Rashba Term Research Articles

Intrinsic spin Hall conductivity in a generalized Rashba model

We calculate the intrinsic spin Hall conductivity ${\ensuremath{\sigma}}^{\mathrm{sH}}$ of a two-dimensional electron system within a generalized Rashba model, showing that it is, in general, finite and model dependent. Considering arbitrary band dispersion, we find that ${\ensuremath{\sigma}}^{\mathrm{sH}}$ in the presence of the linear-in-momentum spin-orbit coupling of the Rashba form does not vanish in the presence of impurities except for the precisely parabolic spectrum. We show, using the linear response Kubo formalism, how the exact cancellation happens for the quadratic dispersion, and why it does not occur in general. We derive a simple quasiclassical formula for ${\ensuremath{\sigma}}^{\mathrm{sH}}$ in terms of the Fermi momenta for the two electron chiralities, and find that ${\ensuremath{\sigma}}^{\mathrm{sH}}$ is in general of the order of the squared strength of the Rashba term.

Spin-dependent magnetotransport through one or more rings in the presence of the Rashba and Dresselhaus terms of the spin–orbit interaction

Magnetotransport through one or several quasi-one-dimensional rings, in the presence of the Rashba (RSOI) and Dresselhaus (DSOI) terms of the spin–orbit interaction (SOI) and of a magnetic field B, is investigated. The RSOI field and an effective DSOI field are taken as E R = E R ( sin γ 1 e r + cos γ 1 e z ) and E D = E D ( sin γ 2 e r + cos γ 2 e z ) , their strengths are denoted by α and β , respectively. The exact one-electron eigenvalues and eigenfunctions are obtained and used to evaluate the transmission as a function of α , β , and of the angles γ 1 , γ 2 . Because the RSOI term couples the electronic orbit (along the θ direction) with the Pauli matrices σ z and σ r while the DSOI term couples it with σ θ , they affect the electronic spin transport through a ring in distinctly different ways. The resulting transmission shows a considerable structure as a function of the angles γ 1 or γ 2 . The same holds for the transmission, versus α or β , with the SOI present only in one arm of the ring and for that through two rings with the same or different radii. Various results of the literature, valid for β = 0 , are readily recovered. For weak magnetic fields B ⩽ 1 T the influence of the Zeeman term on the transmission, assessed by perturbation theory, is negligible.

Spin Hall effect in two-dimensionalp-type semiconductors in a magnetic field

We calculate the spin Hall conductivity driven by Rashba spin-orbit interaction in $p$-type two-dimensional semiconductors in the presence of a perpendicular magnetic field. For a highly confined quantum well, the system is described by a $k$-cubic Rashba term for two-dimensional heavy holes. The eigenstates of the system can be described by Landau spinor states. First we consider the conventional spin Hall conductivity. The contribution of the interband transitions to the Kubo-Greenwood formula gives the density dependent intrinsic spin Hall conductivity, which approaches its universal value $\sigma^z_{xy}=9e/8\pi$ for weak spin-orbit coupling and low Fermi energies, in agreement with previous work. However two intraband contribution terms cancel this effect leading to zero conventional spin Hall conductivity. Adding the torque dipole contribution to the definition of spin current, we also study the {\it effective} spin conductivity. This is shown to be proportional to the total magnetization plus surface terms which exactly cancel it for small spin-orbit coupling. If in low magnetic field the intraband transitions evolve to vertex corrections, the fact that both {effective} and conventional spin Hall conductivities vanish is unexpected. This suggests that the zero magnetic field limit of the model is singular.

Single electron control in n-type semiconductor quantum dots using non-Abelian holonomies generated by spin orbit coupling

We propose that n-type semiconductor quantum dots with the Rashba and Dresselhaus spin orbit interactions may be used for single electron manipulation through adiabatic transformations between degenerate states. All the energy levels are discrete in quantum dots and possess a double degeneracy due to time reversal symmetry in the presence of the Rashba and/or Dresselhaus spin orbit coupling terms. We find that the presence of double degeneracy does not necessarily give rise to a finite non-Abelian (matrix) Berry phase. We show that a distorted two-dimensional harmonic potential may give rise to non-Abelian Berry phases. The presence of the non-Abelian Berry phase may be tested experimentally by measuring the optical dipole transitions.

