Rashba spin-orbit coupling probed by the weak antilocalization analysis in InAlAs/InGaAs/InAlAs quantum wells as a function of quantum well asymmetry

Light-Induced Giant Rashba Spin-Orbit Coupling at Superconducting KTaO3 (110) Heterointerfaces

The 2D electron system (2DES) at the KTaO₃ surface or heterointerface with 5d orbitals hosts extraordinary physical properties, including a stronger Rashba spin-orbit coupling (RSOC), higher superconducting transition temperature, and potential of topological superconductivity. Herein, a huge enhancement of RSOC under light illumination achieved at a superconducting amorphous-Hf_0.5 Zr_0.5 O₂ /KTaO₃ (110) heterointerfaces is reported. The superconducting transition is observed with T_c = 0.62 K and the temperature-dependent upper critical field reveals the interaction between spin-orbit scattering and superconductivity. A strong RSOC with B_so = 1.9 T is revealed by weak antilocalization in the normal state, which undergoes sevenfold enhancement under light illumination. Furthermore, RSOC strength develops a dome-shaped dependence of carrier density with the maximum of B_so = 12.6 T achieved near the Lifshitz transition point n_c ≈ 4.1 × 10¹³ cm^-2 . The highly tunable giant RSOC at KTaO₃ (110)-based superconducting interfaces show great potential for spintronics.

A spin modulating device, tuned by the Fermi energy, in honeycomb-like substrates periodically stubbed with transition-metal-dichalkogenides

We investigate spin transport through graphene-like substrates stubbed vertically with transition-metal-dichalcogenides (TMDs). A tight-binding model is used based on a graphene-like Hamiltonian that includes different types of spin-orbit coupling (SOC) terms permitted by theC_3vsymmetry group in TMDs/graphene-like heterostructures. The results show a spin modulation obtained by tuning the strength and sign of the Fermi energyE_Fand not by varying the SOC strength as is mainly the case of Datta and Das. The spin conductance is directly controlled by the value ofE_F. In addition, a perfect electron-spin modulation is obtained when a vertical strain is introduced. In this case, the spin conductance exhibits a strong energy dependence. The results may open the route to a combination of graphene-like substrates with TMD stubs and the development of spin-transistor devices controlled by the Fermi energy rather than the SOC strength.

Experimental Evidence of t_{2g} Electron-Gas Rashba Interaction Induced by Asymmetric Orbital Hybridization

We report the control of Rashba spin-orbit interaction by tuning asymmetric hybridization between Ti orbitals at the LaAlO_{3}/SrTiO_{3} interface. This asymmetric orbital hybridization is modulated by introducing a LaFeO_{3} layer between LaAlO_{3} and SrTiO_{3}, which alters the Ti-O lattice polarization and traps interfacial charge carriers, resulting in a large Rashba spin-orbit effect at the interface in the absence of an external bias. This observation is verified through high-resolution electron microscopy, magnetotransport and first-principles calculations. Our results open hitherto unexplored avenues of controlling Rashba interaction to design next-generation spin orbitronics.

Electrically tunable spin-orbit interaction in an InAs nanosheet

We report an experimental study of the spin-orbit interaction (SOI) in an epitaxially grown free-standing InAs nanosheet in a dual-gate field-effect device. Gate-transfer characteristic measurements show that independent tuning of the carrier density in the nanosheet and the potential difference across the nanosheet can be efficiently achieved with the use of a dual gate. The quantum transport characteristics of the InAs nanosheet are investigated by magnetoconductance measurements at low temperatures. It is shown that the electron transport in the nanosheet can be tuned from the weak antilocalization to the weak localization and then back to the weak antilocalization regime with a voltage applied over the dual gate without a change in the carrier density. The spin-orbit length extracted from the magnetoconductance measurements at a constant carrier density exhibits a peak value at which the SOI of the Rashba type is suppressed and the spin relaxation due to the presence of an SOI of the Dresselhaus type in the nanosheet can be revealed. Energy band diagram simulations have also been carried out for the device under the experimental conditions and the physical insights into the experimental observations have been discussed in light of the results of simulations.

Benchmarking Noise and Dephasing in Emerging Electrical Materials for Quantum Technologies

As quantum technologies develop, a specific class of electrically conducting materials is rapidly gaining interest because they not only form the core quantum-enabled elements in superconducting qubits, semiconductor nanostructures, or sensing devices, but also the peripheral circuitry. The phase coherence of the electronic wave function in these emerging materials will be crucial when incorporated in the quantum architecture. The loss of phase memory, or dephasing, occurs when a quantum system interacts with the fluctuations in the local electromagnetic environment, which manifests in "noise" in the electrical conductivity. Hence, characterizing these materials and devices therefrom, for quantum applications, requires evaluation of both dephasing and noise, although there are very few materials where these properties are investigated simultaneously. Here, the available data on magnetotransport and low-frequency fluctuations in electrical conductivity are reviewed to benchmark the dephasing and noise. The focus is on new materials that are of direct interest to quantum technologies. The physical processes causing dephasing and noise in these systems are elaborated, the impact of both intrinsic and extrinsic parameters from materials synthesis and devices realization are evaluated, and it is hoped that a clearer pathway to design and characterize both material and devices for quantum applications is thus provided.

