Dresselhaus Spin-orbit Coupling Research Articles

Persistent spin helix manipulation by optical doping of a CdTe quantum well

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 pattern is observed. The kinetic theory framework of spin diffusion allows for modeling of this finding by incorporating the photocarrier density into the Rashba ($\alpha$) and the Dresselhaus ($\beta_3$) parameters. Corresponding calculations are further validated by an excitation-density dependent measurement. This work shows universality of the persistent spin helix by its observation in a II-VI compound and the ability to fine-tune it by optical doping.

A tunable spatial spin splitter based on a spin–orbit-coupling modulated magnetic nanostructure

We investigate theoretically the spin-dependent Goos–Hänchen (GH) effect in a magnetic nanostructure modulated by spin–orbit coupling (SOC), which can be experimentally realized by depositing a ferromagnetic (FM) stripe and a Schottky-metal (SM) stripe on the top and bottom of an InAs/AlxIn1−xAs heterostructure, respectively. We consider two kinds of different SOCs (Rashba and Dresselhaus types), and calculate the GH shift and its spin polarization for the electrons across the device. Results show that the GH shift still is spin-polarized after including the SOC, and the behavior of the spin-polarized electrons can be manipulated by the Rashba and/or Dresselhaus SOC. These interesting properties provide an alternative scheme for spatially realizing spin injection into a semiconductor, and the magnetic nanostructure can be employed as a controllable spatial spin splitter for a spin-polarized source in spintronics.

Electronic States and Persistent Currents in Nanowire Quantum Ring

The new model of a quantum ring (QR) defined inside a nanowire (NW) is proposed. The one-particle Hamiltonian for electron in [111]-oriented NW QR is constructed taking into account both Rashba and Dresselhaus spin-orbit coupling (SOC). The energy levels as a function of magnetic field are found using the exact numerical diagonalization. The persistent currents (both charge and spin) are calculated. The specificity of SOC and arising anticrossings in energy spectrum lead to unusual features in persistent current behavior. The variation of magnetic field or carrier concentration by means of gate can lead to pure spin persistent current with the charge current being zero.

Effect of cubic Dresselhaus interaction on the longitudinal optical conductivity of a spin-orbit coupled system

We investigate the effect of the oft-neglected cubic terms of the Dresselhaus spin-orbit coupling on the longitudinal current response of a two-dimensional electron gas with both Rashba and linear Dresselhaus interactions. For a quantum well grown in the [001] direction, the changes caused by these nonlinear-in-momentum terms on the absorption spectrum become more notable under SU(2) symmetry conditions, when the Rashba and linear Dresselhaus coupling strengths are tuned to be equal. The longitudinal optical response no longer vanishes then and shows a strong dependence on the direction of the externally applied electric field, giving a signature of the relative size of several spin-orbit contributions. This anisotropic response arises from the nonisotropic splitting of the spin states induced by the interplay of Rashba and Dresselhaus couplings. However, the presence of cubic terms introduces characteristic spectral features and can modify the overall shape of the spectra for some values of the relative sizes of the spin-orbit parameters. We compare this behavior to the case of a sample with [110] crystal orientation which, under conditions of spin-preserving symmetry, has a collinear spin-orbit vector field that leads to vanishing conductivity, even in the presence of cubic terms. In addition to the control through the driven frequency or electrical gating, such a directional aspect of the current response suggests new ways of manipulation and supports the use of interband optics as a sensitive probe of spin-orbit mechanisms in semiconductor spintronics.

Calculations of spin-polarized Goos–Hänchen displacement in magnetically confined GaAs/AlxGa1−xAs nanostructure modulated by spin–orbit couplings

We theoretically investigate Goos–Hänchen (GH) displacement by modelling the spin transport in an archetypal device structure—a magnetically confined GaAs/AlxGa1−xAs nanostructure modulated by spin–orbit coupling (SOC). Both Rashba and Dresselhaus SOCs are taken into account. The degree of spin-polarized GH displacement can be tuned by Rashba or Dresselhaus SOC, i.e. interfacial confining electric field or strain engineering. Based on such a semiconductor nanostructure, a controllable spatial spin splitter can be proposed for spintronics applications.