Resonant Intrinsic Spin Hall Effect inp-Type GaAs Quantum Well Structure

We study intrinsic spin Hall effect in p-type GaAs quantum well structure described by Luttinger Hamiltonian and a Rashba spin-orbit coupling arising from the structural inversion symmetry breaking. The Rashba term induces an energy level crossing in the lowest heavy hole subband, which gives rise to a resonant spin Hall conductance. The resonance may be used to identify the intrinsic spin Hall effect in experiments.

Spin-photovoltaic effect in quantum wires due to intersubband transitions

We consider the current induced in a quantum wire by external electromagnetic radiation. The photocurrent is caused by the interplay of spin-orbit interaction (Rashba and Dresselhaus terms) and external in-plane magnetic field. We calculate this current using a Wigner functions approach taking into account radiation-induced transitions between transverse subbands. The magnitude and the direction of the current depend on the Dresselhaus and Rashba constants, strength of magnetic field, radiation frequency and intensity. The current can be controlled by changing some of these parameters.

Spin-dependent magnetotransport through a mesoscopic ring in the presence of spin-orbit interaction

The Schr\"odinger equation for an electron in a mesoscopic ring, in the presence of the Rashba and linear Dresselhaus terms of the spin-orbit interaction (SOI) and of a magnetic field $B$, is solved exactly. The effective electric fields of these terms as well as $B$ have perpendicular and radial components. The interplay between them and $B$ and their influence on the spectrum is studied. The transmission through such a ring, with two leads connected to it, is evaluated as a function of the SOI strengths and of the orientations of these fields. The Rashba and Dresselhaus terms affect the transmission in different ways. The transmission through a series of rings with different radii and with SOI in both arms of the rings or only in one of them is also evaluated. For weak magnetic fields $B\ensuremath{\leqslant}1\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ the influence of the Zeeman term on the transmission, assessed by perturbation theory, is negligible.

Band structure and magnetotransport of a two-dimensional electron gas in the presence of spin-orbit interaction

The band structure and magnetotransport of a two-dimensional electron gas (2DEG), in the presence of the Rashba (RSOI) and Dresselhaus (DSOI) terms of the spin-orbit interaction and of a perpendicular magnetic field, is investigated. Exact and approximate analytical expressions for the band structure are obtained and used to calculate the density of states (DOS) and the longitudinal magnetoresitivity assuming a Gaussian type of level broadening. The interplay between the Zeeman coupling and the two terms of the SOI is discussed. If the strengths $\alpha$ and $ \beta$, of the RSOI and DSOI, respectively, are equal and the $g$ factor vanishes, the two spin states are degenerate and a shifted Landau-level structure appears. With the increase of the difference $\alpha- \beta$, a novel beating pattern of the DOS and of the Shubnikov-de Haas (SdH) oscillations appears distinctly different from that occurring when one of these strengths vanishes.

Spin-orbit coupling in a quantum dot at high magnetic field

We describe the simultaneous effects of the spin-orbit (SO) perturbation and a magnetic field $B$ on a disk shaped quantum dot (QD). {As it is known the} combination of electrostatic forces among the $N$ electrons confined in the QD and the Pauli principle can induce a spin polarization when $B$ (applied in the direction orthogonal to the QD) is above a threshold value. In the presence of an electric field parallel to $B$, coupled to the spin $ S $ by a Rashba term, we demonstrate that a symmetry breaking takes place: we can observe it by analyzing the splitting of the levels belonging to an unperturbed multiplet. We also discuss the competitive effects of the magnetic field, the SO perturbation and the electron electron interaction, in order to define the hierarchy of the states belonging to a multiplet. We demonstrate how this hierarchy depends on the QD's size. We show the spin texture due to the combined effects of the Rashba effect and the interaction responsible for the polarization.

Symmetries and anisotropies of the electronic states within full spin–orbit coupling

AbstractWe have analyzed how the symmetries and the anisotropies of energy dispersions and of the spinor states, within full spin–orbit interaction, form the two independent circular spin polarizations. We also compare how the effects produced by Rashba and Dresselhauss interaction terms act on the structure of the Hilbert space. These aspects are used to envisage a voltage controlled multichannel spin‐filtering regime in nonmagnetic diode structures. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Zero-field spin splitting in modulation-doped AlxGa1−xN∕GaN two-dimensional electron systems

Low-temperature magnetotransport measurements were performed on AlxGa1−xN∕GaN two-dimensional electron systems. By studying the beating pattern in the Shubnikov–de Haas oscillations in a perpendicular magnetic field, we are able to measure the zero-field spin-splitting energies in our systems. Our experimental results demonstrate that the Rashba term due to structural inversion asymmetry is the dominant mechanism which gives rise to the measured zero-field spin splitting in our wurzite AlGaN∕GaN structures. By utilizing the persistent photoconductivity (PPC) effect, we are able to increase the carrier density n in our AlGaN∕GaN two-dimensional electron system. It is found that the Rashba spin-orbit splitting parameter α decreases with increasing n. We suggest that the formation of long-lived electron-hole pairs induced by the PPC effect decreases the large electric field near the AlGaN∕GaN interface, causing α to decrease with increasing n.

