Magnetizing weak links by time-dependent spin-orbit interactions: Momentum conserving and non-conserving processes

The spin dynamics in solid state systems is governed by the competition between spin-orbit interaction (SOI) and the Zeeman effect. The SOI couples orbital motion of electron spins with an electric field. The Zeeman effect lifts the spin degeneracy in a magnetic field. In InGaAs -based 2DEGs, it is known that the Rashba SOI energy E SOI can be controlled by an electric field applied on the gate electrode.1 In the presence of SOI, weak localization (WL) due to time reversal symmetric interference changes to weak anti-localization (WAL). We have found crossover from WL to WAL by applying the gate voltage in InGaAs 2DEGs. Applying an in-plane magnetic field to the 2DEG does not affect the orbital motion of the electrons, but only modifies the Zeeman spin splitting energy E Z . This allows tuning the ratio between E SOI and E Z very accurately. We have studied how the interplay between SOI and Zeeman coupling affects the electron transport and the spin dynamics in InGaAs -based 2DEGs. From the quantitative analysis of the magnetoconductance, measured in the presence of an in-plane magnetic field, we conclude that this interplay results in a spin-induced breaking of time reversal symmetry (TRS) and in an enhancement of the spin relaxation time. Both effects are due to a partial alignment of the electron spin along the applied magnetic field, and are found to be in excellent agreement with recent theoretical predictions.2 We find that the electron dephasing time saturates when E Z becomes comparable to E SOI . Moreover, we show that the spin-induced electron dephasing time is a universal function of the ratio E Z /E SOI within the experimental accuracy, i.e. it is independent of any details of the quantum well.3 This universal behavior is explained by the recent theory.4 The suppression of WAL is observed by applying in-plane magnetic field because of the enhancement of the spin relaxation time, and this suppression also appears in narrow InGaAs wires since the effective magnetic field direction is confined by wires. In gate fitted narrow wires, the large enhancement of spin relaxation time is obtained when the Rashba SOI is decreased. The spin relaxation time is more than one order longer than that of 2DEG case. This enhancement suggests that the Rashba SOI strength approaches the Dresselhaus SOI strength. We have numerically investigated the angular dependence of in-plane magnetoconductance in disordered wires with both Rashba and Dresselhaus SOIs. A new method is proposed to determine the relative strength of Rashba and Dresselhaus SOI from transport measurements without the need of fitting parameters.5 This in-plane magnetic field measurement provides fruitful information on spin related transport. Note from Publisher: This article contains the abstract only.

Spin-orbit interaction based spintronics

A Datta-Das spin field effect transistor is built of a one-dimensional weak link, with Rashba spin orbit interactions (SOI), which connects two magnetized reservoirs. The particle and spin currents between the two reservoirs are calculated to lowest order in the tunneling through the weak link and in the wide-band approximation, with emphasis on their dependence on the origins of the `bare' magnetizations in the reservoirs. The SOI is found to generate magnetization components in each reservoir, which rotate in the plane of the electric field (generating the SOI) and the weak link, only if the `bare' magnetization of the other reservoir has a non-zero component in that plane. The SOI affects the charge current only if both reservoirs are polarized. The charge current is conserved, but the transverse rotating magnetization current is not conserved since the SOI in the weak link generates extra spin polarizations which are injected into the reservoirs.