Electrically Controllable Kondo Correlation in Spin-Orbit-Coupled Quantum Point Contacts

Integrating the Kondo correlation and spin-orbit interactions, each of which have individually offered unprecedented means to manipulate electron spins, in a controllable way can open up new possibilities for spintronics. We demonstrate electrical control of the Kondo correlation by coupling the bound spin to leads with tunable Rashba spin-orbit interactions, realized in semiconductor quantum point contacts. We observe a transition from single to double peak zero-bias anomalies in nonequilibrium transport-the manifestation of the Kondo effect-indicating a controlled Kondo spin reversal using only spin-orbit interactions. Universal scaling of the Kondo conductance is demonstrated, implying that the spin-orbit interactions could enhance the Kondo temperature. A theoretical model based on quantum master equations is also developed to calculate the nonequilibrium quantum transport.

Strain Effects on Rashba Spin-Orbit Coupling of 2D Hole Gases in GeSn/Ge Heterostructures

A demonstration of 2D hole gases in GeSn/Ge heterostructures with a mobility as high as 20 000 cm² V^-1 s^-1 is given. Both the Shubnikov-de Haas oscillations and integer quantum Hall effect are observed, indicating high sample quality. The Rashba spin-orbit coupling (SOC) is investigated via magneto-transport. Further, a transition from weak localization to weak anti-localization is observed, which shows the tunability of the SOC strength by gating. The magneto-transport data are fitted to the Hikami-Larkin-Nagaoka formula. The phase-coherence and spin-relaxation times, as well as spin-splitting energy and Rashba coefficient of the k-cubic term, are extracted. The analysis reveals that the effects of strain and confinement potential at a high fraction of Sn suppress the Rashba SOC caused by the GeSn/Ge heterostructures.

Highly Efficient Electric-Field Control of Giant Rashba Spin-Orbit Coupling in Lattice-Matched InSb/CdTe Heterostructures

Spin-orbit coupling (SOC), the relativistic effect describing the interaction between the orbital and spin degrees of freedom, provides an effective way to tailor the spin/magnetic orders using electrical means. Here, we report the manipulation of the spin-orbit interaction in the lattice-matched InSb/CdTe heterostructures. Owing to the energy band bending at the heterointerface, the strong Rashba effect is introduced to drive the spin precession where pronounced weak antilocalization cusps are observed up to 100 K. With effective quantum confinement and suppressed bulk conduction, the SOC strength is found to be enhanced by 75% in the ultrathin InSb/CdTe film. Most importantly, we realize the electric-field control of the interfacial Rashba effect using a field-effect transistor structure and demonstrate the gate-tuning capability which is 1-2 orders of magnitude higher than other materials. The adoption of the InSb/CdTe integration strategy may set up a general framework for the design of strongly spin-orbit coupled systems that are essential for CMOS-compatible low-power spintronics.

Kramers Degeneracy and Spin Inversion in a Lateral Quantum Dot

We show that the axial symmetry of the Bychkov–Rashba interaction can be exploited to produce electron spin-flip in a circular quantum dot, without lifting the time reversal symmetry. In order to elucidate this effect, we consider ballistic electron transmission through a two-dimensional circular billiard coupled to two one-dimensional electrodes. Using the tight-binding approximation, we derive the scattering matrix and the effective Hamiltonian for the considered system. Within this approach, we found the conditions for the optimal realization of this effect in the transport properties of the quantum dot. Numerical analysis of the system, extended to the case of two-dimensional electrodes, confirms our findings. The relatively strong quantization of the quantum dot can make this effect robust against the temperature effects.

Rashba Effect in Functional Spintronic Devices

Exploiting spin transport increases the functionality of electronic devices and enables such devices to overcome physical limitations related to speed and power. Utilizing the Rashba effect at the interface of heterostructures provides promising opportunities toward the development of high-performance devices because it enables electrical control of the spin information. Herein, the focus is mainly on progress related to the two most compelling devices that exploit the Rashba effect: spin transistors and spin-orbit torque devices. For spin field-effect transistors, the gate-voltage manipulation of the Rashba effect and subsequent control of the spin precession are discussed, including for all-electric spin field-effect transistors. For spin-orbit torque devices, recent theories and experiments on interface-generated spin current are discussed. The future directions of manipulating the Rashba effect to realize fully integrated spin logic and memory devices are also discussed.

