We theoretically study the profile of a supercurrent in two-dimensional Josephson junctions with Rashba-Dresselhaus spin-orbit interaction (RDSOI) in the presence of a Zeeman field. Through investigating self-biased supercurrent (so called $φ_0$-Josephson state), we obtain explicit expressions for the functionality of the $φ_0$ state with respect to RDSOI parameters ($α,β$) and in-plane Zeeman field components ($h_x,h_y$). Our findings reveal that, when the chemical potential ($μ$) is high enough compared to the energy gap ($Δ$) in superconducting electrodes, i.e., $μ\gg Δ$, RSOI and DSOI with equal strengths ($|α|=|β|$) cause vanishing $φ_0$ state independent of magnetization and the type of RDSOI. A Zeeman field with unequal components, i.e., $|h_x|\neq |h_y|$, however, can counteract and nullify the destructive impact of equal-strength RDSOIs (for one type only), where $μ\simΔ$, although $|h_x|= |h_y|$ can still eliminate the $φ_0$ state. Remarkably, in the $μ\simΔ$ limit, the $φ_0$ state is proportional to the multiplication of both components of an in-plane Zeeman field, i.e., $h_xh_y$, which is absent in the $μ\gg Δ$ limit. Furthermore, our results of critical supercurrents demonstrate that the persistent spin helices can be revealed in a high enough chemical potential regime $μ\gg Δ$, while an opposite regime, i.e., $μ\simΔ$, introduces an adverse effect. In the ballistic regime, the "maximum" of the critical supercurrent occurs at $|α|=|β|$ and the Zeeman field can boost this feature. The presence of disorder and nonmagnetic impurities change this picture drastically so the "minimum" of the critical supercurrent occurs at and around the symmetry lines $|α|=|β|$.
A weak parallel Zeeman field combined with the spin-orbit coupling can induce the supercurrent in an s-wave two-dimensional superconductor. At the same time, the thermodynamically equilibrium state of such a system is characterized by the helix phase where the order parameter varies in space as $\exp(i\mathbf{Qr})$. In this state the electric current that is induced by the Zeeman interaction is exactly counterbalanced by the current produced by the gradient of the order-parameter. We studied the interplay of the helix state and magnetoelectric current in the case of a varying in space Zeeman f…
We study the lifetime of the persistent spin helix in semiconductor quantum wells with equal Rashba- and linear Dresselhaus spin-orbit interactions. In order to address the temperature dependence of the relevant spin relaxation mechanisms we derive and solve semiclassical spin diffusion equations taking into account spin-dependent impurity scattering, cubic Dresselhaus spin-orbit interactions and the effect of electron-electron interactions. For the experimentally relevant regime we find that the lifetime of the persistent spin helix is mainly determined by the interplay of cubic Dresselhaus s…
We derive a spin diffusion equation for a spin-orbit coupled two-dimensional electron gas including the Hartree-Fock field resulting from 1st order electron-electron interactions. We find that the lifetime of the persistent spin helix, which emerges for equal linear Rashba- and Dresselhaus spin-orbit interactions, can be enhanced considerably for large initial spin polarizations due to the Hartree-Fock field. The reason is a reduction of the symmetry-breaking cubic Dresselhaus scattering rate by the Hartree-Fock field. Also higher harmonics are generated and the polarization of the persistent …
We demonstrate that a homogeneous spin polarization in one-dimensional structures of finite length in the presence of Bychkov-Rashba spin-orbit coupling decays spontaneously toward a persistent spin helix. The analysis of formation of spin helical state is presented within a novel approach based on a mapping of spin drift-diffusion equations into a heat equation for a complex field. Such a strikingly different and simple method allows generating robust spin structures whose properties can be tuned by the strength of the spin orbit interaction and/or structure's length. We generalize our result…
We experimentally investigate the dynamics of a persistent spin helix in etched GaAs wire structures of 2 to 80 um width. Using magneto-optical Kerr rotation with high spatial resolution, we determine the lifetime of the spin helix. A few nanoseconds after locally injecting spin polarization into the wire, the polarization is strongly enhanced as compared to the two-dimensional case. This is mostly attributed to a transition to one-dimensional diffusion, strongly suppressing diffusive dilution of spin polarization. The intrinsic lifetime of the helical mode is only weakly increased, which indi…
The persistent spin helix (PSH) that has been widely and exclusively studied in zinc-blende structures is revealed for the first time on the surface of a wurtzite structure. Through first-principles calculations of the ZnO(10-10) surface, a quasi-one dimensional orientation of the spin textures is identified. Further, the wavelength of this particular PSH is smaller than that observed with various zinc-blende quantum well structures, thus indicating that wurtzite-structured surfaces are suitable for spintronics applications.