Spin filters using spin–orbit interaction (SOI) are very important in the field of spintronics. Therefore, a theory of devices using SOI is necessary for designing the spin filters. The spin-filtering devices can be used to generate and detect spin polarized currents. Many researchers have reported on the spin-filters using linear Rashba SOI. However, the spin-filters using square and cubic Rashba SOIs are not yet reported. This is surely because the Aharonov–Casher (AC) phases acquired under square and cubic Rashba SOIs are ambiguous. In this paper, we try to derive the AC phases acquired under [Formula: see text]th order Rashba SOIs, which we call general Rashba SOIs, using non-Abelian SU (2) gauge theory. As a result, we have successfully derived these AC phases without completing the square methods which is useless except for linear Rashba SOI. In the process of derivation of AC phases, we have also found another expression of adiabatic approximation for a pure gauge. This finding will lead to the starting point for deeply understanding the adiabatic approximation. Using the above AC phases under general Rashba SOIs, we investigate the spin filter effect in Aharonov–Bohm (AB) ring with double quantum dots (QDs) under general Rashba SOIs. The spin transport is investigated from left nanowire to right nanowire in this structure within tight binding approximation. Especially, we focus on the difference of spin filter effects among general Rashba SOIs. We have obtained the penetrating magnetic flux dependence of spin polarization for the AB ring subject to general Rashba SOIs. It is found that the perfect spin filtering is achieved for all the Rashba SOIs. This result indicates that this AB ring under general Rashba SOIs can be a promising device for spin current generation without ferromagnetic metals. Moreover, this device under different order Rashba SOI behaves in totally different ways in response to penetrating magnetic flux, which is attributed to [Formula: see text] times rotation of directions of the effective magnetic field in the in-plane momentum. This fact means that we can determine the order of Rashba SOIs according to the peak position. We consider that this is very useful for many researchers.

Over the last decade, rapid progress in the field of nanoscience has been increasingly driving the attention of the scientific community as well as society at large on the corresponding technological applications, which are the object of so-called nanotechnology. A strong interest in assessing the current state of the art of this fast growing field, as well as stimulating research networking, prompted the organization of the International School and Workshop 'Nanoscience & Nanotechnology (n&n2007)', under the patronage of the Italian Institute for Nuclear Physics (INFN), the University of Rome Tor Vergata, the Tor Vergata Polyclinic, and the Catholic University of Rome, with generous sponsorship from 3M, 2M Strumenti, MTS, Ape Research, Crisel Instruments, Veeco and Amira. The aims of this event were as follows:

The investigations of the spectral and dynamical delocalization-localization (DL) transition have revealed intriguing features in a wide range of non-Hermitian systems. The present study aims at exploring the spectral and dynamical properties in a non-Hermitian quasiperiodic system with asymmetric hopping in the presence of Rashba Spin-Orbit (RSO) interaction. In particular, in such systems, we have identified that the DL transition is associated with a concurrent change in the energy spectrum, where the eigenstates always break the time-reversal symmetry for all strenghts of the quasiperiodic potential, contrary to the systems without RSO interaction. Remarkably, we find that the reality of energy spectrum under the open boundary condition that is frequently symbolised as a hallmark of the skin-effect, is a system-size dependent phenomena, and appears even when the associated energies are indeed complex. In addition, it is demonstrated that the spin-flip term in the RSO interaction in fact possesses a tendency to diminish the directionality of the skin-effect. On scrutinizing the dynamical attributes in our non-Hermitian system, we unveil that in spite of the fact that the spectral DL transition accords with the dynamical phase transition, interestingly, the system comes across hyper-diffusive and negative diffusion dynamical regimes depending upon the strength of the RSO interaction, in the spectrally localized regime.

This chapter focuses on the electron spin degree of freedom in semiconductor spintronics. In particular, the electrostatic control of the spin degree of freedom is an advantageous technology over metal-based spintronics. Spin–orbit interaction (SOI), which gives rise to an effective magnetic field. The essence of SOI is that the moving electrons in an electric field feel an effective magnetic field even without any external magnetic field. Rashba spin–orbit interaction is important since the strength is controlled by the gate voltage on top of the semiconductor’s two-dimensional electron gas. By utilizing the effective magnetic field induced by the SOI, spin generation and manipulation are possible by electrostatic ways. The origin of spin-orbit interactions in semiconductors and the electrical generation and manipulation of spins by electrical means are discussed. Long spin coherence is achieved by special spin helix state where both strengths of Rashba and Dresselhaus SOI are equal.

We investigate the effects of Rashba spin-orbit (RSO) interactions on the electronic band structure and corresponding wave functions of graphene. By exactly solving a tight-binding model Hamiltonian we obtain the expected splitting of the bands---due to the SU(2) spin symmetry breaking---that is accompanied by the appearance of additional Dirac points. These points are originated by valence-conduction-band crossings. By introducing a convenient gauge transformation we study a model for zigzag nanoribbons with RSO interactions. We show that RSO interactions lift the quasidegeneracy of the edge band while introducing a state-dependent spin separation in real space. Calculation of the average magnetization perpendicular to the ribbon plane suggest that RSO could be used to produce spin-polarized currents. Comparisons with the intrinsic spin-orbit interaction proposed to exist in graphene are also presented.