Polarization envelope helicity dependent photovoltage in GaAs/Al0.3Ga0.7As modulation-doped quantum well

In this study, we demonstrate the switching of the direction of the photocurrent in an n-type GaAs/Al_0.3Ga_0.7As modulation-doped quantum well using a polarization pulse-shaping apparatus containing a 4f setup. The right- and left-polarization-twisting pulses with a polarization rotation frequency in the THz-regime are incident on a modulation-doped quantum well. The results show that the sign of the photovoltage is dependent on the direction of rotation of the polarization-twisting pulses, which can be explained by the circular photogalvanic effect combined with the production of a classical edge photocurrent from the acceleration of free electrons in the vicinity of the sample edge by the incident optical electric field. The wide range over which the polarization-rotation frequency may be tuned makes this method a powerful tool to investigate the response of an extensive variety of materials in the THz-regime.

Weak anti-localization of two-dimensional holes in germanium beyond the diffusive regime

Gate-controllable spin-orbit coupling is often one requisite for spintronic devices. For practical spin field-effect transistors, another essential requirement is ballistic spin transport, where the spin precession length is shorter than the mean free path such that the gate-controlled spin precession is not randomized by disorder. In this letter, we report the observation of a gate-induced crossover from weak localization to weak anti-localization in the magneto-resistance of a high-mobility two-dimensional hole gas in a strained germanium quantum well. From the magneto-resistance, we extract the phase-coherence time, spin-orbit precession time, spin-orbit energy splitting, and cubic Rashba coefficient over a wide density range. The mobility and the mean free path increase with increasing hole density, while the spin precession length decreases due to increasingly stronger spin-orbit coupling. As the density becomes larger than ∼6 × 1011 cm-2, the spin precession length becomes shorter than the mean free path, and the system enters the ballistic spin transport regime. We also report here the numerical methods and code developed for calculating the magneto-resistance in the ballistic regime, where the commonly used HLN and ILP models for analyzing weak localization and anti-localization are not valid. These results pave the way toward silicon-compatible spintronic devices.

Strong Spin-Orbit Contribution to the Hall Coefficient of Two-Dimensional Hole Systems

Classical charge transport, such as longitudinal and Hall currents in weak magnetic fields, is usually not affected by quantum phenomena. Yet relativistic quantum mechanics is at the heart of the spin-orbit interaction, which has been at the forefront of efforts to realize spin-based electronics, new phases of matter, and topological quantum computing. In this work we demonstrate that quantum spin dynamics induced by the spin-orbit interaction is directly observable in classical charge transport. We determine the Hall coefficient R_{H} of two-dimensional hole systems at low magnetic fields and show that it has a sizable spin-orbit contribution, which depends on the density p, is independent of temperature, is a strong function of the top gate electric field, and can reach ∼20% of the total. We provide a general method for extracting the spin-orbit parameter from magnetotransport data, applicable even at higher temperatures where Shubnikov-de Haas oscillations and weak antilocalization are difficult to observe. Our work will enable experimentalists to measure spin-orbit parameters without requiring large magnetic fields, ultralow temperatures, or optical setups.

Ferroelectric control of Rashba spin orbit coupling at the GeTe(111)/InP(111) interface

GeTe is a prototypical compound of a new class of multifunctional materials, i.e., ferroelectric Rashba semiconductors (FRS). In the present work, by combining the first-principles calculations and Rashba model analysis, we reexamine Rashba spin-orbit coupling (SOC) in a GeTe(111) crystal and clarify its linear Rashba SOC strength. We further investigate Rashba SOC at the interface of a GeTe(111)/InP(111) superlattice and demonstrate the ferroelectric manipulation of Rashba SOC in detail. A large modulation of Rashba SOC is obtained, and surprisingly, we find that Rashba SOC does not monotonically increase with the increase of ferroelectric displacement, due to the parabola opening reversal of Rashba splitting bands. In addition, a reversal of the spin texture is realized by tuning the ferroelectric polarization. Our investigation provides a deep insight into the ferroelectric control of Rashba SOC, which is of great importance in FRS spin field effect transistors.

Extraction of the Rashba spin-orbit coupling constant from scanning gate microscopy conductance maps for quantum point contacts

We study the possibility for the extraction of the Rashba spin-orbit coupling constant for a two-dimensional electron gas with the conductance microscopy technique. Due to the interplay between the effective magnetic field due to the Rashba spin-orbit coupling and the external magnetic field applied within the plane of confinement, the electron backscattering induced by a charged tip of an atomic force microscope located above the sample leads to the spin precession and spin mixing of the incident and reflected electron waves between the QPC and the tip-induced 2DEG depletion region. This mixing leads to a characteristic angle-dependent beating pattern visible in the conductance maps. We show that the structure of the Fermi level, bearing signatures of the spin-orbit coupling, can be extracted from the Fourier transform of the interference fringes in the conductance maps as a function of the magnetic field direction. We propose a simple analytical model which can be used to fit the experimental data in order to obtain the spin-orbit coupling constant.