Quantum anomalous Hall phase in a one-dimensional optical lattice

We propose to simulate and detect quantum anomalous Hall phase with ultracold atoms in a one-dimensional optical lattice, with the other synthetic dimension being realized by modulating spin–orbit coupling. We show that the system manifests a topologically nontrivial phase with two chiral edge states which can be readily detected in this synthetic two-dimensional system. Moreover, it is interesting that at the phase transition point there is a flat energy band and this system can also be in a topologically nontrivial phase with two Fermi zero modes existing at the boundaries by considering the synthetic dimension as a modulated parameter. We also show how to measure these topological phases experimentally in ultracold atoms. Another model with a random Rashba and Dresselhaus spin–orbit coupling strength is also found to exhibit topological nontrivial phase, and the impact of the disorder to the system is revealed.

Spin-helix Larmor mode

A two-dimensional electron gas (2DEG) with equal-strength Rashba and Dresselhaus spin-orbit coupling sustains persistent helical spin-wave states, which have remarkably long lifetimes. In the presence of an in-plane magnetic field, there exist single-particle excitations that have the character of propagating helical spin waves. For magnon-like collective excitations, the spin-helix texture reemerges as a robust feature, giving rise to a decoupling of spin-orbit and electronic many-body effects. We prove that the resulting spin-flip wave dispersion is the same as in a magnetized 2DEG without spin-orbit coupling, apart from a shift by the spin-helix wave vector. The precessional mode about the persistent spin-helix state is shown to have an energy given by the bare Zeeman splitting, in analogy with Larmor’s theorem. We also discuss ways to observe the spin-helix Larmor mode experimentally.

Lateral shift in a spin-orbit-coupling modulated magnetic-barrier nanostructure

Spin-dependent Goos–Hänchen（GH）effect of the electron in a magnetic barrier nanostructure modulated by the spin-orbit coupling (SOC) is investigated. Two kinds of intrinsic SOCs (Rashba and Dresselhaus types) are taken into account, and spin-dependent lateral shifts are obtained by the transfer matrix method and the stationary phase approximation. The spin-dependent lateral shift is found to be related closely to the SOC. Both magnitude and sign of the spin-polarised lateral shift can be controlled by properly adjusting the strength of Rashba or Dresselhaus SOC. These interesting features can provide an alternative approach to manipulate spin-polarised electrons in the semiconductor, and such a nanostructure can serve as a controllable spatial spin splitter for spintronics applications.

Electronic states and persistent currents in nanowire quantum ring

AbstractA new model of a quantum ring defined inside a nanowire is proposed. The one-particle Hamiltonian for electron in [111]-oriented nanowire quantum ring is constructed taking into account both Rashba and Dresselhaus spin-orbit coupling. The energy levels as a function of magnetic field are found using the exact numerical diagonalization. The persistent currents (both charge and spin) are calculated. The specificity of spin-orbit coupling and arising anticrossings in energy spectrum lead to unusual features in persistent current behavior. The variation of magnetic field or carrier concentration by means of gates can lead to pure spin persistent current with the charge current being zero.

Magnetoconductance correction in zinc-blende semiconductor nanowires with spin-orbit coupling

We study the effects of spin-orbit coupling on the magnetoconductivity in diffusive cylindrical semiconductor nanowires. Following up on our former study on tubular semiconductor nanowires, we focus in this paper on nanowire systems where no surface accumulation layer is formed but instead the electron wave function extends over the entire cross section. We take into account the Dresselhaus spin-orbit coupling resulting from a zinc-blende lattice and the Rashba spin-orbit coupling, which is controlled by a lateral gate electrode. The spin relaxation rate due to Dresselhaus spin-orbit coupling is found to depend neither on the spin density component nor on the wire growth direction and is unaffected by the radial boundary. In contrast, the Rashba spin relaxation rate is strongly reduced for a wire radius that is smaller than the spin precession length. The derived model is fitted to the data of magnetoconductance measurements of a heavily doped back-gated InAs nanowire and transport parameters are extracted. At last, we compare our results to previous theoretical and experimental studies and discuss the occurring discrepancies.

