Rashba Coupling Parameter Research Articles

Rashba effect on linear and nonlinear optical properties of a cylindrical core/shell heterojunction quantum dot

Rashba effect may play an important role in the nonlinear optical properties of heterojunction quantum dots. In this work, we have theoretically examined the effects of Rashba spin-orbit interaction on an electron in a cylindrical core/shell quantum dot (CCSQD). The modifications of various properties of cylindrical core/shell quantum dot such as transition energies, dipole transition matrix elements and linear and nonlinear optical properties due to change in Rashba coupling parameter, magnetic field and effective Rydberg energy were studied. We solved the Schrödinger equation using numerical methods and obtained energy eigenvalues as functions of the aforementioned parameters. It was observed that, the magnetic field has a considerable effect on absorption coefficients and refractive index. It was also observed that increasing the magnetic field shifts the resonances towards higher energies. Additionally, increasing in the Rashba coupling coefficient (αR) was found out to result an increase in absorption coefficients and refractive index. Our results demonstrated that, we can manipulate optical properties of cylindrical core/shell quantum dot using an external magnetic field.

Berry curvature induced magnetotransport in 3D noncentrosymmetric metals

We study the magnetoelectric and magnetothermal transport properties of noncentrosymmetric metals using semiclassical Boltzmann transport formalism by incorporating the effects of Berry curvature (BC) and orbital magnetic moment (OMM). These effects impart quadratic-B dependence to the magnetoelectric and magnetothermal conductivities, leading to intriguing phenomena such as planar Hall effect, negative magnetoresistance (MR), planar Nernst effect and negative Seebeck effect. The transport coefficients associated with these effects show the usual oscillatory behavior with respect to the angle between the applied electric field and magnetic field. The bands of noncentrosymmetric metals are split by Rashba spin–orbit coupling except at a band touching point (BTP). For Fermi energy below (above) the BTP, giant (diminished) negative MR is observed. This difference in the nature of MR is related to the magnitudes of the velocities, BC and OMM on the respective Fermi surfaces, where the OMM plays the dominant role. The absolute MR and planar Hall conductivity show a decreasing (increasing) trend with Rashba coupling parameter for Fermi energy below (above) the BTP.

High-harmonic generation in spin-orbit coupled systems

We study high-harmonic generation in two-dimensional electron systems with Rashba and Dresselhaus spin-orbit coupling and derive harmonic generation selection rules with the help of group theory. Based on the bandstructures of these minimal models and explicit simulations we reveal how the spin-orbit parameters control the cutoff energy in the high-harmonic spectrum. We also show that the magnetic field and polarization dependence of this spectrum provides information on the magnitude of the Rashba and Dresselhaus spin-orbit coupling parameters. The shape of the Fermi surface can be deduced at least qualitatively and if only one type of spin-orbit coupling is present, the coupling strength can be determined.

Efficient gate control of spin–orbit interaction in InSb nanowire FET with a nearby back gate

Electrical tuning of spin–orbit interaction (SOI) is important for spintronics. Here we report that InSb nanowire with a nearby back gate structure enables efficient tuning of the Rashba SOI with small gate voltage. Consequently, the Rashba coupling parameter is larger than those obtained for various previously reported III–V nanowire devices. Our findings demonstrate that InSb nanowire with this back gate structure will provide prominent and easy-to-use devices in the fields of spintronics and spin–orbitronics.

Thermodynamic properties of graphene in a magnetic field and Rashba coupling

We study the thermodynamic properties of massless Dirac fermions in graphene subjected to a uniform magnetic field B together with a Rashba coupling parameter λR. The thermodynamic functions such as the Helmholtz free energy, internal energy, heat capacity and entropy are obtained in the high temperature regime using an approach based on the zeta function. These functions will be numerically examined by considering two cases related to λR smaller or greater than B. In particular, we show that the Dulong–Petit law is verified for both cases.

Periodicity of probability density and effects of Rashba Spin–orbit interaction on excitation energy of bound polaron in quantum pseudodot

Abstract We study the probability density and the excitation energy of the bound polaron in the quantum pseudodot under the Rashba spin–orbit interaction by using the unitary transformation of Lee–Low–Pines and the variational method of Pekar. The results of a numerical calculation show that the probability density of the bound polaron in the superposition state is periodic and oscillates with the period T 0 . Due to the Rashba spin–orbit interaction, the excitation energy splits into different branches. It also can be seen that the excitation energy changes with the phonon wave vector when the two-dimensional electron gas’s chemical potential, the electron–LO phonon coupling, the Coulomb bound potential and the Rashba coupling parameter take different values.

