topological insulator phases. In the trivial phase BiTeI, we find that for ferromagnets with a magnetization orthogonal to the interface, the exchange coupling is reminiscent of that of a conventional three-dimensional met…
Motivated by proposals to employ RKKY-coupled spins as building blocks in a solid-state quantum computer, we analyze how the RKKY interaction in a 2D electron gas is influenced by spin-orbit interactions. Using a two-impurity Kondo model with added Dresselhaus and Rashba spin-orbit interactions we find that spin-rotational invariance of the RKKY interaction - essential for having a well-controllable two-qubit gate - is restored when tuning the Rashba coupling to have the same strength as the Dresselhaus coupling. We also discuss the critical properties of the two-impurity Kondo model in the pr…
In a recent Rapid Communication (Phys. Rev. B {\bf 63}, 121210(R) (2001)), Haüsler showed that the interaction between electrons in quantum wires may enhance the persistent spin current arising from Rashba spin-orbital coupling. In this Comments, we would like to point out that this 'enhancement' comes from a misunderstanding to the boosting persistent current in the Luttinger liquid theory. A correct calculation will not give such an enhancement of the persistent spin current. Meanwhile, we provide a Luttinger liquid theory with Rashba spin-orbital interaction by bosonization, which may show …
We discuss the calculation of evanescent states in quasi-one-dimensional quantum wires in the presence of Rashba spin-orbit interaction. We suggest a computational algorithm devised for cases in which longitudinal and transverse motions are coupled. The dispersion relations are given for some selected cases, illustrating the feasibility of the proposed computational method. As a practical application, we discuss the solutions for a wire containing a potential step.
We demonstrate in theory that it is possible to all-electrically manipulate the RKKY interaction in a quasi-one-dimensional electron gas embedded in a semiconductor heterostructure, in the presence of Rashba and Dresselhaus spin-orbit interaction. In an undoped semiconductor quantum wire where intermediate excitations are gapped, the interaction becomes the short-ranged Bloembergen-Rowland super-exchange interaction. Owing to the interplay of different types of spin-orbit interaction, the interaction can be controlled to realize various spin models, e.g., isotropic and anisotropic Heisenberg-l…
We investigate the electronic transport in a quantum wire with localized Rashba interaction. The Rashba field forms quasi-bound states which couple to the continuum states with an opposite spin direction. The presence of this Rashba dot causes Fano-like antiresonances and dips in the wire's linear conductance. The Fano lineshape arises from the interference between the direct transmission channel along the wire and the hopping through the Rashba dot. Due to the confinement, we predict the observation of large charging energies in the local Rashba region which lead to Coulomb-blockade effects i…
We present analytical and numerical results for the effect of Rashba spin-orbit coupling on band structure, transport, and interaction effects in quantum wires when the spin precession length is comparable to the wire width. In contrast to the weak-coupling case, no common spin-quantization axis can be defined for eigenstates within a single-electron band. The situation with only the lowest spin-split subbands occupied is particularly interesting because electrons close to Fermi points of the same chirality can have approximately parallel spins. We discuss consequences for spin-dependent trans…
Rashba spin-orbit coupling and a magnetic field perpendicular to the Rashba axis have been predicted to open a partial gap ("helical gap") in the energy spectrum of noninteracting or weakly interacting one-dimensional quantum wires. By comparing kinetic energy and Coulomb energy we show that this gap opening typically occurs at low electron densities where the Coulomb energy dominates. To address this strongly correlated limit, we investigate Rashba wires using Wigner crystal theory. We find that the helical gap exists even in the limit of strong interactions but its dependence on electron den…
We study the ground-state properties of electrons confined to a quantum wire and subject to a smoothly modulated Rashba spin-orbit coupling. When the period of the modulation becomes commensurate with the band filling, the Rashba coupling drives a quantum phase transition to a nonmagnetic insulating state. Using bosonization and a perturbative renormalization group approach, we find that this state is robust against electron-electron interactions. The gaps to charge- and spin excitations scale with the amplitude of the Rashba modulation with a common interaction-dependent exponent. An estimate…
We analyze the interactions between two Kondo Quantum Dots connected to a Rashba-active Quantum Wire. We find that the Kondo-doublet interaction, at an inter-dot distance of the order of the wire Fermi length, is over an order of magnitude greater than the RKKY interaction. The effects induced on the Kondo-doublet interaction by the wire spin-orbit coupling can be used to control the Quantum Dots spin-spin correlation. These results imply that the widely used assumption that the RKKY is the dominant interaction between Anderson impurities must be revised.