Effects of Rashba and Dresselhaus spin-orbit couplings on itinerant ferromagnetism

Based on Stoner model for itinerant ferromagnet, effects of spin-orbit coupling (SOC) on ferromagnetism were investigated at zero temperature. It was found that SOC will enhance the critical ferromagnetic exchange interaction for spontaneous magnetization, and then suppress ferromagnetism. In case of the coexistence of Rashba and Dresselhaus SOCs, the mixture of the two spin-orbit couplings showed stronger suppressed effect on ferromagnetism than only one kind of SOC alone. When the two SOCs mixed with equal magnitude, ferromagnetism in itinerant ferromagnet was suppressed to minimum.

Effect of asymmetric interface on charge and spin transport across two dimensional electron gas with Dresselhaus spin-orbit coupling/ferromagnet junction

We theoretically studied the effect of interfacial scattering on the transport of charge and spin across the junction of a two-dimensional electron gas with Dresselhaus spin-orbit coupling and ferromagnetic material junction, via the conductance (G) and the spin-polarization of the conductance spectra (P) using the scattering method. At the interface, not only were the effects of spin-conserving (Z0) and spin-flip scattering (Zf) considered, but also the interfacial Rashba spin-orbit coupling scattering (ZRSOC), which was caused by the asymmetry of the interface, was taken into account, and all of them were modeled by the delta potential. It was found that G was suppressed with increasing Z0, as expected. Interestingly, a particular value of Zf can cause G and P to reach a maximum value. In particular, ZRSOC plays a crucial role to reduce G and P in the metallic limit, but its influence on the tunneling limit was quite weak. On the other hand, the effect of ZRSOC was diminished in the tunneling limit of the magnetic junction.

Current-induced spin polarization in InGaAs and GaAs epilayers with varying doping densities

The current-induced spin polarization and momentum-dependent spin-orbit field were measured in ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ epilayers with varying indium concentrations and silicon doping densities. Samples with higher indium concentrations and carrier concentrations and lower mobilities were found to have larger electrical spin generation efficiencies. Furthermore, current-induced spin polarization was detected in GaAs epilayers despite the absence of measurable spin-orbit fields, indicating that the extrinsic contributions to the spin-polarization mechanism must be considered. Theoretical calculations based on a model that includes extrinsic contributions to the spin dephasing and the spin Hall effect, in addition to the intrinsic Rashba and Dresselhaus spin-orbit coupling, are found to reproduce the experimental finding that the crystal direction with the smaller net spin-orbit field has larger electrical spin generation efficiency and are used to predict how sample parameters affect the magnitude of the current-induced spin polarization.

Effect of electric field on the ratio between the rashba and dresselhaus parameters in III–V heterostructures

The size-quantized energy subbands and envelope wave functions for [001] quantum wells based on zinc-blende III–V semiconductors are numerically calculated using the eight-band Kane model and finite-difference discretization scheme in coordinate space. The effect of the quantum-well band parameters and external electric field oriented along the structure growth direction on the ratio between the Rashba and Dresselhaus spin–orbit coupling parameters is studied. It is demonstrated that at certain electric-field values the spin–orbit coupling parameters in GaAs/InGaAs structures can be equal, which ensures the condition for forming stable spin helices. In addition, it is established that the spin–orbit coupling linear in wave vector in symmetric GaAs/InGaAs wells can disappear under certain well widths and barrier chemical compositions.

Spin conductance in three-terminal rings subject to Rashba and Dresselhaus spin-orbit coupling

Based on the Green's function formalism, we investigated spin transport properties in one-dimensional three-terminal rings in the presence of the Rashba spin-orbit coupling (RSOC) and Dresselhaus spin-orbit coupling (DSOC). The conductance as a function of the Fermi energy shows typical resonance and antiresonance (conductance zero) characteristics in the absence of spin-orbit coupling (SOC). When one type of SOC (RSOC or DSOC) is introduced, the original conductance zeros are lifted, but new conductance zeros emerge. It is found that all the conductance zeros depend sensitively on the disorder, and the fluctuate weakens and smoothens the oscillations of the conductance. In the presence of both types of SOCs, the interplay between the RSOC and the DSOC opens a gap in the energy spectrum and breaks the cylindrical symmetry of the ring. Consequently, symmetrically coupled three-terminal rings show anisotropic conductances, which are robust against weak disorders.