Weak Localization and Antilocalization in Topological Materials with Impurity Spin-Orbit Interactions

Topological materials have attracted considerable experimental and theoretical attention. They exhibit strong spin-orbit coupling both in the band structure (intrinsic) and in the impurity potentials (extrinsic), although the latter is often neglected. In this work, we discuss weak localization and antilocalization of massless Dirac fermions in topological insulators and massive Dirac fermions in Weyl semimetal thin films, taking into account both intrinsic and extrinsic spin-orbit interactions. The physics is governed by the complex interplay of the chiral spin texture, quasiparticle mass, and scalar and spin-orbit scattering. We demonstrate that terms linear in the extrinsic spin-orbit scattering are generally present in the Bloch and momentum relaxation times in all topological materials, and the correction to the diffusion constant is linear in the strength of the extrinsic spin-orbit. In topological insulators, which have zero quasiparticle mass, the terms linear in the impurity spin-orbit coupling lead to an observable density dependence in the weak antilocalization correction. They produce substantial qualitative modifications to the magnetoconductivity, differing greatly from the conventional Hikami-Larkin-Nagaoka formula traditionally used in experimental fits, which predicts a crossover from weak localization to antilocalization as a function of the extrinsic spin-orbit strength. In contrast, our analysis reveals that topological insulators always exhibit weak antilocalization. In Weyl semimetal thin films having intermediate to large values of the quasiparticle mass, we show that extrinsic spin-orbit scattering strongly affects the boundary of the weak localization to antilocalization transition. We produce a complete phase diagram for this transition as a function of the mass and spin-orbit scattering strength. Throughout the paper, we discuss implications for experimental work, and, at the end, we provide a brief comparison with transition metal dichalcogenides.

Highly gate-tuneable Rashba spin-orbit interaction in a gate-all-around InAs nanowire metal-oxide-semiconductor field-effect transistor

III-V semiconductors have been intensively studied with the goal of realizing metal-oxide-semiconductor field-effect transistors (MOSFETs) with high mobility, a high on-off ratio, and low power consumption as next-generation transistors designed to replace current Si technology. Of these semiconductors, a narrow band-gap semiconductor InAs has strong Rashba spin-orbit interaction, thus making it advantageous in terms of both high field-effect transistor (FET) performance and efficient spin control. Here we report a high-performance InAs nanowire MOSFET with a gate-all-around (GAA) structure, where we simultaneously control the spin precession using the Rashba interaction. Our FET has a high on-off ratio (10⁴~10⁶) and a high field-effect mobility (1200 cm²/Vs) and both values are comparable to those of previously reported nanowire FETs. Simultaneously, GAA geometry combined with high- κ dielectric enables the creation of a large and uniform coaxial electric field (>10⁷ V/m), thereby achieving highly controllable Rashba coupling (1 × 10^-11 eVm within a gate-voltage swing of 1 V), i.e. an operation voltage one order of magnitude smaller than those of back-gated nanowire MOSFETs. Our demonstration of high FET performance and spin controllability offers a new way of realizing low-power consumption nanoscale spin MOSFETs.

Universal modeling of weak antilocalization corrections in quasi-two-dimensional electron systems using predetermined return orbitals

We have developed a method to calculate the weak localization and antilocalization corrections based on the real-space simulation, where we provide 147 885 predetermined return orbitals of quasi-two-dimensional electrons with up to 5000 scattering events that are repeatedly used. Our model subsumes that of Golub [L. E. Golub, Phys. Rev. B 71, 235310 (2005)PRBMDO1098-012110.1103/PhysRevB.71.235310] when the Rashba spin-orbit interaction (SOI) is assumed. Our computation is very simple, fast, and versatile, where the numerical results, obtained all at once, cover wide ranges of the magnetic field under various one-electron interactions H^{'} exactly. Thus, it has straightforward extensibility to incorporate interactions other than the Rashba SOI, such as the linear and cubic Dresselhaus SOIs, Zeeman effect, and even interactions relevant to the valley and pseudo spin degrees of freedom, which should provide a unique tool to study new classes of materials like emerging 2D materials. Using our computation, we also demonstrate the robustness of a persistent spin helix state against the cubic Dresselhaus SOI.

Emergent spin-valley-orbital physics by spontaneous parity breaking

The spin-orbit coupling in the absence of spatial inversion symmetry plays an important role in realizing intriguing electronic states in solids, such as topological insulators and unconventional superconductivity. Usually, the inversion symmetry breaking is inherent in the lattice structures, and hence, it is not easy to control these interesting properties by external parameters. We here theoretically investigate the possibility of generating the spin-orbital entanglement by spontaneous electronic ordering caused by electron correlations. In particular, we focus on the centrosymmetric lattices with local asymmetry at the lattice sites, e.g. zigzag, honeycomb, and diamond structures. In such systems, conventional staggered orders, such as charge order and antiferromagnetic order, break the inversion symmetry and activate the antisymmetric spin-orbit coupling, which is hidden in a sublattice-dependent form in the paramagnetic state. Considering a minimal two-orbital model on a honeycomb structure, we scrutinize the explicit form of the antisymmetric spin-orbit coupling for all the possible staggered charge, spin, orbital, and spin-orbital orders. We show that the complete table is useful for understanding of spin-valley-orbital physics, such as spin and valley splitting in the electronic band structure and generalized magnetoelectric responses in not only spin but also orbital and spin-orbital channels, reflecting in peculiar magnetic, elastic, and optical properties in solids.