In a one-dimensional weak-link wire the spin-orbit interaction (SOI) alone cannot generate a nonzero spin current. We show that a Zeeman field acting in the wire in conjunction with the Rashba SOI there does yield such a current, whose magnitude and direction depend on the direction of the field. When this field is not parallel to the effective field due to the SOI, both the charge and the spin currents oscillate with the length of the wire. Measuring the oscillating anisotropic magnetoresistance can thus yield information on the SOI strength. These features are tuned by applying a magnetic and/or an electric field, with possible applications to spintronics.

We present a theory of quantum tunneling between 2D layers with account for Rashba and Dresselhaus spin-orbit interaction (SOI) in the layers. Energy and momentum conservation results in a single resonant peak in the tunnel conductance between two 2D layers as has been experimentally observed for two quantum wells (QW) in GaAs/AlGaAs heterostructures. The account for SOI in the layers leads to a complex pattern in the tunneling characteristic with typical features corresponding to SOI energy. For this manifestation of SOI to be observed experimentally the characteristic energy should exceed the resonant broadening related to the particles quantum lifetime in the layers. We perform an accurate analysis of the known experimental data on electron and hole 2D-2D tunneling in AlGaAs/GaAs heterostructures. It appears that for the electron tunneling the manifestation of SOI is difficult to observe, but for the holes tunneling the parameters of the real structures used in the experiments are very close to those required by the resolution criteria. We also consider a new promising candidate for the effect to be observed, that is p-doped SiGe strained heterostructures. The reported parameters of cubic Rashba SOI and quantum lifetime in strained Ge QWs fabricated up to date already match the criteria for observing SOI in 2D-2D heavy holes tunneling. As supported by our calculations small adjustments of the parameters for AlGaAs/GaAs p-type QWs or simply designing a 2D-2D tunneling experiment for SiGe case are very likely to reveal the SOI features in the 2D-2D tunneling.

We investigate coherent electronic quantum transport in a narrow channel with Rashba and Dresselhaus spin-orbit interaction in the presence of an external in-plane magnetic field that is applied along the channel direction. The spin-split energy spectrum is horizontally shifted respectively by the Rashba and the Dresselhaus effects and is vertically shifted by the applied magnetic field. First, we consider the Rashba spin-orbit interaction and the in-plane magnetic field in the narrow channel, there is a pseudo-gap in the energy spectrum. With the increasing magnetic field, we investigate the variation of the spin orientation. Furthermore, we find the hole-like quasi bound state and electron-like quasi-bound state features in conductance. When we consider the Rashba, Dresselhaus and Zeeman effects simultaneously, energy spectrum becomes asymmetry. In some specific cases, except for the quasi-bound state feature, we find the Fano effect in transport properties. Hence, in the presence of the Rashba spin-orbit interaction and the in-plane magnetic field, the Dresselhaus effect significantly affects coherent magneto-quantum transport properties.

Dirac-fermions in graphene d-wave superconducting heterojunction with the spin orbit interaction

We study electron transport through an Aharonov-Bohm (AB) interferometer with a noninteracting quantum dot in each of its arms. Both a magnetic flux ϕ threading through the AB ring and the Rashba spin-orbit (SO) interaction inside the two dots are taken into account. Due to the existence of the SO interaction, the electrons flowing through different arms of the AB ring will acquire a spin-dependent phase factor in the tunnel-coupling strengths. This phase factor, as well as the influence of the magnetic flux, will induce various interesting interference phenomena. We show that the conductance and the local density of states can become spin polarized by tuning the magnetic flux and the Rashba interaction strength. Under certain circumstances, a pure spin-up or spin-down conductance can be obtained when a spin-unpolarized current is injected from the external leads. Therefore, the electron spin can be manipulated by adjusting the Rashba spin-orbit strength and the structure parameters.

Spin–orbit interaction effect on nonlinear optical rectification of quantum wire in the presence of electric and magnetic fields

Spin–orbit interaction effect on the linear and nonlinear properties of quantum wire in the presence of electric and magnetic fields