Dresselhaus Spin Orbit Research Articles

Beyond the standard model of topological Josephson junctions: From crystalline anisotropy to finite-size and diode effects

A planar Josephson junction is a versatile platform to realize topological superconductivity over a large parameter space and host Majorana bound states. With a change in the Zeeman field, this system undergoes a transition from trivial to topological superconductivity accompanied by a jump in the superconducting phase difference between the two superconductors. A standard model of these Josephson junctions, which can be fabricated to have a nearly perfect interfacial transparency, predicts a simple universal behavior. In that model, at the same value of Zeeman field for the topological transition, there is a π phase jump and a minimum in the critical superconducting current, while applying a controllable phase difference yields a diamond-shaped topological region as a function of that phase difference and a Zeeman field. In contrast, even for a perfect interfacial transparency, we find a much richer and nonuniversal behavior as the width of the superconductor is varied or the Dresselhaus spin–orbit coupling is considered. The Zeeman field for the phase jump, not necessarily π, is different from the value for the minimum critical current, while there is a strong deviation from the diamond-like topological region. These Josephson junctions show a striking example of a nonreciprocal transport and superconducting diode effect, revealing the importance of our findings not only for topological superconductivity and fault-tolerant quantum computing but also for superconducting spintronics.

Laser-field-mediated Rashba and Dresselhaus spin–orbit control in GaInAs/AlInAs quantum wells

For more possibilities in exploring the spin–orbit (SO) control in two-dimensional (2D) semiconductor quantum wells, we resort to the laser field by constructing a generic model including both the axial and transverse field components relative to the well-growth direction, with the axial one primarily modifying the structural potential of the well and the transverse one mainly altering the electron density of states and so the Hartree potential. For GaInAs/AlInAs quantum wells with two-subband occupation, we obtain the full scenario of the laser-field response of the Rashba and Dresselhaus SO couplings, including both the intrasubband (αν and βν with ν = 1,2 denoting the subband index) and intersubband (η and Γ) types, by solving the Poisson–Schrödinger equations. Remarkably, for the Dresselhaus coupling, which is insensitive to the electrical manipulation, we demonstrate that it can be substantially tuned by the laser field and unified SO control of different subbands is possible, suggesting that the optical manner is an effective supplement to the electrical means. Moreover, symmetric (α1=−α2) and selective (α1=0, α2≠0) control of the Rashba coupling of different subbands are also observed with the interplay of the two laser components, which are desirable for the realization of skyrmion lattice and the suppression of spin relaxation of given subbands. Besides, for the intersubband coupling, the Rashba term η is optically tunable while the Dresselhaus term Γ is basically immune to the laser field, i.e., selective control of the intersubband coupling by virtue of optical means. These diverse laser-field-mediated SO features offer exciting possibilities in incorporating 2D quantum wells for new applications in the field of spintronics.

Role of Rashba and Dresselhaus spin–orbit interactions on an off-center donor impurity in a Gaussian quantum dot

The Rashba and Dresselhaus spin–orbit interactions (SOIs) and the magnetic field effects on off-center hydrogen donor impurity D0 in a two-dimensional Gaussian GaAs quantum dot (QD) are investigated. By performing a unitary transformation, the effect of the SOI incorporated and retained terms up to quadratic in the SOI constants (λR,λD). The variational method is engaged for the ensuing Hamiltonian with improved wave functions to determine the ground, first exited state energies, binding energies, transition energy and susceptibility of a (D0) impurity. The results show that the Rashba spin–orbit interaction (RSOI) reduces, the Dresselhaus spin–orbit interaction (DSOI) and magnetic field enhances the energy of the (D0) impurity. By equating the maximum binding energy of the D0 system with KBT, we calculated the temperatures of the stable D0 impurity. Finally, we calculated the oscillator strength (OS) and compared it to the available literature. OS shows remarkable behaviour to SOIs and QD parameters.