Point-Like Rashba Interactions as Singular Self-Adjoint Extensions of the Schrödinger Operator in One Dimension

We consider singular self-adjoint extensions for the Schr\{o}dinger operator of spin-$1/2$ particle in one dimension. The corresponding boundary conditions at a singular point are obtained. There are boundary conditions with the spin-flip mechanism, i.e. for these point-like interactions the spin operator does not commute with the Hamiltonian. One of these extensions is the analog of zero-range $\delta$-potential. The other one is the analog of so called $\delta^{(1)}$-interaction. We show that in physical terms such contact interactions can be identified as the point-like analogues of Rashba Hamiltonian (spin-momentum coupling) due to material heterogeneity of different types. The dependence of the transmissivity of some simple devices on the strength of the Rashba coupling parameter is discussed. Additionally, we show how these boundary conditions can be obtained in the non-relativistic limit of Dirac Hamiltonian.

Spin-orbit coupling mediated tunable electron heat capacity of quantum wells

The heat capacity of conduction electrons obtained from the Sommerfeld expansion is shown to be tunable via the Rashba and Dresselhaus spin-orbit coupling parameters. Using AlInSb/InSb/AlInSb as a representative heterostructure with alterable well and asymmetric barrier regions, the heat capacity is higher for the spin-down electrons and suffers a reduction for wider wells. A further lowering is obtained through the application of a uniaxial strain. Finally, we suggest a method to determine the spin lifetimes for spin relaxing via the D'yakonov-Perel' mechanism from experimental estimates of thermodynamic potentials such as the Helmholtz free energy and the heat capacity.

Thermodynamic behaviour of Rashba quantum dot in the presence of magnetic field**Project support by the University Grants Commission, India, the Department of Science and Technology, and the University Grants Commission–Basic Science Research (UGC-BSR).

The thermodynamic properties of an InSb quantum dot have been investigated in the presence of Rashba spin–orbit interaction and a static magnetic field. The energy spectrum and wave-functions for the system are obtained by solving the Schrodinger wave-equation analytically. These energy levels are employed to calculate the specific heat, entropy, magnetization and susceptibility of the quantum dot system using canonical formalism. It is observed that the system is susceptible to maximum heat absorption at a particular value of magnetic field which depends on the Rashba coupling parameter as well as the temperature. The variation of specific heat shows a Schottky-like anomaly in the low temperature limit and rapidly converges to the value of 2kB with the further increase in temperature. The entropy of the quantum dot is found to be inversely proportional to the magnetic field but has a direct variation with temperature. The substantial effect of Rashba spin–orbit interaction on the magnetic properties of quantum dot is observed at low values of magnetic field and temperature.

Tunable chirality and circular dichroism of a topological insulator with C2v symmetry as a function of Rashba and Dresselhaus parameters

Polarization-sensitive devices rely on meta-materials to exhibit varying degrees of absorption of light of a given handedness. The chiral surface states of a topological insulator selectively absorb right- and left-circularly polarized light in the vicinity of the Dirac cone reaching its maximum of unity at the Γ point. In this letter, we show that a band gap open topological insulator with C2v symmetry, which is represented through a combination of Rashba and Dresselhaus Hamiltonians, alters the preferential absorption of left- and right-circularly polarized light allowing a smooth variation of the circular dichroism. This variation in circular dichroism, in a range of positive and negative values, is shown to be a function of the Rashba and Dresselhaus coupling parameters.

Temperature dependence of spin photocurrent spectra induced by Rashba- and Dresselhaus-type circular photogalvanic effect at inter-band excitation in InGaAs/AlGaAs quantum wells.

Spin photocurrent spectra induced by Rashba- and Dresselhaus-type circular photogalvanic effect (CPGE) at inter-band excitation have been experimentally investigated in InGaAs/AlGaAs quantum wells at a temperature range of 80 to 290 K. It is found that, the sign of Rashba-type current reverses at low temperatures, while that of Dresselhaus-type remains unchanged. The temperature dependence of ratio of Rashba and Dresselhaus spin-orbit coupling parameters, increasing from -6.7 to 17.9, is obtained, and the possible reasons are discussed. We also develop a model to extract the Rashba-type effective electric field at different temperatures. It is demonstrated that excitonic effect will significantly influence the Rashba-type CPGE, while it has little effect on Dresselhaus-type CPGE.