Strong and Tunable Spin-Orbit Coupling in a Two-Dimensional Hole Gas in Ionic-Liquid Gated Diamond Devices

Hydrogen-terminated diamond possesses due to transfer doping a quasi-two-dimensional (2D) hole accumulation layer at the surface with a strong, Rashba-type spin-orbit coupling that arises from the highly asymmetric confinement potential. By modulating the hole concentration and thus the potential using an electrostatic gate with an ionic-liquid dielectric architecture the spin-orbit splitting can be tuned from 4.6-24.5 meV with a concurrent spin relaxation length of 33-16 nm and hole sheet densities of up to 7.23 × 10(13) cm(-2). This demonstrates a spin-orbit interaction of unprecedented strength and tunability for a 2D hole system at the surface of a wide band gap semiconductor. With a spin relaxation length that is experimentally accessible using existing nanofabrication techniques, this result suggests that hydrogen-terminated diamond has great potential for the study and application of spin transport phenomena.

Persistent current in a correlated quantum ring with electron-phonon interaction in the presence of Rashba interaction and Aharonov-Bohm flux

Persistent current in a correlated quantum ring threaded by an Aharonov-Bohm flux is studied in the presence of electron-phonon interactions and Rashba spin-orbit coupling. The quantum ring is modeled by the Holstein-Hubbard-Rashba Hamiltonian and the energy is calculated by performing the conventional Lang-Firsov transformation followed by the diagonalization of the effective Hamiltonian within a mean-field approximation. The effects of Aharonov-Bohm flux, temperature, spin-orbit and electron-phonon interactions on the persistent current are investigated. It is shown that the electron-phonon interactions reduce the persistent current, while the Rashba coupling enhances it. It is also shown that temperature smoothens the persistent current curve. The effect of chemical potential on the persistent current is also studied.

2D Electronic Transport with Strong Spin-Orbit Coupling in Bi(2-) Square Net of Y2O2Bi Thin Film Grown by Multilayer Solid-Phase Epitaxy

Highly crystalline Y2O2Bi epitaxial thin film with monatomic Bi(2-) square net layer was grown by newly developed multilayer solid phase epitaxy. High reactivity of the nanometer-scale multilayered precursor enabled efficient formation of single crystalline Y2O2Bi phase with one-step heating. The reductive state of Bi(2-) square net was observed by X-ray photoemission spectroscopy. The electrical resistivity was one order lower than that of polycrystalline powder in previous study. The magnetotransport showed weak antilocalization effect well fitted by the Hikami-Larkin-Nagaoka model, exhibiting two-dimensional electronic nature with strong spin-orbit coupling in the Bi(2-) square net.

Quantum transport in Rashba spin-orbit materials: a review

In this review article we describe spin-dependent transport in materials with spin-orbit interaction of Rashba type. We mainly focus on semiconductor heterostructures, however we consider topological insulators, graphene and hybrid structures involving superconductors as well. We start from the Rashba Hamiltonian in a two dimensional electron gas and then describe transport properties of two- and quasi-one-dimensional systems. The problem of spin current generation and interference effects in mesoscopic devices is described in detail. We address also the role of Rashba interaction on localisation effects in lattices with nontrivial topology, as well as on the Ahronov-Casher effect in ring structures. A brief section, in the end, describes also some related topics including the spin-Hall effect, the transition from weak localisation to weak anti localisation and the physics of Majorana fermions in hybrid heterostructures involving Rashba materials in the presence of superconductivity.

Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

Generation of Rashba spin-orbit coupling in CdSe nanowire by ionic liquid gate

Spintronic devices rely on the spin degree of freedom (DOF), and spin orbit coupling (SOC) is the key to manipulate spin DOF. Quasi-one-dimensional structures, possessing marked anisotropy gives more choice for the manipulation of the spin DOF since the concrete SOC form varies along with crystallographic directions. The anisotropy of the Dresselhaus SOC in cadmium selenide (CdSe) nanobelt and nanowire was studied by circular photogalvanic effect. It was demonstrated that the Dresselhaus SOC parameter is zero along the [0001] crystallographic direction, which suppresses the spin relaxation and increases the spin diffusion length, and thus is beneficial to the spin manipulation. To achieve a device structure with Rashba SOC presence and Dresselhaus SOC absence for manipulating the spin DOF, an ionic liquid gate was produced on a nanowire grown along the [0001] crystallographic direction, and the Rashba SOC was induced by gating, as expected.

Weak antilocalization of high mobility holes in a strained germanium quantum well heterostructure

We present the observation of weak antilocalization due to the Rashba spin-orbit interaction, through magnetoresistance measurements performed at low temperatures and low magnetic fields on a high mobility (777,000 cm(2) V(-1) s(-1)) p-Ge/SiGe quantum well heterostructure. The measured magnetoresistance over a temperature range of 0.44 to 11.2 K shows an apparent transition from weak localization to weak antilocalization. The temperature dependence of the zero field conductance correction is indicative of weak localization using the simplest model, despite the clear existence of weak antilocalization. The Rashba interaction present in this material, and the absence of the un-tuneable Dresselhaus interaction, indicates that Ge quantum well heterostructures are highly suitable for semiconductor spintronic applications, particularly the proposed spin field effect transistor.

