Gate-controlled spin-orbit quantum interference effects in lateral transport

Robust topological superconductivity in spin-orbit coupled systems at higher-order van Hove filling

Van Hove singularities in proximity to the Fermi level promote electronic interactions and generate diverse competing instabilities. It is also known that a nontrivial Berry phase derived from spin-orbit coupling can introduce an intriguing decoration into the interactions and thus alter correlated phenomena. However, it is unclear how and what type of new physics can emerge in a system featured by the interplay between van Hove singularities (VHSs) and the Berry phase. Here, based on a general Rashba model on the square lattice, we comprehensively explore such an interplay and its significant influence on the competing electronic instabilities by performing a parquet renormalization group analysis. Despite the existence of a variety of comparable fluctuations in the particle-particle and particle-hole channels associated with higher-order VHSs, we find that the chiral p±ip pairings emerge as two stable fixed trajectories within the generic interaction parameter space, namely the system becomes a robust topological superconductor. The chiral pairings stem from the hopping interaction induced by the nontrivial Berry phase. The possible experimental realization and implications are discussed. Our work sheds new light on the correlated states in quantum materials with strong spin-orbit coupling (SOC) and offers fresh insights into the exploration of topological superconductivity.

Piezoelectric manipulation of spin-orbit coupling in a Wurtzite heterostructure

The combination of piezoelectricity and spin-orbit coupling (SOC) effect makes wurtzite semiconductors attractive for the development of exotic spin-related physics as well as spintronic applications. Triggering piezoelectricity, particularly by an external stimulus, provides a new perspective for manipulating SOC, but until now, a comprehensive understanding of this mechanism is lacking. Herein, by means of self-consistent calculations and Löwdin perturbation approach, we have explored the manipulation of SOC in the wurtzite (Al, Ga)N/GaN heterostructure by external stress-induced piezoelectric polarization. The results suggest that the Rashba SOC depends weakly on stress due to the wide-gap feature of the wurtzite crystal that makes Rashba SOC predominant by a bulk term instead of the structural inversion term. The piezoelectric polarization diminishes and even turns off Dresselhaus coupling by reducing the interfacial electric field. Moreover, piezoelectricity is shown to improve the poorly gate-tunable SOC. In the heterostructure with two occupied subbands, the Dresselhaus coupling of the second subband is more sensitive than the first one in response to stress. As an extension, we further demonstrate that the correlation effect in the wurtzite heterostructure can be significantly enhanced by piezoelectric polarization. This study offers an in-depth insight into piezoelectric modulation of spin-orbit physics, which has the potential for stimulating new quantum correlation states or designing functional spintronic devices.

Controlled Rotation of Electrically Injected Spins in a Nonballistic Spin-Field-Effect Transistor

Electrically controlled rotation of spins in a semiconducting channel is a prerequisite for the successful realization of many spintronic devices, like, e.g., the spin-field-effect transistor (sFET). To date, there have been only a few reports on electrically controlled spin precession in sFET-like devices. These devices operate in the ballistic regime, as postulated in the original sFET proposal, and hence need high SOC channel materials in practice. Here, we demonstrate gate-controlled precession of spins in a nonballistic sFET using an array of narrow diffusive wires as a channel between a spin source and a spin drain. Our study shows that spins traveling in a semiconducting channel can be coherently rotated on a distance far exceeding the electrons' mean free path, and spin-transistor functionality can be thus achieved in nonballistic channels with relatively low SOC, relaxing two major constraints of the original sFET proposal.