Rashba effect in single-layer antimony telluroiodide SbTeI

Exploring spin-orbit coupling (SOC) in single-layer materials is important for potential spintronics applications. In this paper, using first-principles calculations, we show that single-layer antimony telluroiodide SbTeI behaves as a two-dimensional semiconductor exhibiting a G0W0 band gap of 1.82 eV. More importantly, we observe the Rashba spin splitting in the SOC band structure of single-layer SbTeI with a sizable Rashba coupling parameter of 1.39 eV A, which is significantly larger than that of a number of two-dimensional systems including surfaces and interfaces. The low formation energy and real phonon modes of single-layer SbTeI imply that it is stable. Finally, our study suggests that single-layer SbTeI is a candidate single-layer material for applications in spintronics devices.

Rashba-coupling modelling for two-dimensional and high-order Rashba Hamiltonian for one-dimensional confined heavy holes

Based on the standard multiband Hamiltonian, we have deduced an explicit analytical expression for the Rashba-coupling parameter which clarifies its anomalous behavior for heavy holes , gated in quasi–two-dimensional (Q2D) systems, by letting the density grow. Our modelling agrees remarkably better with experimental results in comparison with earlier theoretical models, while it recovers the expected cubic dependence on the quasi-momentum. For quasi–one-dimensional (Q1D) hh systems, we have formally derived an effective Rashba Hamiltonian with two competitive terms on the quasi-momentum, a linear term and a cubic one as predicted from suitable approximations to the Q2D scope. The Rashba-coupling parameters also behave anomalously and qualitatively support recent experiments in core/shell nanowires. Furthermore, they exhibit an essential asymptotic discontinuity in the low-density regime as a function of the lateral confinement length. For hh, we present closed schemes to accurately quote the Rashba-coupling parameters both for the Q2D and Q1D systems, which become unprecedented for holes.

Nonlinear optical conductivity of two-dimensional semiconductors with Rashba spin-orbit coupling in terahertz regime

We reveal that two-dimensional semiconductors with Rashba spin-orbit interaction (R2DG) exhibit exceptionally strong nonlinear optical response (NOR) in the terahertz frequency regime. The spin-split of the parabolic energy band in R2DG allows strong multiple-photon process to occur via inter-subband mechanism. We show sharp multiple photon edges in the nonlinear conductivity. The edges correspond to the cut-off effect produced by the multiple-photon process. For Rashba coupling parameter of λ R ≈ 10−10 eV m, electric field strength in the order of only 102 V/cm is required for the NOR to dominate over the linear response. Furthermore, the roles of the parabolic ‘free electron’ term H 0 and the linear Rashba term H R on NOR of R2DG are also investigated. Although the NOR is made possible due to the presence of a finite H R , H 0 does play an important role on the NOR especially in high temperature regime. H 0 has rendered R2DG a strong optical nonlinearity at elevated temperature which is not found in a purely linear system such as graphene. The results suggest the possibilities of Rashba spintronic system in the application of nonlinear terahertz devices.

Dielectric function, screening, and plasmons of graphene in the presence of spin-orbit interactions

We study the dielectric properties of graphene in the presence of Rashba and intrinsic spin-orbit interactions in their most general form, i.e., for arbitrary frequency, wave vector, doping, and spin-orbit coupling (SOC) parameters. The main result consists in the derivation of closed analytical expressions for the imaginary as well as for the real part of the polarization function. Several limiting cases, e.g., the case of purely Rashba or purely intrinsic SOC, and the case of equally large Rashba and intrinsic coupling parameters are discussed. In the static limit the asymptotic behavior of the screened potential due to charged impurities is derived. In the opposite limit ($q=0$, $\omega\to0$), an analytical expression for the plasmon dispersion is obtained and afterwards compared to the numerical result. Our result can also be applied to related systems such as bilayer graphene or topological insulators.

Variational analysis of the Rashba splitting in III–V semiconductor inversion layers

A spin-dependent variational theory is used to analyze the Rashba spin-orbit splitting in two-dimensional electron gases formed in III--V semiconductor inversion layers. The spin split conduction subbands in CdTe/InSb, insulator/InAs, InP/InGaAs, InAlAs/InGaAs, and AlGaAs/GaAs heterojunctions are calculated. The theory, presented here in detail, is based on the 8 $\ifmmode\times\else\texttimes\fi{}$ 8 $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ Kane model and on the introduction of simple and convenient spin-dependent Fang-Howard trial functions, and leads to analytical expressions for the split subbands, as well as allows for a detailed knowledge of the Rashba spin-orbit coupling, including its explicit dependence on structure parameters and its decomposition into separate contributions. The Rashba coupling parameter and the population difference in the spin-split subbands, as experimentally determined from the beating pattern of the Shubnikov-de Haas (SdH) oscillations, are obtained as a function of the electron density (${n}_{s}$). The separate contributions to the particularly large Rashba splitting in CdTe/InSb heterojunctions are also computed and discussed. It is shown, for example, that due to the spin-dependent boundary conditions, the direct Rashba spin-orbit coupling term in the effective Hamiltonian dominates the splitting only for ${n}_{s}>{10}^{10}$ cm${}^{\ensuremath{-}2}$ while it is the barrier penetration kinetic energy term that gives the largest contribution to the Rashba effect at lower densities.