Spin relaxation time enhancement induced by polarization field screening in an InGaN/GaN quantum well

A correlation between the spin-polarized carrier transfer and spin relaxation processes of a two-dimensional electron gas (2DEG) in an InGaN/GaN quantum well (QW) is investigated by time-resolved Kerr rotation spectroscopy at low temperature. Upon resonant excitation with the GaN barrier band edge energy, the spin polarization of the 2DEG in the QW is acquired from the transfer of spin-polarized photoexcited carriers. Significantly, the spin relaxation time of the 2DEG is enhanced to be as long as 1 ns along with the carrier transfer. It is demonstrated that by tailoring the Rashba and Dresselhaus spin–orbit couplings to approach a spin-degenerate surface, the screening effect of the polarization field leads to a longer spin relaxation time and effective manipulation of the spin relaxation. The polarization field screening induced enhancement of the spin relaxation time is significant in the way for the development of GaN-based spintronic devices.

Linear and nonlinear spin current response of anisotropic spin-orbit coupled systems

We calculate the linear and the second harmonic (SH) spin current response of two anisotropic systems with spin–orbit (SO) interaction. General expressions of wide applicability for the these response functions are first derived for a generic two-band Hamiltonian. The first system is a two-dimensional (2D) electron gas in the presence of Rashba and k-linear Dresselhaus SO couplings. The calculations show how narrow or wide the response spectra can be, what is their overall shape and size, and frequency shiftings, depending on which crystal orientation is selected. The quantitative knowing of this makes possible a comparative study for several orientations, which would allow to select a spectrum with particular characteristic. We find that vanishing linear and second order response tensors are achievable under SU(2) symmetry conditions, characterized by a collinear SO vector field. Additional conditions under which specific tensor components vanish are possible, without having such collinearity. Thus, a proper choice of the growth direction and SO strengths allows to select the polarization of the linear and SH spin currents according to the direction of flowing. The second system is an anisotropic 2D free electron gas with anisotropic Rashba interaction, which has been employed to study the optical conductivity of 2D puckered structures with anisotropic energy bands. The presence of mass anisotropy and an energy gap open several distinct scenarios for the allowed optical interband transitions, which manifest in the linear and SH response contrastingly. The linear response displays only out-of-plane spin polarized currents, while the SH spin currents flow with spin orientation lying parallel to the plane of the system strictly. The models illustrate the possibility of the nonlinear spin Hall effect in systems with SO interaction, under the presence or absence of time-reversal symmetry. The results suggest different ways to manipulate the linear and nonlinear optical generation of spin currents which could find spintronic applications.

A Theoretical Analysis of Spin-Dependent Tunneling in ZnO-Based Heterostructures

The electron tunneling in ZnO/ZnCdO semiconductor heterostructure is studied using the matrix method. The spin-polarization is examined due to Dresselhaus spin–orbit interaction and Rashba spin–orbit interaction. The total spin-polarization is mainly due to Dresselhaus spin–orbit interaction and the Rashba spin–orbit interaction is small. The high degree of spin polarization can be achieved at a high barrier width. With the increasing cadmium concentration in this heterostructure, the spin polarization efficiency is enhanced. The dwell time is reported and discussed.

Customizing topological phases in the twisted bilayer superconductors with even-parity pairings

We investigate the topological properties of twisted bilayer superconductors with different even-parity pairings in each layer. In the presence of spin–orbit coupling, the Hamiltonian is mapped into an effective odd-parity superconductor. Based on this, we deduce the topological properties by examining the relative configuration between Fermi surface and Dirac pairing node. We show that mixed Rashba and Dresselhaus spin–orbit coupling and anisotropic hopping terms, which break the C 4 symmetry of the Fermi surface, can induce first-order topological superconductors with non-zero bulk Chern number. This provides a versatile way to control the topological phases of bilayer superconductors by adjusting the twisted angle and chemical potential. We demonstrate our results using a typical twisted angle of 53.13°, at which the translation symmetry is restored and the Chern number and edge state are calculated using the Moiré momentum.