All-electric all-semiconductor spin field-effect transistors

The spin field-effect transistor envisioned by Datta and Das opens a gateway to spin information processing. Although the coherent manipulation of electron spins in semiconductors is now possible, the realization of a functional spin field-effect transistor for information processing has yet to be achieved, owing to several fundamental challenges such as the low spin-injection efficiency due to resistance mismatch, spin relaxation and the spread of spin precession angles. Alternative spin transistor designs have therefore been proposed, but these differ from the field-effect transistor concept and require the use of optical or magnetic elements, which pose difficulties for incorporation into integrated circuits. Here, we present an all-electric and all-semiconductor spin field-effect transistor in which these obstacles are overcome by using two quantum point contacts as spin injectors and detectors. Distinct engineering architectures of spin-orbit coupling are exploited for the quantum point contacts and the central semiconductor channel to achieve complete control of the electron spins (spin injection, manipulation and detection) in a purely electrical manner. Such a device is compatible with large-scale integration and holds promise for future spintronic devices for information processing.

Spin-orbit-coupled superconductivity

Superconductivity and spin-orbit (SO) interaction have been two separate emerging fields until very recently that the correlation between them seemed to be observed. However, previous experiments concerning SO coupling are performed far beyond the superconducting state and thus a direct demonstration of how SO coupling affects superconductivity remains elusive. Here we investigate the SO coupling in the critical region of superconducting transition on Al nanofilms, in which the strength of disorder and spin relaxation by SO coupling are changed by varying the film thickness. At temperatures T sufficiently above the superconducting critical temperature T_c, clear signature of SO coupling reveals itself in showing a magneto-resistivity peak. When T < T_c, the resistivity peak can still be observed; however, its line-shape is now affected by the onset of the quasi two-dimensional superconductivity. By studying such magneto-resistivity peaks under different strength of spin relaxation, we highlight the important effects of SO interaction on superconductivity.

Dirac versus Weyl fermions in topological insulators: Adler-Bell-Jackiw anomaly in transport phenomena

Dirac metals (gapless semiconductors) are believed to turn into Weyl metals when perturbations, which break either time reversal symmetry or inversion symmetry, are employed. However, no experimental evidence has been reported for the existence of Weyl fermions in three dimensions. Applying magnetic fields near the topological phase transition from a topological insulator to a band insulator in Bi1-xSbx we observe not only the weak antilocalization phenomenon in magnetoconductivity near zero magnetic fields (B<0.4  T), but also its upturn above 0.4 T only for E//B. This "incompatible" coexistence between weak antilocalization and "negative" magnetoresistivity is attributed to the Adler-Bell-Jackiw anomaly ("topological" E·B term) in the presence of weak antilocalization corrections.

Effect of Pauli blockade on spin-dependent diffusion in a degenerate electron gas

Spin-polarized transport of photoelectrons in bulk, p-type GaAs is investigated in the Pauli blockade regime. In contrast to usual spin diffusion processes in which the spin polarization decreases with distance traveled due to spin relaxation, images of the polarized photoluminescence reveal a spin-filter effect in which the spin polarization increases during transport over the first 2  μm from 26% to 38%. This is shown to be a direct consequence of the Pauli principle and the associated quantum degeneracy pressure which results in a spin-dependent increase in the minority carrier diffusion constants and mobilities. The central role played by the quantum degeneracy pressure is confirmed via the observation of a spin-dependent increase in the photoelectron volume and a spin-charge coupling description of this is presented.

Nonlinear anomalous Hall effect and negative magnetoresistance in a system with random Rashba field

We predict two spin-dependent transport phenomena in two-dimensional electron systems, which are induced by a spatially fluctuating Rashba spin-orbit interaction. When the electron gas is magnetized, the random Rashba interaction leads to the anomalous Hall effect. An example of such a system is a narrow-gap magnetic semiconductor-based symmetric quantum well. We show that the anomalous Hall conductivity reveals a strongly nonlinear dependence on the magnetization, decreasing exponentially at large spin density. We also show that electron scattering from a fluctuating Rashba field in a two-dimensional nonmagnetic electron system leads to a negative magnetoresistance arising solely due to spin-dependent effects.

Electric field-driven coherent spin reorientation of optically generated electron spin packets in InGaAs

Full electric-field control of spin orientations is one of the key tasks in semiconductor spintronics. We demonstrate that electric-field pulses can be utilized for phase-coherent ±π spin rotation of optically generated electron spin packets in InGaAs epilayers detected by time-resolved Faraday rotation. Through spin-orbit interaction, the electric-field pulses act as local magnetic field pulses. By the temporal control of the local magnetic field pulses, we can turn on and off electron spin precession and thereby rotate the spin direction into arbitrary orientations in a two-dimensional plane. Furthermore, we demonstrate a spin-echo-type spin drift experiment and find an unexpected partial spin rephasing, which is evident by a doubling of the spin dephasing time.