Time-resolved Kerr-rotation microscopy explores the influence of optical doping on the persistent spin helix in a [001]-grown CdTe quantum well at cryogenic temperatures. Electron spin diffusion dynamics reveal a momentum-dependent effective magnetic field providing SU(2) spin-rotation symmetry, consistent with kinetic theory. The Dresselhaus and Rashba spin-orbit coupling parameters are extracted independently from rotating the spin helix with external magnetic fields applied parallel and perpendicular to the effective magnetic field. Most importantly, a non-uniform spatiotemporal precession …
We re-express the Rashba and Dresselhaus interactions as non-Abelian spin-orbit gauges and provide a new perspective in understanding the persistent spin helix [Phys. Rev. Lett. 97, 236601 (2006)]. A spin-orbit interacting system can be transformed into a free electron gas in the equal-strength Rashba-Dresselhaus [001] linear model, the Dresselhaus [110] linear model, and a one-dimensional system. A general tight-binding Hamiltonian for non-uniform spin-orbit interactions and hoppings along arbitrary directions, within the framework of finite difference method, is obtained. As an application b…
We report that spin supercurrents in magnetic superconductors and superconductor/ferromagnetic insulator bilayers can induce the Dzyaloshinskii-Moriya interaction which strength is proportional to the superconducting order parameter amplitude. This effect leads to the existence of inhomogeneous parity-breaking ground states combining the chiral magnetic helix and the pair density wave orders. The formation of such states takes place via the penetration of chiral domain walls at the threshold temperature below the superconducting transition. We find regimes with both the single and the re-entra…
A persistent spin helix (PSH) in spin-orbit-coupled two-dimensional electron systems was recently predicted to exist in two cases: [001] quantum wells (QWs) with equal coupling strengths of the Rashba and the Dresselhaus interactions (RD), and Dresselhaus-only [110] QWs. Here we present supporting results and further investigations, using our previous results [Phys. Rev. B 72, 153305 (2005)]. Refined PSH patterns for both RD [001] and Dresselhaus [110] QWs are shown, such that the feature of the helix is clearly seen. We also discuss the time dependence of spin to reexamine the origin of the p…
Conventional transport theory focuses on either the diffusive or ballistic regimes and neglects the crossover region between the two. In the presence of spin-orbit coupling, the transport equations are known only in the diffusive regime, where the spin precession angle is small. In this paper, we develop a semiclassical theory of transport valid throughout the diffusive - ballistic crossover of a special SU(2) symmetric spin-orbit coupled system. The theory is also valid in the physically interesting regime where the spin precession angle is large. We obtain exact expressions for the density a…
According to Noethers theorem, for every symmetry in nature there is a corresponding conservation law. For example, invariance with respect to spatial translation corresponds to conservation of momentum. In another well-known example, invariance with respect to rotation of the electrons spin, or SU(2) symmetry, leads to conservation of spin polarization. For electrons in a solid, this symmetry is ordinarily broken by spin-orbit coupling, allowing spin angular momentum to flow to orbital angular momentum. However, it has recently been predicted that SU(2) can be achieved in a two-dimensional el…
The spin-orbit interaction (SOI) in zincblende semiconductor quantum wells can be set to a symmetry point, in which spin decay is strongly suppressed for a helical spin mode. Signatures of such a persistent spin helix (PSH) have been probed using the transient spin grating technique, but it has not yet been possible to observe the formation and the helical nature of a PSH. Here we directly map the diffusive evolution of a local spin excitation into a helical spin mode by a time- and spatially resolved magneto-optical Kerr rotation technique. Depending on its in-plane direction, an external mag…
We study electron spin relaxation in one-dimensional structures of finite length in the presence of Bychkov-Rashba spin-orbit coupling and boundary spin relaxation. Using a spin kinetic equation approach, we formulate boundary conditions for the case of a partial spin polarization loss at the boundaries. These boundary conditions are used to derive corresponding boundary conditions for spin drift-diffusion equation. The later is solved analytically for the case of relaxation of a homogeneous spin polarization in 1D finite length structures. It is found that the spin relaxation consists of thre…