Polaron induced local spin texture and anomalous Hall effect in the quadrilateral prism-shaped nanotube with Rashba and Dresselhaus spin–orbit coupling

We theoretically study the spin-texture dynamics and the transverse asymmetric charge deflection induced by the polaron in a quadrilateral prism-shaped nanotube with the Rashba and Dresselhaus spin–orbit coupling (SOC). We reveal the polaron gives rise to the nontrivial local spin textures in the nanotube within the cross section plane. The spins demonstrate oscillations and the oscillating patterns are dependent on the SOC type. For the nanotube containing a segment of the ferromagnetic domain, the sizable asymmetric charge deflections could additionally take place, namely, the anomalous Hall effect. The amount of the deflected charges is determined by the strength and orientations of the ferromagnetic magnetization as well as the SOC type. The work provides a valuable insight of the coherent transport of polaron through a quasi-one-dimensional nanotube with Rashba and Dresselhaus SOC and open avenues for the potential device applications.

Characterization of the out-of-plane Dresselhaus effective magnetic field in InGaAs/InAlAs (110) multiple quantum wells at room temperature

Recently, we directly observed the out-of-plane Dresselhaus spin–orbit (SO) interaction field and extracted the SO coefficient from InGaAs (110) quantum wells (QWs). However, the extracted was much larger than that of the (001) QWs, which yielded an in-plane Dresselhaus SO field. In this study, we perform Monte-Carlo simulations and reproduce the results of time-resolved and spatiotemporally resolved Kerr rotation measurements in InGaAs (110) QWs. The results conclusively show that InGaAs (110) QWs have a strong out-of-plane Dresselhaus SO field as compared with (001) QWs.

Spin-polarised wave-packets transport through one-dimensional nonlinear multiple barriers: Rashba and Dresselhaus Spin–Orbit interactions

ABSTRACT The time evolution of a Gaussian wave packet travelling through a one- dimensional semiconductor based on multiple potential barriers has been explored in order to obtain the spin-based transmission, reflection, and trapping coefficients. We have used a split-step finite difference method to solve the resulting nonlinear coupled Schrodinger equations. The related behaviour of scattering properties of the system as a function of Rashba and Dresselhaus Spin–Orbit interactions, wave-packet velocity, the geometry of the barriers, and the number of neighbouring barriers have been discussed. Based on the results, it is found that by tuning the Rashba and the Dresselhaus coupling strengths, and the characteristics of the system, one can control the spin polarisation of the wave-packet and its propagation coefficients.

The diagrammatic method of Berezinskii for one-dimensional disordered wire with spin–orbit interaction

We extend Berezinskii’s diagram technique to the one-dimensional disordered wire containing Rashba and Dresselhaus spin–orbit interactions. The retarded and advanced Green’s functions are factorized in coordinates space in the presence of spin–orbit interactions. This factorization allows us to transform all coordinate dependence of the Green’s functions from lines to the impurity vertices. Our calculations show that all possible impurity vertices giving a contribution to the correlators do not differ from those given in the conventional technique, except that they are written in a 2 × 2 matrix form and the Fermi velocity vF∗ now depends on the spin–orbit coupling constants. The diagrammatic method of Berezinskii with spin–orbit interaction is used to obtain the distribution of the electron density of the localized state p∞(y).

Spin-Hall conductivity and Hall angle in a two-dimensional system with impurities in the presence of spin–orbit interactions

We investigate the spin-torque-dependent Spin Hall phenomenon in a two-dimensional tight-binding system in the presence of Rashba and Dresselhaus spin–orbit interactions and random static impurities. We employ the Matsubara Green function techniques to calculate the relaxation time caused by the scattering of electrons by impurities. The longitudinal and transverse conductivities are next calculated with the help of the Kubo formalism. We have also calculated the spin Hall angle for the present model and studied its dependence on spin–orbit interactions and impurity strength. Finally, we explore the effect of interplay between the Rashba and Dresselhaus interactions on the spin-Hall effect.