Electric-Field Control of Spin Diffusion Length and Electric-Assisted D'yakonov-Perel' Mechanism in Ultrathin Heavy Metal and Ferromagnetic Insulator Heterostructure

Electric-field control of spin dynamics is significant for spintronic device applications. Thus far, effectively electric-field control of magnetic order, magnetic damping factor and spin-orbit torque (SOT) has been studied in magnetic materials, but the electric field control of spin relaxation still remains unexplored. Here, we use ionic liquid gating to control spin-related property in the ultra-thin (4 nm) heavy metal (HM) platinum (Pt) and ferromagnetic insulator (FMI) yttrium iron garnet (Y₃Fe₅O₁₂, YIG) heterostructure. It is found that the anomalous Hall effect (AHE), spin relaxation time and spin diffusion length can be effectively controlled by the electric field. The anomalous Hall resistance is almost twice as large as at 0 voltage after applying a small voltage of 5.5 V. The spin relaxation time can vary by more than 50 percent with the electric field, from 41.6 to 64.5 fs. In addition, spin relaxation time at different gate voltage follows the reciprocal law of the electron momentum scattering time, which indicates that the D'yakonov-Perel' mechanism is dominant in the Pt/YIG system. Furthermore, the spin diffusion length can be effectively controlled by an ionic gate, which can be well explained by voltage-modulated interfacial spin scattering. These results help us to improve the interface spin transport properties in magnetic materials, with great contributions to the exploration of new physical mechanisms and spintronics device.

Spin-Hall conductivity and Hall angle in a two-dimensional system with impurities in the presence of spin–orbit interactions

We investigate the spin-torque-dependent Spin Hall phenomenon in a two-dimensional tight-binding system in the presence of Rashba and Dresselhaus spin–orbit interactions and random static impurities. We employ the Matsubara Green function techniques to calculate the relaxation time caused by the scattering of electrons by impurities. The longitudinal and transverse conductivities are next calculated with the help of the Kubo formalism. We have also calculated the spin Hall angle for the present model and studied its dependence on spin–orbit interactions and impurity strength. Finally, we explore the effect of interplay between the Rashba and Dresselhaus interactions on the spin-Hall effect.

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.

Interplay of spin-orbit coupling and Coulomb interaction in ZnO-based electron system

Spin-orbit coupling (SOC) is pivotal for various fundamental spin-dependent phenomena in solids and their technological applications. In semiconductors, these phenomena have been so far studied in relatively weak electron-electron interaction regimes, where the single electron picture holds. However, SOC can profoundly compete against Coulomb interaction, which could lead to the emergence of unconventional electronic phases. Since SOC depends on the electric field in the crystal including contributions of itinerant electrons, electron-electron interactions can modify this coupling. Here we demonstrate the emergence of the SOC effect in a high-mobility two-dimensional electron system in a simple band structure MgZnO/ZnO semiconductor. This electron system also features strong electron-electron interaction effects. By changing the carrier density with Mg-content, we tune the SOC strength and achieve its interplay with electron-electron interaction. These systems pave a way to emergent spintronic phenomena in strong electron correlation regimes and to the formation of quasiparticles with the electron spin strongly coupled to the density.

Chirality relaxation in low-temperature strongly Rashba-coupled systems

We study the relaxation dynamics of non-equilibrium chirality distributions of charge carriers in Rashba systems. We find that at low temperature inter-Rashba band transitions become suppressed due to the combined effect of the Rashba momentum split and the chiral spin texture of a Rashba system. Specifically, we show that momentum exchange between carriers and the phonon bath is effectively absent at temperatures where the momentum of thermal phonons is less than twice the Rashba momentum. This allows us to identify inter-carrier scattering as the dominant process by which non-equilibrium chirality distributions relax. We show that the magnitude of inter-carrier scattering is strongly influenced by the opposing spin structure of the Rashba bands. Finally, we provide an explicit result for the inter-band relaxation timescale associated with inter-carrier Coulomb scattering. We develop a general framework and assess its implications for GeTe, a bulk Rashba semiconductor with a strong Rashba momentum split.

Signatures of Majorana doublet in the Fano-Rashba interferometer

We theoretically study the quantum transport through a Fano-Rashba interferometer with an embedded Majorana doublet which generates at one end of the DIII-class topological superconductor. It shows that the Rasbha spin-orbit interaction in the reference arm drives the apparent and terminal-dependence spin polarization of the electron tunneling and crossed Andreev reflection, accompanied by their opposite directions. However, spin degeneracy holds in the local Andreev reflection. Next once the Majorana doublet is replaced by the Andreev bound state, the spin-polarization properties of the Andreev reflections are interchanged. Therefore, the Fano-Rashba interferometer can be a promising candidate for differentiating the Majorana doublet from other bound states.