Electrical manipulation of Majorana fermions in an interdigitated superconductor-ferromagnet device

We show that a topological phase supporting Majorana fermions can form in a two-dimensional electron gas (2DEG) adjacent to an interdigitated superconductor-ferromagnet structure. An advantage of this setup is that the 2DEG can induce the required Zeeman splitting and superconductivity from a single interface, allowing one to utilize a wide class of 2DEGs including the surface states of bulk InAs. We demonstrate that the interdigitated device supports a robust topological phase when the finger spacing λ is smaller than half of the Fermi wavelength λ(F). In this regime, the electrons effectively see a "smeared" Zeeman splitting and pairing field despite the interdigitation. The topological phase survives even in the opposite limit λ > λ(F)/2, although with a reduced bulk gap. We describe how to electrically generate a vortex in this setup to trap a Majorana mode, and predict an anomalous Fraunhofer pattern that provides a sharp signature of chiral Majorana edge states.

Spin-orbit echo

Preserving and controlling the quantum information content of spins is a central challenge of spintronics. In solids, the relativistic spin-orbit interaction (SOI) leads to a finite spin lifetime. Here, we show that spin information is preserved by the hidden conserved "twisted spin" and survives elastic disorder scatterings. This twisted spin is an adiabatic invariant with respect to a slow change in the SOI. We predict an echo phenomenon, spin-orbit echo, which indicates the recovery of the spin moment when the SOI is tuned off adiabatically, even after spin relaxation has occurred; this is confirmed by numerical simulations. A concrete experiment in two-dimensional semiconductor quantum wells with Rashba-Dresselhaus SOI is proposed to verify our prediction.

Strong tuning of Rashba spin-orbit interaction in single InAs nanowires

A key concept in the emerging field of spintronics is the gate voltage or electric field control of spin precession via the effective magnetic field generated by the Rashba spin-orbit interaction. Here, we demonstrate the generation and tuning of electric field induced Rashba spin-orbit interaction in InAs nanowires where a strong electric field is created by either a double gate or a solid electrolyte surrounding gate. In particular, the electrolyte gating enables 6-fold tuning of Rashba coefficient and nearly 3 orders of magnitude tuning of spin relaxation time within only 1 V of gate bias. Such a dramatic tuning of spin-orbit interaction in nanowires may have implications in nanowire-based spintronic devices.

Experimental evidence of cubic Rashba effect in an inversion-symmetric oxide

We present evidence of cubic Rashba spin splitting in a quasi-two-dimensional electron gas formed at a surface of (001) SrTiO3 single crystal from the weak localization or antilocalization (WAL) analysis of the low-temperature magnetoresistance. Our WAL data were well fitted by the model assuming mj=±3/2 for the spin-split pair, in which 2π rotation of the electron wave vector k∥ in the kx-ky plane accompanies 6π rotation of the spin quantization axis. This finding pertains to the p symmetry of the t2g electronic band derived from d electrons in SrTiO3, which provides insights into the surface electronic state of (001) SrTiO3.

Magnetotransport properties of a magnetically modulated two-dimensional electron gas with the spin-orbit interaction

We study the electrical transport properties of a two-dimensional electron gas (2DEG) with the Rashba spin-orbit interaction in the presence of a constant perpendicular magnetic field (B(0)( ̂z) which is weakly modulated by B1 = B1 cos(qx) ̂z, where B(1) ≪ B(0) and q = 2π/a with a the modulation period. We obtain the analytical expressions of the diffusive conductivities for spin-up and spin-down electrons. The conductivities for spin-up and spin-down electrons oscillate with different frequencies and produce beating patterns in the amplitude of the Weiss and Shubnikov-de Haas oscillations. We show that the Rashba strength can be determined by analyzing the beating pattern in the Weiss oscillation. We find a simple equation which determines the Rashba spin-orbit interaction strength if the number of Weiss oscillations between any two successive nodes is known from the experiment. We compare our results with the electrically modulated 2DEG with the Rashba interaction. For completeness, we also study the beating pattern formation in the collisional and the Hall conductivities.

Effects of the Rashba spin-orbit coupling on Hofstadter's butterfly

We study the effect of Rashba spin-orbit coupling on the Hofstadter spectrum of a two-dimensional tight-binding electron system in a perpendicular magnetic field. We obtain the generalized coupled Harper spin-dependent equations which include the Rashba spin-orbit interaction and solve for the energy spectrum and spin polarization. We investigate the effect of spin-orbit coupling on the fractal energy spectrum and the spin polarization for some characteristic states as a function of the magnetic flux α and the spin-orbit coupling parameter. We characterize the complexity of the fractal geometry of the spin-dependent Hofstadter butterfly with the correlation dimension and show that it grows quadratically with the amplitude of the spin-orbit coupling. We study some ground state properties and the spin polarization shows a fractal-like behavior as a function of α, which is demonstrated with the exponent close to unity of the decaying power spectrum of the spin polarization. Some degree of spin localization or distribution around +1 or -1, for small spin-orbit coupling, is found with the determination of the entropy function as a function of the spin-orbit coupling. The excited states show a more extended (uniform) distribution of spin states.