The spin orbit interaction plays a crucial role in diverse fields of condensed matter, including the investigation of Majorana fermions, topological insulators, quantum information and spintronics. In III V zinc blende semiconductor heterostructures, two types of spin orbit interaction, Rashba and Dresselhaus act on the electron spin as effective magnetic fields with different directions. They are characterized by coefficients alpha and beta, respectively. When alpha is equal to beta, the so called persistent spin helix symmetry is realized. In this condition, invariance with respect to spin r…
A non-vanishing electric field inside a non-centrosymmetric bulk crystal transforms into a momentum- dependent magnetic field, namely, a spin-orbit field (SOF). SOFs are of great use in spintronics because they enable spin manipulation via the electric field. At the same time, however, spintronic applications are severely limited by the SOF, as electrons traversing the SOF easily lose their spin information. Here, we propose that in-plane ferroelectricity in (001)-oriented SnTe thin films harness the Janus-faced SOF in a reconcilable way to enable electrical spin controllability and suppress s…
Energy-saving spintronics are believed to be implementable on the systems hosting persistent spin helix (PSH) since they support an extraordinarily long spin lifetime of carriers. However, achieving the PSH requires a unidirectional spin configuration in the momentum space, which is practically non-trivial due to the stringent conditions for fine-tuning the Rashba and Dresselhaus spin-orbit couplings. Here, we predict that the PSH can be intrinsically achieved on a two-dimensional (2D) group-IV monochalcogenide M X monolayer, a new class of the noncentrosymmetric 2D materials having in-plane f…
In layered semiconductors with spin-orbit interaction (SOI) a persistent spin helix (PSH) state with suppressed spin relaxation is expected if the strengths of the Rashba and Dresselhaus SOI terms, alpha and beta, are equal. Here we demonstrate gate control and detection of the PSH in two-dimensional electron systems with strong SOI including terms cubic in momentum. We consider strain-free InGaAs/InAlAs quantum wells and first determine alpha/beta ~ 1 for non-gated structures by measuring the spin-galvanic and circular photogalvanic effects. Upon gate tuning the Rashba SOI strength in a compl…
Spin-orbit coupling plays an important role in various properties of very different materials. Moreover efforts are underway to control the degree and quality of spin-orbit coupling in materials with a concomitant control of transport properties. We calculate the frequency dependent optical conductivity in systems with both Rashba and Dresselhaus spin-orbit coupling. We find that when the linear Dresselhaus spin-orbit coupling is tuned to be equal to the Rashba spin-orbit coupling, the interband optical conductivity disappears. This is taken to be the signature of the recovery of SU(2) symmetr…
We present a detailed theoretical investigation of persistent spin helices in two-dimensional electron systems with spin-orbit coupling. For this purpose we consider a single-particle effective mass Hamiltonian with generalized linear-in-k spin-orbit coupling term corresponding to a quantum well grown in an arbitrary crystallographic direction, and derive the general condition for the formation of the persistent spin helix. This condition applied for the Hamiltonians describing quantum wells with different growth directions indicates the possibility of existence of the persistent spin helix in…
We exploit the high-symmetry spin state obtained for equal Rashba and linear Dresselhaus interactions to derive a closed-form expression for the weak localization magnetoconductivity -- the paradigmatic signature of spin-orbit coupling in quantum transport. The small parameter of the theory is the deviation from the symmetry state introduced by the mismatch of the linear terms and by the cubic Dresselhaus term. In this regime, we perform quantum transport experiments in GaAs quantum wells. Top and back gates allow independent tuning of the Rashba and Dresselhaus terms in order to explore the b…
We study the phase diagram of the interacting two-dimensional electron gas (2DEG) with equal Rashba and Dresselhaus spin-orbit coupling, which for weak coupling gives rise to the well-known persistent spin-helix phase. We construct the full Hartree-Fock phase diagram using a classical Monte-Carlo method analogous to that used in Phys.Rev.B 96, 235425 (2017). For the 2DEG with only Rashba spin-orbit coupling, it was found that at intermediate values of the Wigner-Seitz radius rs the system is characterized by a single Fermi surface with an out-of-plane spin polarization, while at slightly large…