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.

Calculations of spin-polarized Goos-Hänchen displacement in magnetically confined GaAs/Al x Ga1-x As nanostructure modulated by spin-orbit couplings

We theoretically investigate Goos-Hänchen (GH) displacement by modelling the spin transport in an archetypal device structure-a magnetically confined GaAs/Al _x Ga_1-x As nanostructure modulated by spin-orbit coupling (SOC). Both Rashba and Dresselhaus SOCs are taken into account. The degree of spin-polarized GH displacement can be tuned by Rashba or Dresselhaus SOC, i.e. interfacial confining electric field or strain engineering. Based on such a semiconductor nanostructure, a controllable spatial spin splitter can be proposed for spintronics applications.

Confinement sensitivity in quantum dot singlet-triplet relaxation

Spin-orbit mediated phonon relaxation in a two-dimensional quantum dot is investigated using different confining potentials. Elliptical harmonic oscillator and cylindrical well results are compared to each other in the case of a two-electron GaAs quantum dot subjected to a tilted magnetic field. The lowest energy set of two-body singlet and triplet states are calculated including spin-orbit and magnetic effects. These are used to calculate the phonon induced transition rate from the excited triplet to the ground state singlet for magnetic fields up to where the states cross. The roll of the cubic Dresselhaus effect, which is found to be much more important than previously assumed, and the positioning of 'spin hot-spots' are discussed and relaxation rates for a few different systems are exhibited.

Rashba and Dresselhaus Couplings in Halide Perovskites: Accomplishments and Opportunities for Spintronics and Spin-Orbitronics

In halide hybrid organic-inorganic perovskites (HOPs), spin-orbit coupling (SOC) presents a well-documented large influence on band structure. However, SOC may also present more exotic effects, such as Rashba and Dresselhaus couplings. In this Perspective, we start by recalling the main features of this effect and what makes HOP materials ideal candidates for the generation and tuning of spin-states. Then, we detail the main spectroscopy techniques able to characterize these effects and their application to HOPs. Finally, we discuss potential applications in spintronics and in spin-orbitronics in those nonmagnetic systems, which would complete the skill set of HOPs and perpetuate their ride on the crest of the wave of popularity started with optoelectronics and photovoltaics.

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.

Electrical spin injection and detection in high mobility 2DEG systems

In this review paper we present the current status of research related to the topic of electrical spin injection and detection in two-dimensional electron gas (2DEG) systems, formed typically at the interface between two III-V semiconductor compounds. We discuss both theoretical aspects of spin injection in case of ballistic transport as well as give an overview of available reports on spin injection experiments performed on 2DEG structures. In the experimental part we focus particularly on our recent work on all-semiconductor structures with a 2DEG confined at an inverted GaAs/(Al,Ga)As interface and with a ferromagnetic semiconductor (Ga,Mn)As employed as a source of spin-polarized electrons.

Quantum Transport and Observation of Dyakonov-Perel Spin-Orbit Scattering in Monolayer MoS_{2}

Monolayers of group 6 transition metal dichalcogenides are promising candidates for future spin-, valley-, and charge-based applications. Quantum transport in these materials reflects a complex interplay between real spin and pseudospin (valley) relaxation processes, which leads to either positive or negative quantum correction to the classical conductivity. Here we report experimental observation of a crossover from weak localization to weak antilocalization in highly n-doped monolayer MoS_{2}. We show that the crossover can be explained by a single parameter associated with electron spin lifetime of the system. At low temperatures and high carrier densities, the spin lifetime is inversely proportional to momentum relaxation time; this indicates that spin relaxation occurs via a Dyakonov-Perel mechanism.

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.