We theoretically study the impacts of linear spin-orbit coupling (SOC) on the Ruderman-Kittel-Kasuya-Yosida interaction between magnetic impurities in two kinds of three-dimensional noncentrosymmetric systems. It has been found that linear SOCs lead to the Dzyaloshinskii-Moriya interaction and the Ising interaction, in addition to the conventional Heisenberg interaction. These interactions possess distinct range functions from three dimensional electron gases and Dirac/Weyl semimetals. In the weak SOC limit, the Heisenberg interaction dominates over the other two interactions in a moderately l…
We analyze the transport properties of two artificial magnetic impurities coupled togethervia a tunable RKKY interaction mediated by conduction electrons of a finite size one dimensional wire. We show that the sign of the RKKY interaction can be controlled by gating the wire. We investigate the interplay between finite size effects and RKKY interaction and found that the two artificial impurities start to interact each-other as soon as the Kondo screening cloud length becomes larger that the length of the wire. This should allow to give a lower experimental estimate of the Kondo screening clou…
We study the transport properties for a Luttinger-liquid (LL) quantum wire in the presence of both Rashba spin-orbit coupling (SOC) and a weak external in-plane magnetic field. The bosonized Hamiltonian of the system with an externally applied longitudinal electric field is established. And then the equations of motion for the bosonic phase fields are solved in the Fourier space, with which the both charge and spin conductivities for the system are calculated analytically based on the linear response theory. Generally, the ac conductivity is an oscillation function of the strengths of electron…
The length over which electron spins reverse direction due to the Rashba effect when injected with an initial polarization along the axes of a quantum wire is investigated theoretically. A soft wall confinement of the wire renormalizes the spin-orbit parameter (and the effective mass) stronger than hard walls. Electron-electron interactions enhance the Rashba precession while evidence is found that the coupling between transport channels may suppress it.
We present calculations of the g factors for the lower conductance steps of 3D hole quantum wires. Our results prove that the anisotropy with magnetic field orientation, relative to the wire, originates in the Rashba spin-orbit coupling. We also analyze the relevance of the deformation, as the wire evolves from 3D towards a flat 2D geometry. For high enough wire deformations, the perpendicular g factors are greatly quenched by the Rashba interaction. On the contrary, parallel g factors are rather insensistive to the Rashba interaction, resulting in a high g factor anisotropy. For low deformati…
This article presents an overview of results pertaining to electronic structure, transport properties, and interaction effects in ballistic quantum wires with Rashba spin splitting. Limits of weak and strong spin--orbit coupling are distinguished, and spin properties of the electronic states elucidated. The case of strong Rashba spin splitting where the spin--precession length is comparable to the wire width turns out to be particularly interesting. Hybridization of spin--split quantum--wire subbands leads to an unusual spin structure where the direction of motion for electrons can fix their s…
We predict the occurrence of Fano lineshapes in a semiconductor quantum wire with local spin-orbit (Rashba) coupling. We show that the Rashba interaction acts in a strictly one dimensional channel as an attractive impurity, leading to the formation of purely bound states. In a quasi-one dimensional system these bound states couple to the conduction ones through the Rashba intersubband mixing, giving rise to pronounced dips in the linear conductance plateaus. We give exact numerical results and propose an approximate model capturing the main ingredients of the effect.
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.
