Rashba Spin-orbit Term Research Articles

Gate voltage dependent Rashba spin splitting in hole transverse magnetic focusing

Magnetic focussing of charge carriers in two-dimensional systems provides a solid state version of a mass spectrometer. In the presence of a spin-orbit interaction, the first focussing peak splits into two spin dependent peaks, allowing focussing to be used to measure spin polarisation and the strength of the spin-orbit interaction. In hole systems, the k^3 dependence of the Rashba spin-orbit term allows the spatial separation of spins to be changed in-situ using a voltage applied to an overall top gate. Here we demonstrate that this can be used to control the splitting of the magnetic focussing peaks. Additionally, we compare the focussing peak splitting to that predicted by Shubnikov-de Haas oscillations and k.p bandstructure calculations. We find that the focussing peak splitting is consistently larger than expected, suggesting further work is needed on understanding spin dependent magnetic focussing.

Effective spin-orbit gaps in the s and p orbital bands of an artificial honeycomb lattice

Muffin-tin methods have been instrumental in the design of honeycomb lattices that show, in contrast to graphene, separated $s$ and in-plane $p$ bands, a $p$ orbital Dirac cone, and a $p$ orbital flat band. Recently, such lattices have been experimentally realized using the two-dimensional electron gas on Cu(111). A possible next avenue is the introduction of spin-orbit coupling to these systems. Intrinsic spin-orbit coupling is believed to open topological gaps and create a topological flat band. Although Rashba coupling is straightforwardly incorporated in the muffin-tin approximation, intrinsic spin-orbit coupling has only been included either for a very specific periodic system, or only close to the Dirac point. Here, we introduce effective intrinsic and Rashba spin-orbit terms in the Hamiltonian for both periodic and finite-size systems. We observe a strong band opening over the entire Brillouin zone between the $p$ orbital flat band and the Dirac cone hosting a pronounced edge state, robust against the effects of Rashba spin-orbit coupling.

G -factor of electrons in gate-defined quantum dots in a strong in-plane magnetic field

We analyze orbital effects of an in-plane magnetic field on the spin structure of states of a gated quantum dot based in a two-dimensional electron gas. Starting with a $k \cdot p$ Hamiltonian, we perturbatively calculate these effects for the conduction band of GaAs, up to the third power of the magnetic field. We quantify several corrections to the g-tensor and reveal their relative importance. We find that for typical parameters, the Rashba spin-orbit term and the isotropic term, $H_{43} \propto {\bf P}^2 {\bf B} \cdot \boldsymbol{\sigma}$, give the largest contributions in magnitude. The in-plane anisotropy of the g-factor is, on the other hand, dominated by the Dresselhaus spin-orbit term. At zero magnetic field, the total correction to the g-factor is typically 5-10% of its bulk value. In strong in-plane magnetic fields, the corrections are modified appreciably.

Landau levels and magnetic oscillations in gapped Dirac materials with intrinsic Rashba interaction

A new family of the low-buckled Dirac materials which includes silicene, germanene, etc. is expected to possess a more complicated sequence of Landau levels than in pristine graphene. Their energies depend, among other factors, on the strength of the intrinsic spin-orbit (SO) and Rashba SO couplings and can be tuned by an applied electric field ${E}_{z}$. We studied the influence of the intrinsic Rashba SO term on the energies of Landau levels using both analytical and numerical methods. The quantum magnetic oscillations of the density of states are also investigated. A specific feature of the oscillations is the presence of the beats with the frequency proportional to the field ${E}_{z}$. The frequency of the beats becomes also dependent on the carrier concentration when Rashba interaction is present allowing experimental determination of its strength.

Rashba induced magnetoconductance oscillations in the LaAlO3-SrTiO3heterostructure

We report measurements of the normal state in-plane magnetoconductance in gated LaAlO$_3$-SrTiO$_3$ samples. As the orientation of the magnetic field changes within the plane of the interface, the signal displays periodic oscillations with respect to the angle between the field and the direction of the current. We show that in the underdoped to optimally doped range, a Fermi surface reconstruction takes place due to the Rashba spin-orbit term and that the oscillations are due to a magnetic field induced opening and closing of a gap at the $\Gamma$ point for those Ti out-of-plane orbitals having their band minimum close to the Fermi energy of the system.

Magnetic-field instability of Majorana modes in multiband semiconductor wires

We investigate the occurrence of Majorana modes in semiconductor quantum wires in close proximity with a superconductor and when both, Rashba interaction and magnetic field, are present. We consider long, but finite, multiband wires (namely, planar wires with dimensions $L_x\gg L_y$). Our results demonstrate that interband mixing coming from Rashba spin orbit term hybridizes Majorana pairs originating from different transverse modes while simultaneously closing the effective gap. Consequently, multiple Majorana modes do not coexist in general. On the contrary, Majorana physics is robust provided that only one single transverse mode contributes with a Majorana pair. Finally, we analyse the robustness of Majorana physics with respect to magnetic orbital effects.