Effect of Rashba and Dresselhaus spin–orbit coupling on supercurrent rectification and magnetochiral anisotropy of ballistic Josephson junctions

Simultaneous breaking of inversion- and time-reversal symmetry in Josephson junction (JJ) leads to a possible violation of the I(φ) = −I(−φ) equality for the current–phase relation. This is known as anomalous Josephson effect and it produces a phase shift φ 0 in sinusoidal current–phase relations. In ballistic JJs with non-sinusoidal current phase relation the observed phenomenology is much richer, including the supercurrent diode effect and the magnetochiral anisotropy (MCA) of Josephson inductance. In this work, we present measurements of both effects on arrays of JJs defined on epitaxial Al/InAs heterostructures. We show that the orientation of the current with respect to the lattice affects the MCA, possibly as the result of a finite Dresselhaus component. In addition, we show that the two-fold symmetry of the Josephson inductance reflects in the activation energy for phase slips.

Non-equilibrium spin polarization in magnetic two-dimensional electron gas with k-linear and k-cubed Dresselhaus spin–orbit interaction

The current-induced spin polarization (CISP) of charge carriers is one of the main mechanisms of spin-to-charge interconversion effects that can be used in new spintronics devices. Here, CISP is studied theoretically in symmetric quantum wells growing in [001] crystallographic direction, where both k -linear and k -cubed Dresselhaus spin–orbit interactions are present. The exchange interaction responsible for perpendicular to plane net magnetization is also taken into account. The main focus is on the influence of cubic Dresselhaus term on CISP and the interplay between spin–orbit interaction (SOI) and the exchange field. The analytical and numerical results are derived within the linear response theory and Matsubara Green’s function formalism. Apart from detailed numerical results, we also provide some analytical expressions that may be useful for interpretation of experimental results and for characterization of quantum wells with Dresselhaus SOI. Analytical expressions for the relevant Berry curvature are also derived, and it is shown that the Berry curvature in magnetic 2DEG with cubic Dresselhaus interaction oscillates in the k -space, while its averaged value is reduced. We also analyze the temperature behavior of CISP and calculate the low-temperature spin polarizability due to heat current. • The effects of the interplay of Dresselhaus spin–orbit interaction (SOI) (with both k -linear and k -cubed terms) and exchange interaction on the nonequilibrium current-induced spin polarization, have been analyzed. • The k -cubed term in Dresselhaus SOI leads to a decrease in nonequilibrium spin density with increasing chemical potential. • The cubic Dresselhaus SOI in magnetic 2DEG creates Berry curvature oscillations in the k -space and reduces the Berry curvature with increasing energy. • The out of plane magnetization leads to an additional component of spin polarization and also to anomalous Hall conductivity that is robust against impurities. • Thermally-induced spin-polarization is analyzed and is shown to be remarkable in a well-defined range of chemical potential.

Rashba and Dresselhaus Spin-Orbit Interaction Effects on Ground State and First Exited State Properties of D0 Centre in a Gaussian Quantum Dot with Magnetic Field

Rashba and Dresselhaus Spin-Orbit Interaction Effects on Ground State and First Exited State Properties of D0 Centre in a Gaussian Quantum Dot with Magnetic Field

Collapse of quasi-two-dimensional symmetrized Dresselhaus spin-orbit coupled Bose–Einstein condensate

Here, we study the collapse process of quasi-two-dimensional Bose–Einstein condensate with symmetrized Dresselhaus spin–orbit coupling. We show that at a sufficiently strong spin–orbit coupling the arising spin-dependent velocity compensates the attraction between particles and can prevent the collapse of the condensate. As a result, spin–orbit coupling can lead to a stable condensate rather than the collapse process.