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 provide a general procedure to calculate the current-induced spin-transfer torque which acts on a general steep magnetic texture due to the exchange interaction with an applied spin-polarized current. As an example, we consider a one-dimensional ferromagnetic quantum wire and also include a Rashba spin-orbit interaction. The spin-transfer torque becomes generally spatially non-local. Likewise, the Rashba spin-orbit interaction induces a spatially nonlocal field-like nonequilibrium spin-transfer torque. We also find a spatially varying nonadiabaticity parameter and markedly different domain …
We investigate intersubband mixing effects in multichannel quantum wires in the presence of Rashba spin-orbit coupling and attached to two terminals. When the contacts are ferromagnetic and their magnetization direction is perpendicular to the Rashba field, the spin-transistor current is expected to depend in a oscillatory way on the Rashba coupling strength due to spin coherent oscillations of the travelling electrons. Nevertheless, we find that the presence of many propagating modes strongly influences the spin precession effect, leading to (i) a quenching of the oscillations and (ii) strong…
We analyze the linear conductance of a semiconductor quantum wire containing a region where a local Rashba spin-orbit interaction is present. We show that Fano lineshapes appear in the conductance due to the formation of quasi bound states which interfere with the direct transmission along the wire, a mechanism that we term the Fano-Rashba effect. We obtain the numerical solution of the full Schrödinger equation using the quantum-transmitting-boundary method. The theoretical analysis is performed using the coupled-channel model, finding an analytical solution by ansatz. The complete numerical …
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…
We propose a mechanism for spin polarized photocurrent generation in quantum wires. The effect is due to the combined effect of Rashba spin-orbit interaction, external magnetic field and microwave radiation. The time-independent interactions in the wire give rise to a spectrum asymmetry in k-space. The microwave radiation induces transitions between spin-splitted subbands, and, due to the peculiar energy dispersion relation, charge and spin currents are generated at zero bias voltage. We demonstrate that the generation of pure spin currents is possible under an appropriate choice of external c…
We show that the combination of a Dresselhaus interaction and a spatially periodic Rashba interaction leads to the formation of a helical liquid in a quantum wire when the electron-electron interaction is weakly screened. The effect is sustained by a helicity-dependent effective band gap which depends on the size of the Dresselhaus and Rashba spin-orbit couplings. We propose a design for a semiconductor device in which the helical liquid can be realized and probed experimentally.
We propose a method to determine the relative strength of Rashba and Dresselhaus spin-orbit interaction from transport measurements without the need of fitting parameters. To this end, we make use of the conductance anisotropy in narrow quantum wires with respect to the directions of an in-plane magnetic field, the quantum wire and the crystal orientation. We support our proposal by numerical calculations of the conductance of quantum wires based on the Landauer formalism which show the applicability of the method to a wide range of parameters.
Coherent Rashba spin precession along interacting multi-mode quantum channels is investigated, revisiting the theory of coupled Tomonaga-Luttinger liquids. We identify susceptibilities as the key-parameters to govern exponents and Rashba precession lengths. In semiconducting quantum wires spins of different transport channels are found to {\em dephase} in their respective precession angles with respect to one another, as a result of the interaction. This could explain the experimental difficulty to realize the Datta Das transistor. In single walled carbon nanotubes, on the other hand, interact…
We study the interplay of electron-electron interactions and Rashba spin-orbit coupling in one-dimensional ballistic wires. Using the renormalization group approach we construct the phase diagram in terms of Rashba coupling, Tomonaga-Luttinger stiffness and backward scattering strength. We identify the parameter regimes with a dynamically generated spin gap and show where the Luttinger liquid prevails. We also discuss the consequences for the operation of the Datta-Das transistor.