We investigate the possibility of spin-preserving symmetries due to the interplay of Rashba and Dresselhaus spin-orbit coupling in n-doped zinc-blende semiconductor quantum wells of general crystal orientation. It is shown that a conserved spin operator can be realized if and only if at least two growth-direction Miller indices agree in modulus. The according spin-orbit field has in general both in-plane and out-of-plane components and is always perpendicular to the shift vector of the corresponding persistent spin helix. We also analyze higher-order effects arising from the Dresselhaus term, …
In the presence of Rashba-Dresselhaus coupling, strong spin-orbit interactions in liquid crystal optical cavities result in a distinctive spin-split entangled dispersion. Spin coherence between such modes give rise to an optical persistent-spin-helix. In this letter, we introduce optical gain in such a system, by dispersing a molecular dye in a liquid-crystal microcavity. We demonstrate both lasing in the Rashba-Dresselhaus regime and the emergence of an optical persistent spin helix.
We obtain the spin-orbit interaction and spin-charge coupled transport equations of a two-dimensional heavy hole gas under the influence of strain and anisotropy. We show that a simple two-band Hamiltonian can be used to describe the holes. In addition to the well-known cubic hole spin-orbit interaction, anisotropy causes a Dresselhaus-like term, and strain causes a Rashba term. We discover that strain can cause a shifting symmetry of the Fermi surfaces for spin up and down holes. We predict an enhanced spin lifetime associated with a spin helix standing wave similar to the Persistent Spin Hel…
Quasi-two-dimensional superconductors with tunable spin-orbit coupling are very interesting systems with properties that are also potentially useful for applications. In this manuscript we demonstrate that these systems exhibit undamped collective spin oscillations that can be excited by the application of a supercurrent. We propose to use these collective excitations to realize persistent spin oscillators operating in the frequency range of 10 GHz - 1 THz.
The time evolution of a local spin excitation in a (001)-confined two-dimensional electron gas subjected to Rashba and Dresselhaus spin-orbit interactions of similar strength is investigated theoretically and compared with experimental data. Specifically, the consequences of the finite spatial extension of the initial spin polarization is studied for non-balanced Rashba and Dresselhaus terms and for finite cubic Dresselhaus spin-orbit interaction. We show that the initial out-of-plane spin polarization evolves into a helical spin pattern with a wave number that gradually approaches the value $…
In a semiconductor, collective excitations of spin textures usually decay rather fast due to D'yakonov-Perel' spin relaxation. The latter arises from spin-orbit coupling, which induces wave-vector-dependent spin rotations that, in conjunction with random disorder scattering, generate spin decoherence. However, symmetries occurring under certain conditions can prevent the relaxation of particular homogeneous and inhomogeneous spin textures. The inhomogeneous spin texture, termed as persistent spin helix, is especially appealing as it enables us to manipulate the spin orientation while retaining…
Persistent spin texture (PST), a property of solid-state materials maintaining unidirectional spin polarization in the momentum $k$-space, offers a route to deliver the necessary long carrier spin lifetimes through the persistent spin helix (PSH) mechanism. However, most of the discovered PST locally occurred in the small part around certain high symmetry $k$-points or lines in the first Brillouin zone (FBZ), thus limiting the stability of the PSH state. Herein, by symmetry analysis and first-principles calculations, we report the emergence of full-zone PST (FZPST), a phenomenon displaying the…
A persistent spin helix (PSH) is a robust helical spin-density pattern arising in disordered 2D electron gases with Rashba $α$ and Dresselhaus $β$ spin-orbit (SO) tuned couplings, i.e., $α=\pmβ$. Here we investigate the emergence of a Persistent Skyrmion Lattice (PSL) resulting from the coherent superposition of PSHs along orthogonal directions -- crossed PSHs -- in wells with two occupied subbands $ν=1,2$. For realistic GaAs wells we show that the Rashba $α_ν$ and Dresselhaus $β_ν$ couplings can be simultaneously tuned to equal strengths but opposite signs, e.g., $α_1= β_1$ and $α_2=-β_2$. In…
We investigate ramifications of the persistent spin helix symmetry in two-dimensional hole gases in the conductance of disordered mesoscopic systems. To this end we extend previous models by going beyond the axial approximation for III-V semiconductors. For heavy-hole subbands we identify an exact spin-preserving symmetry analogous to the electronic case by analyzing the crossover from weak antilocalization to weak localization and spin transmission as a function of extrinsic spin-orbit interaction strength.