Motion of two-dimensional quantum particle under a linear potential in the presence of Rashba and Dresselhaus spin–orbit interactions

The quantum mechanical problem of a particle moving in the presence of electric field and Rashba and/or Dresselhaus spin–orbit interactions (SOIs) is solved exactly. Existence of the SOI removes the spin degeneracy, yielding two coupled Schrödinger equations for spin-up and spin-down spinor eigenfunctions. Fourier-transform of these equations provides two coupled first-order differential equations, which are shown to be reduced to two decoupled Hermite-like equations with complex coefficients. The convergent solutions of the equations are found to be described in the form of so called Hermite series. The recurrence relations and the integral representation of the Hermite series are provided. In the absence of Rashba and Dresselhaus spin–orbit coupling constants, these interconnected equations are decoupled and reduced to two Schrödinger equations for a quantum particle moving in a linear potential, solution of which is described by Airy functions.

Unusual spin-orbit control in AlInAs/GaInAs triple wells triggered by band crossing and anticrossing

Additional orbital degrees of freedom in multiband quantum systems may offer more intriguing possibilities for spin-orbit (SO) control. Here we explore the Rashba and Dresselhaus SO couplings in realistic AlInAs/GaInAs triple wells subjected to top $({V}_{\mathrm{T}})$ and back $({V}_{\mathrm{B}})$ gate potentials, allowing for flexible triple-occupancy control for electrons. By performing a self-consistent Poisson-Schr\"odinger calculation, we determine all the relevant Rashba (Dresselhaus) SO terms of both intraband ${\ensuremath{\alpha}}_{\ensuremath{\nu}}$ $({\ensuremath{\beta}}_{\ensuremath{\nu}})$ and interband ${\ensuremath{\eta}}_{\ensuremath{\mu}\ensuremath{\nu}}$ $({\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\mu}\ensuremath{\nu}})$ types. For a structurally symmetric triple well, we achieve a crossing of energy levels between the first and second subbands and sequentially an anticrossing between the second and third subbands, accompanied with a double band swapping, simply via adjusting ${V}_{\mathrm{B}}$. As a consequence, when ${V}_{\mathrm{B}}$ varies, an emerging interchange of the first-subband ${\ensuremath{\alpha}}_{1}$ $({\ensuremath{\beta}}_{1})$ and second-subband ${\ensuremath{\alpha}}_{2}$ $({\ensuremath{\beta}}_{2})$ SO terms, and of ${\ensuremath{\alpha}}_{2}$ $({\ensuremath{\beta}}_{2})$ and ${\ensuremath{\alpha}}_{3}$ $({\ensuremath{\beta}}_{3})$ respectively for the second and third subbands, i.e., double SO interchange, occurs, greatly fascinating for selective SO control among distinct subbands in spintronic devices. Further, near the two-band swapping points, across which electron transfer among the three local wells (triple well) takes place, detailed interchanging features of nonlinear SO control are also contrasting. Remarkably, in addition to Rashba terms, we also realize a wide-range control of Dresselhaus couplings, which are usually immune to electrical manipulation. Regarding the interband Rashba and Dresselhaus SO contributions, ${\ensuremath{\eta}}_{\ensuremath{\mu}\ensuremath{\nu}}$ and ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\mu}\ensuremath{\nu}}$ exhibit either a resonant behavior or a steplike jump across band-swapping points, depending on the parity and spatial distribution of electron wave functions. By varying the barrier height of the two inner barriers in the triple-well configuration, dependence of relevant SO terms on engineered structures, which are either structurally symmetric or asymmetric, is also discussed. Interestingly, in the latter asymmetric case, we realize a seemingly symmetric configuration by adjusting ${V}_{\mathrm{B}}$, in which ${\ensuremath{\alpha}}_{1}$ and ${\ensuremath{\alpha}}_{2}$ essentially vanish while ${\ensuremath{\alpha}}_{3}$ is nonzero, providing a handle for suppressing electron spin relaxation of chosen subbands. Our results will stimulate more experiments probing unusual SO features in multiband and multiwell quantum systems and act as a guide for more proposals designed for spintronic devices.