Revelation of topological surface states in Bi2Se3 thin films by in situ Al passivation

Topological insulators (TIs) are extraordinary materials that possess massless, Dirac-like topological surface states in which backscattering is prohibited due to the strong spin-orbit coupling. However, there have been reports on degradation of topological surface states in ambient conditions, which presents a great challenge for probing the original topological surface states after TI materials are prepared. Here, we show that in situ Al passivation inside a molecular beam epitaxy (MBE) chamber could inhibit the degradation process and reveal the pristine topological surface states. Dual evidence from Shubnikov-de Hass (SdH) oscillations and weak antilocalization (WAL) effect, originated from the π Berry phase, suggests that the helically spin-polarized surface states are well preserved by the proposed in situ Al passivation. In contrast, we show the degradation of surface states for the unpassivated control samples, in which the 2D carrier density is increased 39.2% due to ambient n-doping, the SdH oscillations are completely absent, and a large deviation from WAL is observed.

Spin-orbit interaction induced anisotropic property in interacting quantum wires

: We investigate theoretically the ground state and transport property of electrons in interacting quantum wires (QWs) oriented along different crystallographic directions in (001) and (110) planes in the presence of the Rashba spin-orbit interaction (RSOI) and Dresselhaus SOI (DSOI). The electron ground state can cross over different phases, e.g., spin density wave, charge density wave, singlet superconductivity, and metamagnetism, by changing the strengths of the SOIs and the crystallographic orientation of the QW. The interplay between the SOIs and Coulomb interaction leads to the anisotropic dc transport property of QW which provides us a possible way to detect the strengths of the RSOI and DSOI.PACS numbers: 73.63.Nm, 71.10.Pm, 73.23.-b, 71.70.Ej.

Strong and tunable spin--orbit coupling of one-dimensional holes in Ge/Si core/shell nanowires

We investigate the low-temperature magneto-transport properties of individual Ge/Si core/shell nanowires. Negative magneto-conductance was observed, which is a signature of one-dimensional weak antilocalization of holes in the presence of strong spin--orbit coupling. The temperature and back gate dependences of phase coherence length, spin--orbit relaxation time, and background conductance were studied. Specifically, we show that the spin--orbit coupling strength can be modulated by more than five folds with an external electric field. These results suggest the Ge/Si nanowire system possesses strong and tunable spin--orbit interactions and may serve as a candidate for spintronics applications.

High and tunable spin current induced by magnetic-electric fields in a single-mode spintronic device

We proposed that a viable form of spin current transistor is one to be made from a single-mode device which passes electrons through a series of magnetic-electric barriers built into the device. The barriers assume a wavy spatial profile across the conduction path due to the inevitable broadening of the magnetic fields. Field broadening results in a linearly increasing vector potential across the conduction channel, which increases spin polarization. We have identified that the important factors for generating high spin polarization and conductance modulation are the low source-drain bias, the broadened magnetic fields, and the high number of FM gates within a fixed channel length.

Combined electron resonance driven by an all-oscillating potential of patterned magnets

A novel mechanism is proposed for the phenomenon of combined electron resonance. It is shown that the spatially localized microwave fields of an Fe stripe array mediate the intense electronic transitions involving the changes in both spin and orbital quantum numbers when the electron moves along a cyclotron orbit in a semiconductor (e.g., InGaAs-based) quantum well. This discovery bridges the fields of spintronics and quantum computing, paving the way for conceptually new hybrid devices based on ferromagnetic and semiconductor structured materials.

Phonon-induced decoherence of spin-orbit-driven coherent oscillations in a single InGaAs quantum dot

The effect of direct spin-phonon interactions on spin-orbit-driven coherent oscillations in a single quantum dot proposed by Debald and Emary (2005 Phys. Rev. Lett. 94 226803) is investigated theoretically in terms of the perturbation treatment based on a unitary transformation. It is shown that the decoherence rate induced by acoustic phonons strongly depends on the spin-orbit coupling strength, the magnetic field strength and the dot size.

Fano and Dicke effects in a double Rashba-ring system

The electronic transport in a system of two quantum rings side-coupled to a quantum wire is studied via a single-band tunneling tight-binding Hamiltonian. We derived analytical expressions for the conductance and spin polarization when the rings are threaded by magnetic fluxes with Rashba spin-orbit interaction. We show that by using the Fano and Dicke effects this system can be used as an efficient spin filter even for small spin-orbit interaction and small values of magnetic fluxes. We compare the spin-dependent polarization of this design and the polarization obtained with one ring side-coupled to a quantum ring. As a main result, we find better spin polarization capabilities as compared to the one-ring design.