Spin-dependent electron transport in a nonmagnetic nanostructure with both Dresselhaus and Rashba spin-orbit terms

The spin-dependent electron transport is numerically studied in a nonmagnetic nanostructure in the presence of both Dresselhaus and Rashba spin-orbit interactions. It is shown that the large spin polarization can be achieved in such a structure mainly due to the Rashba spin-orbit term induced splitting of the resonant level. It is also shown that the spin polarization strongly depends on the well width and the thickness of the middle barrier as well as the height of the middle barrier.

Electron tunneling in a non-magnetic heterostructure in presence of both Dresselhaus and Rashba spin–orbit terms

In this paper, the electron tunneling in a non-magnetic heterostructure is theoretically investigated in presence of both Dresselhaus and Rashba spin–orbit terms. We find that the considerable spin polarization can be achieved in such a non-magnetic structure, and in the different electron energy regions or for the different barrier heights, the Dresselhaus and Rashba spin–orbit couplings play a different role in the spin polarization. We also find that the transmission probability and the spin polarization both show a periodic profile with the increase of the well width.

Shot noise and spin-orbit coherent control of entangled and spin-polarized electrons

We extend our previous work on shot noise for entangled and spin polarized electrons in a beam-splitter geometry with spin-orbit (\textit{s-o}) interaction in one of the incoming leads (lead 1). Besides accounting for both the Dresselhaus and the Rashba spin-orbit terms, we present general formulas for the shot noise of singlet and triplets states derived within the scattering approach. We determine the full scattering matrix of the system for the case of leads with \textit{two} orbital channels coupled via weak \textit{s-o} interactions inducing channel anticrossings. We show that this interband coupling coherently transfers electrons between the channels and gives rise to an additional modulation angle -- dependent on both the Rashba and Dresselhaus interaction strengths -- which allows for further independent coherent control of the electrons traversing the incoming leads. We derive explicit shot noise formulas for a variety of correlated pairs (e.g., Bell states) and lead spin polarizations. Interestingly, the singlet and \textit{each} of the triplets defined along the quantization axis perpendicular to lead 1 (with the local \textit{s-o} interaction) and in the plane of the beam splitter display distinctive shot noise for injection energies near the channel anticrossings; hence, one can tell apart all the triplets, in addition to the singlet, through noise measurements. We also find that spin-orbit induced backscattering within lead 1 reduces the visibility of the noise oscillations, due to the additional partition noise in this lead. Finally, we consider injection of two-particle wavepackets into leads with multiple discrete states and find that two-particle entanglement can still be observed via noise bunching and antibunching.

Electron spin–orbit splitting in a InGaAs/InP quantum well studied by means of the weak-antilocalization and spin-zero effects in tilted magnetic fields

The coupling between Zeeman spin splitting and Rashba spin–orbit terms has been studied experimentally in a gated InGaAs/InP quantum-well structure by means of simultaneous measurements of the weak antilocalization (WAL) effect and beating in the Shubnikov–de Haas (SdH) oscillations. The strength of the Zeeman splitting was regulated by tilting the magnetic field with the spin-zeros in the SdH oscillations, which are not always present, being enhanced by the tilt. In tilted fields, the spin–orbit and Zeeman splittings are not additive, and a simple expression is given for the energy levels. The Rashba parameter and the electron g-factor were extracted from the position of the spin zeros in tilted fields. A good agreement is obtained for the spin–orbit coupling strength from the spin zeros and WAL measurements.

Optical transition energies for lead-salt semiconductor quantum wells

The quantized states for electrons and holes confined in lead-salt semiconductor quantum wells (QW's) grown on (100) and (111) substrates and the corresponding electric-dipole optical transition energies are calculated analytically, within the envelope function approximation and with the Dimmock two-band $\stackrel{\ensuremath{\rightarrow}}{k}\ensuremath{\cdot}\stackrel{\ensuremath{\rightarrow}}{p}$ model for the bulk. The solution takes into account nonparabolicity, anisotropy, and break of valley and spin degeneracy, due to quantum confinement. Transition energies for different PbTe QW's, calculated as a function of temperature and well width, are shown to give a fair description of the observations of the quantum size effect reported in the literature. Limitations of the spherical and of the parabolic approximations to the electronic structure of the lead-salt QW's are made clear and the Rashba spin-orbit term in the effective Hamiltonian is derived.