Recently, split-ring bosonic condensates of exciton polaritons have been proposed for realisation of qubits. We formulate an analytical model of a polariton condensate in a one-dimensional ring split by a delta-function potential. The persistent current is stopped by the potential defect embedded in a scalar condensate of non-interacting particles, however, it reappears in the presence of an up-critical non-linearity. The nonlinear supercurrents are characterised by fractional orbital momenta while their eigenfunctions may feature grey or dark solitons. The coupling between the spin and the or…
We present an exact solution to the problem of the spin edge states in the presence of equal Bychkov-Rashba and Dresselhaus spin-orbit fields in a two-dimensional electron system, restricted by a hard-wall confining potential and exposed to a perpendicular magnetic field. We find that the spectrum of the spin edge states depends critically on the orientation of the sample edges with respect to the crystallographic axes. Such a strikingly different spectral behavior generates new modes of the persistent spin helix-spin edge helices with novel properties, which can be tuned by the applied electr…
The Rashba and Dresselhaus spin-orbit (SO) interactions in 2D electron gases act as effective magnetic fields with momentum-dependent directions, which cause spin decay as the spins undergo arbitrary precessions about these randomly-oriented SO fields due to momentum scattering. Theoretically and experimentally, it has been established that by fine-tuning the Rashba $α$ and Dresselhaus $β$ couplings to equal $\it{fixed}$ strengths $α=β$, the total SO field becomes unidirectional thus rendering the electron spins immune to dephasing due to momentum scattering. A robust persistent spin helix (PS…
By means the envelope function approximation, 8-band Kane model and a finite-difference scheme with the coordinate space discretization, we numerically performed calculations of the spin-orbit coupling parameters for 2D electron gas confined in both symmetric and asymmetric [0 0 1] quantum wells based on zinc-blende III-V semiconductors. Influence of the quantum well band parameters and width as well as the magnitude of the external electric field applied along the growth direction on the Dresselhaus and Rashba spin-orbit coupling parameters is investigated. It has been found that in the symme…
The question of gauge-covariance in the non-Abelian gauge-field formulation of two space-dimensional systems with spin-orbit coupling relevant to spintronics is investigated. Although, these are generally gauge-fixed models, it is found that for the class of gauge fields that are space-time independent and satisfy a U(1) algebra, thus having a vanishing field strength, there is a residual gauge freedom in the Hamiltonian. The gauge transformations assume the form of a space-dependent rotation of the transformed wave functions with rotation angles and axes determined by the specific form of the…
We report on a theoretical study of spin dynamics of an ensemble of spin-polarized electrons injected in a diffusive microchannel with linear Rashba and Dresselhaus spin-orbit coupling. We explore the dependence of the spin-precession and spin-diffusion lengths on the strengths of spin-orbit interaction and external magnetic fields, microchannel width, and orientation. Our results are based on numerical Monte Carlo simulations and on approximate analytical formulas, both treating the spin dynamics quantum-mechanically. We conclude that spin-diffusion lengths comparable or larger than the prece…
Planar systems with a general linear spin-orbit interaction (SOI) that can be cast in the form of a non-Abelian pure gauge field are investigated using the language of non-Abelian gauge field theory. A special class of these fields that, though a $2\times2$ matrix, are Abelian are seen to emerge and their general form is given. It is shown that the unitary transformation that gauges away these fields induces at the same time a rotation on the wavefunction about a fixed axis but with a space-dependent angle, both of which being characteristics of the SOI involved.The experimentally important ca…