Spin transport in a chain of polygonal quantum rings with Dresselhaus spin–orbit coupling**Project supported by the National Natural Science Foundation of China (Grant Nos. 61176089 and 11504083) and the Foundation of Shijiazhuang University, China (Grant No. XJPT002).

Using a transfer matrix method, we investigate spin transport through a chain of polygonal rings with Dresselhaus spin–orbit coupling (DSOC). The spin conductance is dependent on the number of sides in the polygons. When DSOC is considered in a chain which also has Rashba spin–orbit coupling (RSOC) of the same magnitude, the total conductance is the same as that for the same chain with no SOC. However, when the two types of SOC have different values, there results a unique anisotropic conductance.

Spin and tunneling dynamics in an asymmetrical double quantum dot with spin-orbit coupling: Selective spin transport device

In this article, we study the spin and tunneling dynamics as a function of magnetic field in a one-dimensional GaAs double quantum dot with both the Dresselhaus and Rashba spin-orbit coupling. In particular, we consider different spatial widths for the spin-up and spin-down electronic states. We find that the spin dynamics is a superposition of slow as well as fast Rabi oscillations. It is found that the Rashba interaction strength as well as the external magnetic field strongly modifies the slow Rabi oscillations which is particularly useful for implementing solid state selective spin transport device.

Lateral Shifts for Spin Electrons in a Hybrid Magnetic-Electric-Barrier Nanostructure Modulated by Spin-Orbit Couplings

We theoretically investigate how to modulate spin-dependent lateral shifts by the spin-orbit coupling (SOC) in a hybrid magnetic-electric-barrier (MEB) nanostructure, which can be experimentally realized by depositing a ferromagnetic (FM) stripe and a Schottky metal (SM) stripe on the top and bottom of the semiconductor heterostructure, respectively. Two kinds of ROCs, Rashba SOC (RSOC) and Dresselhaus SOC (DSOC), are taken into account fully. The Schrodinger equation of the spin electron in the hybrid MEB nanostructure is exactly solved by using the improved transfer-matrix method (ITMM), and the lateral shift and its spin polarization are numerically calculated with the help of the stationary phase method (SPM). Theoretical analysis indicates that the spin polarization effect in the lateral shift still exists in the hybrid MEB nanostructure when the SOCs are considered. Numerical simulations show that both magnitude and sign of the spin polarization effect in lateral shifts vary strongly with the strengths of RSOC and DSOC. These interesting features may offer an effective means to control the behavior of spin-polarized electrons in the semiconductor nanostructure, and such a hybrid MEB nanostructure serves as a SOC-manipulable spatial spin splitter for spintronic applications.

Second and third harmonic generations of a quantum ring with Rashba and Dresselhaus spin-orbit couplings: Temperature and Zeeman effects

In current article, the Zeeman effect is considered in the presence of simultaneous Rashba and Dresselhaus spin-orbit interactions (SOI) and under such circumstances the second and third harmonic generations (SHG and THG) of a GaAs quantum ring are investigated at finite temperature. The effective Hamiltonian is derived in cylindrical coordinate while the angular part is eliminated because of axial symmetry and the energy eigenvalues and eigenvectors of two lowest levels are obtained numerically. Eventually, the optical properties of such system are studied hiring compact density matrix approach. The results show that, an increase in the magnetic field, leads to blue shift in resonant peaks of both SHG and THG. Furthermore, by reducing the temperature, all the resonant peaks of both SHG and THG experience a red shift. Finally, the effect of the structure dimension is studied and results illustrate that variation of size leads to both red and blue shifts in resonant peaks.

Geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space

In the spirit of the thin-layer quantization approach, we give the formula of the geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space. The geometric contributions can result from the reduced commutation relation between the acted function depending on normal variable and the normal derivative. According to the formula, we obtain the geometric potential, geometric momentum, geometric orbital angular momentum, geometric linear Rashba and cubic Dresselhaus spin-orbit couplings. As an example, a truncated cone surface is considered. We find that the geometric orbital angular momentum can provide an azimuthal polarization for spin, and the sign of the geometric Dresselhaus spin-orbit coupling can be flipped through the inclination angle of generatrix.