Direct determination of spin-orbit interaction coefficients and realization of the persistent spin helix symmetry

The spin-orbit interaction plays a crucial role in diverse fields of condensed matter, including the investigation of Majorana fermions, topological insulators, quantum information and spintronics. In III-V zinc-blende semiconductor heterostructures, two types of spin-orbit interaction--Rashba and Dresselhaus--act on the electron spin as effective magnetic fields with different directions. They are characterized by coefficients α and β, respectively. When α is equal to β, the so-called persistent spin helix symmetry is realized. In this condition, invariance with respect to spin rotations is achieved even in the presence of the spin-orbit interaction, implying strongly enhanced spin lifetimes for spatially periodic spin modes. Existing methods to evaluate α/β require fitting analyses that often include ambiguity in the parameters used. Here, we experimentally demonstrate a simple and fitting parameter-free technique to determine α/β and to deduce the absolute values of α and β. The method is based on the detection of the effective magnetic field direction and the strength induced by the two spin-orbit interactions. Moreover, we observe the persistent spin helix symmetry by gate tuning.

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.

Gate control of the electron spin-diffusion length in semiconductor quantum wells

The spin diffusion length is a key parameter to describe the transport properties of spin polarized electrons in solids. Electrical spin injection in semiconductor structures, a major issue in spintronics, critically depends on this spin diffusion length. Gate control of the spin diffusion length could be of great importance for the operation of devices based on the electric field manipulation and transport of electron spin. Here we demonstrate that the spin diffusion length in a GaAs quantum well can be electrically controlled. Through the measurement of the spin diffusion coefficient by spin grating spectroscopy and of the spin relaxation time by time-resolved optical orientation experiments, we show that the diffusion length can be increased by more than 200% with an applied gate voltage of 5 V. These experiments allow at the same time the direct simultaneous measurements of both the Rashba and Dresselhaus spin-orbit splittings.

Maximum intrinsic spin-Hall conductivity in two-dimensional systems with k-linear spin-orbit interaction

We analytically calculate the intrinsic spin-Hall conductivities (ISHCs) (σ(z)(xy) and σ(z)(yx)) in a clean, two-dimensional system with generic k-linear spin-orbit interaction. The coefficients of the product of the momentum and spin components form a spin-orbit matrix β̃. We find that the determinant of the spin-orbit matrix detβ̃ describes the effective coupling of the spin sz and orbital motion Lz. The decoupling of spin and orbital motion results in a sign change of the ISHC and the band-overlapping phenomenon. Furthermore, we show that the ISHC is in general unsymmetrical (σ(z)(xy) ≠ -σ(z)(yx)), and it is governed by the asymmetric response function Δβ̃, which is the difference in band-splitting along two directions: those of the applied electric field and the spin-Hall current. The obtained non-vanishing asymmetric response function also implies that the ISHC can be larger than e/8π, but has an upper bound value of e/4π. We will show that the unsymmetrical properties of the ISHC can also be deduced from the manifestation of the Berry curvature in the nearly degenerate area. On the other hand, by investigating the equilibrium spin current, we find that detβ̃ determines the field strength of the SU(2) non-Abelian gauge field.

Hall voltages without a magnetic field in a non-uniform two-dimensional electron system

We report on a measurement of giant second-harmonic Hall voltages which occur without a magnetic field and do not change their sign on current reversal in a two-dimensional electron system with a transverse density gradient. A quadratic dependence on the electric field, a strong temperature dependence, and both magnitude and directional dependence on the magnetic field are also observed. Such behavior points towards a plausible explanation based on a novel spin Hall effect with in-plane spin polarization.

Chiral spin waves in Fermi liquids with spin-orbit coupling

We predict the existence of chiral spin waves-collective modes in a two-dimensional Fermi liquid with the Rashba or Dresselhaus spin-orbit coupling. Starting from the phenomenological Landau theory, we show that the long-wavelength dynamics of magnetization is governed by the Klein-Gordon equations. The standing-wave solutions of these equations describe ''particles" with effective masses, whose magnitudes and signs depend on the strength of the electron-electron interaction. The spectrum of the spin-chiral modes for arbitrary wavelengths is determined from the Dyson equation for the interaction vertex. We propose to observe spin-chiral modes via microwave absorption by standing waves confined by an in-plane profile of the spin-orbit splitting.