Effect of hetero‐interface on weak localization in InSb thin film layers

Magnetoresistance (MR) effects caused by the quantum interference have been investigated in the InSb thin films grown on GaAs(100) substrates by MBE. The positive MR arising from the weak anti-localization (WAL) found in the accumulation layer at the InSb/GaAs interface for a 0.1 µm thick undoped film has been explained by taking account of the spin-Zeeman effect on spin-orbit interaction (SOI) caused by the asymmetric potential at the hetero interface (Rashba term) with SO scattering rate τso–1 ∼ 1.7 × 1012 s–1 from the fits of MR. In Sn-doped films, the negative MR found in extremely weak magnetic fields crossovers to the positive MR with decreasing the film thickness from d = 1 µm to 0.1 µm. These results have been analyzed using a two-layer model for the films; the SO scattering rate in the intrinsic InSb film due to the bulk inversion asymmetry (Dresselhaus term) has been found to be as small as τso–1 ≤ 2 × 109 s–1 and when the interface is approached in the film the WL crossovers to the WAL with the increase of SOI in the layers caused by the increased influence of the Rashba electric field. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Ballistic spin currents in mesoscopic metal/In(Ga)As/metal junctions

We investigate the ballistic spin transport through a two-dimensional mesoscopic metal/semiconductor/metal double junctions in the presence of spin-orbit interactions. It is shown that \emph{real} longitudinal and/or transverse spin currents can flow in the presence of the Rashba and Dresselhaus terms.

Spin precession due to spin-orbit coupling in a two-dimensional electron gas with spin injection via ideal quantum point contact

We present the analytical result of the expectation value of spin resulting from an injected spin polarized electron into a semi-infinitely extended 2DEG plane with [001] growth geometry via ideal quantum point contact. Both the Rashba and Dresselhaus spin-orbit couplings are taken into account. A pictorial interpretation of the spin precession along certain transport directions is given. The spin precession due to the Rashba term is found to be especially interesting since it behaves simply like a windshield wiper which is very different from the ordinary precession while that due to the Dresselhaus term is shown to be crystallographic-direction-dependent. Some crystallographic directions with interesting and handleable behavior of spin precession are found and may imply certain applicability in spintronic devices.

Beating of oscillations in transport coefficients of a one-dimensionally periodically modulated two-dimensional electron gas in the presence of spin-orbit interaction

Transport properties of a two-dimensional electron gas (2DEG) are studied in the presence of a perpendicular magnetic field $B$, of a {\it weak} one-dimensional (1D) periodic potential modulation, and of the spin-orbit interaction (SOI) described only by the Rashba term. In the absence of the modulation the SOI mixes the spin-up and spin-down states of neighboring Landau levels into two new, unequally spaced energy branches. The levels of these branches broaden into bands in the presence of the modulation and their bandwidths oscillate with the field $B$. Evaluated at the Fermi energy, the $n$-th level bandwidth of each series has a minimum or vanishes at different values of the field $B$. In contrast with the 1D-modulated 2DEG without SOI, for which only one flat-band condition applies, here there are two flat-band conditions that can change considerably as a function of the SOI strength $\alpha$ and accordingly influence the transport coefficients of the 2DEG. The phase and amplitude of the Weiss and Shubnikov-de Haas (SdH) oscillations depend on the strength $\alpha$. For small values of $\alpha$ both oscillations show beating patterns. Those of the former are due to the independently oscillating bandwidths whereas those of the latter are due to modifications of the density of states, exhibit an even-odd filling factor transition, and are nearly independent of the modulation strength. For strong values of $\alpha$ the SdH oscillations are split in two.

Level structure and spin-orbit effects in quasi-one-dimensional semiconductor nanostructures

We investigate theoretically how the spin-orbit Dresselhaus and Rashba effects influence the electronic structure of quasi-one-dimensional semiconductor quantum dots, similar to those that can be formed inside semiconductor nanorods. We calculate electronic energy levels, eigenfunctions, and effective $g$-factors for coupled, double dots made out of different materials, especially GaAs and InSb. We show that by choosing the form of the lateral confinement, the contributions of the Dresselhaus and Rashba terms can be tuned and suppressed, and we consider several possible cases of interest. We also study how, by varying the parameters of the double-well confinement in the longitudinal direction, the effective $g$-factor can be controlled to a large extent.