Experimental approaches to zero-field spin splitting in a gated high-mobility In0.53Ga0.47As/InP quantum well structure: Weak antilocalization and beating pattern

We report on the strong spin-orbit (SO) interaction in a gated high-mobility In0.53Ga0.47As/InP quantum well two-dimensional electron gas. We establish that the SO interaction is dominated by the Rashba mechanism. The Rashba coupling parameters determined from analysis of both weak antilocalization and the beating pattern in the Shubnikov–de Haas oscillations are in reasonable agreement, and the small difference between them was explained by a magnetic-field-dependent effective g factor. The zero-field spin splitting shows nonmonotonic behavior with a maximum as the electron density is varied with the applied gate voltage. This is related to strong Rashba SO coupling in our sample.

Zero-field spin splitting and spin-dependent broadening in high-mobilityInSb/In1−xAlxSbasymmetric quantum well heterostructures

We present high field magneto-transport data from a range of 30nm wide InSb/InAlSb quantum wells. The low temperature carrier mobility of the samples studied ranged from 18.4 to 39.5 m2V-1s-1 with carrier densities between 1.5x1015 and 3.28x1015 m-2. Room temperature mobilities are reported in excess of 6 m2V-1s-1. It is found that the Landau level broadening decreases with carrier density and beating patterns are observed in the magnetoresistance with non-zero node amplitudes in samples with the narrowest broadening despite the presence of a large g-factor. The beating is attributed to Rashba splitting phenomenon and Rashba coupling parameters are extracted from the difference in spin populations for a range of samples and gate biases. The influence of Landau level broadening and spin-dependent scattering rates on the observation of beating in the Shubnikov-de Haas oscillations is investigated by simulations of the magnetoconductance. Data with non-zero beat node amplitudes are accompanied by asymmetric peaks in the Fourier transform, which are successfully reproduced by introducing a spin-dependent broadening in the simulations. It is found that the low-energy (majority) spin up state suffers more scattering than the high-energy (minority) spin down state and that the absence of beating patterns in the majority of (lower density) samples can be attributed to the same effect when the magnitude of the level broadening is large.

Weak antilocalization in high mobilityGaxIn1−xAs∕InPtwo-dimensional electron gases with strong spin-orbit coupling

We have studied the spin-orbit interaction in a high mobility two-dimensional electron gas in a $\mathrm{Ga}\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ heterostructure as a function of an applied gate voltage as well as a function of temperature. Highly sensitive magnetotransport measurements of weak antilocalization as well as measurements of Shubnikov--de Haas oscillations were performed in a wide range of electron sheet concentrations. In our samples, the electron transport takes place in the strong spin precession regime in the whole range of applied gate voltages, which is characterized by the spin precession length being shorter than the elastic mean free path. The magnitude of the Rashba spin-orbit coupling parameter was determined by fitting the experimental curves by a simulated quantum conductance correction according to a model proposed recently by Golub [Phys. Rev. B 71, 235310 (2005)]. A comparison of the Rashba coupling parameter extracted using this model with the values estimated from the analysis of the beating pattern in the Shubnikov--de Haas oscillations showed a good agreement.

Theory of anisotropic spin relaxation in quantum dots

We study theoretically phonon-assisted spin relaxation of an electron confined in an elliptical quantum dot (QD) subjected to a tilted magnetic field. In the presence of both Rashba and Dresselhaus spin-orbit terms, the relaxation rate is anisotropic with respect to the in-plane field orientation. This anisotropy originates from the interference, at nonzero tilt angle, between the two spin-orbit terms. We show that, in a narrow range of magnetic field orientations, the relaxation rate exhibits anomalous sensitivity to variations of the QD parameters. In this range, the relative change in the relaxation rate with in-plane field orientation is determined solely by the spin-orbit coupling strengths and by the dot geometry. This allows simultaneous determination of both Rashba and Dresselhaus coupling parameters and the dot ellipticity from analysis of the angular dependence of the relaxation rate.