Interface involved Dresselhaus spin-orbit coupling in GaInAs/AlInAs heterostructures

The interfacial effect in nanosystems is crucial for diverse fields of physics. Here we explore in detail the interface associated Dresselhaus spin-orbit (SO) coupling, which comprises the usual linear ${\ensuremath{\beta}}_{\ensuremath{\nu},\mathrm{u}}$ (${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{u}}$) and cubic ${\ensuremath{\beta}}_{\ensuremath{\nu},3}$ (${\mathrm{\ensuremath{\Gamma}}}_{3}$) contributions as well as the interface-induced term ${\ensuremath{\beta}}_{\ensuremath{\nu},\mathrm{int}}$ (${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{int}}$) of intrasubband (intersubband) kinds. Focusing on ordinary ${\mathrm{Al}}_{0.48}{\mathrm{In}}_{0.52}\mathrm{As}/{\mathrm{Ga}}_{0.47}{\mathrm{In}}_{0.53}\mathrm{As}$ heterostructures with either one or two occupied subbands, we perform a self-consistent Poisson-Schr\"odinger calculation to determine all the relevant SO contributions. We observe that the interface SO term becomes intensifying for heterostructures with either a weaker bulk Dresselhaus strength of the barrier layer or a lower interface smoothness. Remarkably, it is found that the renormalized linear Dresselhaus coefficient, which accounts for the interfacial contribution, may change sign as the interface smoothness varies, opening up the feasibility of the interface-engineered topological matter of persistent skyrmion lattice [J. Y. Fu, P. H. Penteado, M. O. Hachiya, D. Loss, and J. C. Egues, Phys. Rev. Lett. 117, 226401 (2016)]. Moreover, we also determine the intersubband Dresselhaus contributions including an emergent quadratic term (${\mathrm{\ensuremath{\Gamma}}}_{2}$) depending on the interfacial effect and the parity of wave functions. As opposed to intersubband terms of the usual linear (${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{u}}$) and cubic (${\mathrm{\ensuremath{\Gamma}}}_{3}$) kinds, the quadratic contribution leads to unusual avoided crossings of the band dispersion and thus may hybridize spin textures of distinct spin branches. Our results should stimulate experiments probing interface-mediated intra- and intersubband Dresselhaus SO effects and provide an extra leverage for extracting reliable bulk Dresselhaus SO parameters.

Spatial order in a two-dimensional spin–orbit-coupled spin-1/2 condensate: superlattice, multi-ring and stripe formation

We demonstrate the formation of stable spatially-ordered states in a uniform and also trapped quasi-two-dimensional (quasi-2D) Rashba or Dresselhaus spin–orbit (SO) coupled pseudo spin-1/2 Bose–Einstein condensate using the mean-field Gross–Pitaevskii equation. For weak SO coupling, one can have a circularly-symmetric (0, +1)- or (0, −1)-type multi-ring state with intrinsic vorticity, for Rashba or Dresselhaus SO coupling, respectively, where the numbers in the parentheses denote the net angular momentum projection in the two components, in addition to a circularly-asymmetric degenerate state with zero net angular momentum projection. For intermediate SO couplings, in addition to the above two types, one can also have states with stripe pattern in component densities with no periodic modulation in total density. The stripe state continues to exist for large SO coupling. In addition, a new spatially-periodic state appears in the uniform system: a superlattice state, possessing some properties of a supersolid, with a square-lattice pattern in component densities and also in total density. In a trapped system the superlattice state is slightly different with multi-ring pattern in component density and a square-lattice pattern in total density. For an equal mixture of Rashba and Dresselhaus SO couplings, in both uniform and trapped systems, only stripe states are found for all strengths of SO couplings. In a uniform system all these states are quasi-2D solitonic states.