We investigate theoretically the spin-dependent electron transport in a Rashba quantum wire with rough edges. The charge and spin conductances are calculated as function of the electron energy or the wire length by adopting the spinresolved lattice Green function method. For a single disordered Rashba wire, it is found that the charge conductance quantization is destroyed by the edge disorder. However, a nonzero spin conductance can be generated and its amplitude can be manipulated by the wire length, which is attributed to the broken structure symmetries and the spin-dependent quantum interfe…
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…
We focus on inducing topological state from regular, or irregular scattering in (i) p-wave superconducting wires and (ii) Rashba wires proximity coupled to an s-wave superconductor. We find that contrary to common expectations the topological properties of both systems are fundamentally different: In p-wave wires, disorder generally has a detrimental effect on the topological order and the topological state is destroyed beyond a critical disorder strength. In contrast, in Rashba wires, which are relevant for recent experiments, disorder can {\it induce} topological order, reducing the need for…
Rashba precession of spins moving along a one-dimensional quantum channel is calculated, accounting for Coulomb interactions. The Tomonaga--Luttinger model is formulated in the presence of spin-orbit scattering and solved by Bosonization. Increasing interaction strength at decreasing carrier density is found to {\sl enhance} spin precession and the nominal Rashba parameter due to the decreasing spin velocity compared with the Fermi velocity. This result can elucidate the observed pronounced changes of the spin splitting on applied gate voltages which are estimated to influence the interface el…
We calculate the nuclear magnetic resonance (NMR) response of a quantum wire where at low temperature a self-sustained electron-nuclear spin order is created. Our model includes the electron mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange, electron spin-orbit interactions, nuclear dipolar interactions, and the static and oscillating NMR fields, all of which play an essential role. The paramagnet to helimagnet transition in the nuclear system is reflected in an unusual response: it absorbs at a frequency given by the internal RKKY exchange field, rather than the external static field, wh…
In this work we show that Rashba-based topological superconductor nanowires, where the spin-orbit coupling may change its sign, support three topological phases protected by chiral symmetry. When a superconducting phase gradient is applied over the interface of the two nontrivial phases, the Andreev spectrum is qualitatively phase shifted by πcompared to usual Majorana weak links. The topological π-junction has the striking property of exhibiting maximum supercurrent in the vicinity of vanishing phase difference. Qualitative features of the junction are robust against disorder and magnetic fie…
We investigate the influence of a perpendicular magnetic field on the spectral and spin properties of a ballistic quasi-one-dimensional electron system with Rashba effect. The magnetic field strongly alters the spin-orbit induced modification to the subband structure when the magnetic length becomes comparable to the lateral confinement. A new subband-dependent energy splitting at k=0 is found which can be much larger than the Zeeman splitting. This is due to the breaking of a combined spin orbital-parity symmetry.
The band structure of a quantum wire with the Rashba spin-orbit coupling develops a pseudogap in the presence of a magnetic field along the wire. In such a system spin mixing at the Fermi wavevectors $-k_F$ and $k_F$ can be different. We have investigated theoretically the collective mode of this system, and found that the velocity of this collective excitation depends sensitively on the strength of the Rashba spin-orbit interaction and magnetic field. Our result suggests that the strength of the spin-orbit interaction can be determined from the measurement of the velocity.