Effect of spin-orbit interaction on the plasma excitations in a quantum wire

Incorporating the spin-orbit interaction into the Hamiltonian of a quantum wire, we have calculated the plasma excitation energies. We include both the Rashba term ($\ensuremath{\alpha}$ coupling) arising from the asymmetry of the heterostructure forming the two-dimensional electron gas, and the $\ensuremath{\beta}$ coupling due to the quantum wire confinement which we model with a harmonic potential. The $\ensuremath{\alpha}$ coupling lifts the degeneracy of the spin states and the $\ensuremath{\beta}$ coupling causes the quantized transverse single-particle energy to have negative dispersion. Our model yields several interesting features which may be observed with the use of inelastic light scattering and electron energy loss spectroscopy (EELS). The collective excitations for the quantum wire are determined by the allowed transitions between subbands. The collective plasma excitations split off from each branch of allowed particle-hole modes. The subband structure gives rise to a plasmon mode with a negative group velocity.

Optical study of spin injection dynamics in InGaN∕GaN quantum wells with GaMnN injection layers

The spin injection dynamics of GaMnN∕InGaN multiquantum well (MQW) light emitting diodes (LEDs) grown by molecular beam epitaxy were examined using picosecond-transient and circularly polarized photoluminescence (PL) measurements. Even with the presence of a room temperature ferromagnetic GaMnN spin injector, the LEDs are shown to exhibit very low efficiency of spin injection. Based on resonant optical orientation spectroscopy, the spin loss in the structures is shown to be largely due to fast spin relaxation within the InGaN MQW, which itself destroys any spin polarization generated by optical spin orientation or electrical spin injection. Typical photoluminescence decay times were 20–40ns in both commercial GaN MQW LEDs with emission wavelengths between 420–470nm and in the GaMnN∕InGaN multi-quantum well MQW LEDs. In the wurtzite InGaN∕GaN system, biaxial strain at the interfaces give rise to large piezoelectric fields directed along the growth axis. This built-in piezofield breaks the reflection symmetry of confining potential leading to the presence of a large Rashba term in the conduction band Hamiltonian which is responsible for the short spin relaxation times.

The Rashba effect on a double-barrier spin polarizer

The Rashba effect on a double-barrier spin polarizer is considered using a formalism that produces accurate results with little computational effort. In previous articles, we proposed a spin polarizer consisting of a well made of a dilute magnetic semiconductor (DMS) enclosed by two non-magnetic barriers. In the absence of Rashba effect, the magnetization of the well produces totally polarized electronic levels separated by 0.15 eV. The highest steady magnetic field obtained in a laboratory could not produce a Zeeman splitting so big. As a consequence the calculated currents are almost totally polarized. The Rashba spin–orbit Hamiltonian produces a spin flip. Therefore, the levels at the well have not well-defined spin polarization and the currents are less polarized. The device presented here would be useful for spintronics because there are DMS ferromagnetic at room temperature. Our tight-binding Hamiltonian, including the Rashba term, is H = H K + H P + H E + H M + H h - i + H h - h + H R . The first term is the kinetic energy. H P describes the double-barrier profile and the third term represent the electric field due to the applied bias. The magnetic H M , the hole-impurity H h - i and the hole–hole H h - h terms are included in the mean field approximation. The profile and the charge distribution are calculated self-consistently. By using a decimation formalism, all these terms are treated exactly. Finally, the Rashba term H R is very small. Therefore, it is treated using second order perturbation theory. The calculation confirm that the Rashba effect on the currents is of second order. Consequently, the resulting depolarization is very small.

Experimental separation of Rashba and Dresselhaus spin splittings in semiconductor quantum wells.

The relative strengths of Rashba and Dresselhaus terms describing the spin-orbit coupling in semiconductor quantum well (QW) structures are extracted from photocurrent measurements on n-type InAs QWs containing a two-dimensional electron gas (2DEG). This novel technique makes use of the angular distribution of the spin-galvanic effect at certain directions of spin orientation in the plane of a QW. The ratio of the relevant Rashba and Dresselhaus coefficients can be deduced directly from experiment and does not relay on theoretically obtained quantities. Thus our experiments open a new way to determine the different contributions to spin-orbit coupling.