We analyze the spectral and transport properties of ballistic quasi one-dimensional systems in the presence of spin-orbit coupling and in-plane agnetic fields. Our results demonstrate that Rashba precession and intersubband coupling must be treated on equal footing for wavevectors near the magnetic field induced gaps. We find that intersubband coupling limits the occurrence of negative effective masses at the gap edges and modifies the linear conductance curves in the strong coupling limit. The effect of the magnetic field on the spin textured orientation of the wire magnetization is discussed…
We calculate the finite-temperature conductance of clean, weakly interacting one-dimensional quantum wires subject to Rashba spin-orbit coupling and a magnetic field. For chemical potentials near the center of the Zeeman gap ($μ= 0$), two-particle scattering causes the leading deviation from the quantized conductance at finite temperatures. On the other hand, for $|μ| > 0$, three-particle scattering processes become more relevant. These deviations are a consequence of the strongly nonlinear single-particle spectrum, and are thus not accessible using Luttinger liquid theory. We discuss the obse…
We present semiclassical and quantum mechanical results for the effects of a strong magnetic field in Quantum Wires in the presence of Rashba Spin Orbit coupling. Analytical and numerical results show how the perturbation acts in the presence of a transverse magnetic field in the ballistic regime and we assume a strong reduction of the backward scattering interaction which could have some consequences for the Tomonaga-Luttinger transport. We analyze the spin texture due to the action of Spin Orbit coupling and magnetic field often referring to the semiclassical solutions that magnify the singu…
We investigate theoretically the spin-polarized electron transport for a wide-narrow-wide (WNW) quantum wire under the modulation of Rashba spin-orbit interaction (SOI). The influence of both the structure of the quantum wire and the interference between different pairs of subbands on the spin-polarized electron transport is taken into account simultaneously via the spin-resolved lattice Green function method. It is found that a very large vertical spin-polarized current can be generated by the SOI-induced effective magnetic field at the structure-induced Fano resonance even in the presence of…
We investigate the transport properties of narrow quantum wires realized in disordered two-dimensional electron gases in the presence of k-linear Rashba and Dresselhaus spin-orbit interaction (SOI), and an applied in-plane magnetic field. Building on previous work [Scheid, et al., PRL 101, 266401 (2008)], we find that in addition to the conductance, the universal conductance fluctuations also feature anisotropy with respect to the magnetic field direction. This anisotropy can be explained solely from the symmetries exhibited by the Hamiltonian as well as the relative strengths of the Rashba an…
We derive the eigenenergies and eigenstates of electrons in a quantum wire subjected to an external magnetic field. These are calculated in the presence of spin orbit interactions arising from the Rashba (structural inversion asymmetry) and Dresselhaus (bulk inversion asymmetry) effects. We consider three cases: the external magnetic field is oriented (i) along the axis of the wire, (ii) perpendicular to the axis but parallel to the electric field associated with structural inversion asymmetry (Rashba effect), and (iii) perpendicular to the axis as well as the electric field. In all cases, the…
The influence of the Rashba spin-orbit coupling on the electron spin dynamics is investigated for a ballistic semiconductor quantum wire with a finite width. We monitor the spin evolution using the time-dependent Schrödinger equation. The pure spin precession characteristic of the 1D limit is lost in a 2D wire with a finite lateral width. In general, the time evolution in the latter case is characterized by several frequencies and a nonrigid spin motion.
We perform a numerical study on the spin-resolved transport in a quantum wire (QW) under the modulation of both Rashba spin-orbit coupling (SOC) and a perpendicular magnetic field (MF) by adopting the developed Usuki transfer-matrix method in combination with the Landauer-Buttiker formalism. Wide spin filtering energy windows can be achieved in this system for a spin-unpolarized injection. In addition, both the width of these energy windows and the magnitude of the spin conductance within these energy widows can be tuned by varying the Rashba SOC strength, which can be apprehended by analyzing…
The electronic transport in a system of two quantum rings side-coupled to a quantum wire is studied via a single-band tunneling tight-binding Hamiltonian. We derived analytical expressions for the conductance and spin polarization when the rings are threaded by magnetic fluxes with Rashba spin-orbit interaction. We show that by using the Fano and Dicke effects this system can be used as an efficient spin-filter even for small spin orbit interaction and small values of magnetic flux. We compare the spin-dependent polarization of this design and the polarization obtained with one ring side coupl…
We study ballistic transport of spin-polarized electrons through quantum wires in which the strength of the Rashba spin-orbit interaction (SOI) is spatially modulated. Subband mixing, due to SOI, between the two lowest subbands is taken into account. Simplified approximate expressions for the transmission are obtained for electron energies close to the bottom of the first subband and near the value for which anticrossing of the two lowest subbands occurs. In structures with periodically varied SOI strength, {\it square-wave} modulation on the spin transmission is found when only one subband is…