Spin-flip transitions induced by time-dependent electric fields in surfaces with strong spin-orbit interaction

We present a comprehensive theoretical investigation of the light absorption rate at a Pb/Ge(111)-β√3 × √3R30° surface with strong spin-orbit coupling. Our calculations show that electron spin-flip transitions cause as much as 6% of the total light absorption, representing 1 order of magnitude enhancement over Rashba-like systems. Thus, we demonstrate that a substantial part of the light irradiating this nominally nonmagnetic surface is attenuated in spin-flip processes. Remarkably, the spin-flip transition probability is structured in well-defined hot spots within the Brillouin zone, where the electron spin experiences a sudden 90° rotation. This mechanism offers the possibility of an experimental approach to the spin-orbit phenomena by optical means.

New directions in the pursuit of Majorana fermions in solid state systems

The 1937 theoretical discovery of Majorana fermions-whose defining property is that they are their own anti-particles-has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review paper highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic 'topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to 'engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions-the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.

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.

Full electrical control of the electron spin relaxation in GaAs quantum wells

The electron spin dynamics in (111)-oriented GaAs/AlGaAs quantum wells is studied by time-resolved photoluminescence spectroscopy. By applying an external electric field of 50 kV/cm a two-order of magnitude increase of the spin relaxation time can be observed reaching values larger than 30 ns; this is a consequence of the electric field tuning of the spin-orbit conduction band splitting which can almost vanish when the Rashba term compensates exactly the Dresselhaus one. The measurements under a transverse magnetic field demonstrate that the electron spin relaxation time for the three space directions can be tuned simultaneously with the applied electric field.

Crystallographic plane tuning of magnetoplasmon excitations in two-dimensional electron gas systems

We investigate theoretically the magnetoplasmon spectrum of two-dimensional electron gas systems grown along different crystallographic directions, which are modulated by both the Dresselhaus spin-orbit interaction (DSOI) and the Rashba spin-orbit interaction (RSOI). Because the DSOI depends on the crystallographic orientation, the magnetoplasmon spectrum in the presence of the DSOI shows distinct features for different crystallographic planes. For some high-index planes, such as (140) and (114), the magnetoplasmon spectrum is anisotropic even under the pure-DSOI modulation, which is different from the isotropic behavior for the high-symmetry (001) plane. The coexistence of the DSOI and the RSOI leads to more drastic variations of the anisotropic magnetoplasmon spectrum in different crystallographic planes, which are revealed from the splittings of the collective excitation modes and the intensity of the spin density excitation at the anticrossing center of the splittings.

Tunable Rashba spin-orbit interaction at oxide interfaces

The quasi-two-dimensional electron gas found at the LaAlO{3}/SrTiO{3} interface offers exciting new functionalities, such as tunable superconductivity, and has been proposed as a new nanoelectronics fabrication platform. Here we lay out a new example of an electronic property arising from the interfacial breaking of inversion symmetry, namely, a large Rashba spin-orbit interaction, whose magnitude can be modulated by the application of an external electric field. By means of magnetotransport experiments we explore the evolution of the spin-orbit coupling across the phase diagram of the system. We uncover a steep rise in Rashba interaction occurring around the doping level where a quantum critical point separates the insulating and superconducting ground states of the system.

A perfect spin filtering device through Mach-Zehnder interferometry in a GaAs/AlGaAs electron gas

A spin filtering device based on quantum spin interference is addressed, for use with a two-dimensional GaAs/AlGaAs electron gas that has both Rashba and Dresselhaus spin-orbit (SO) couplings and an applied external magnetic field. We propose an experimentally feasible electronic Mach-Zehnder interferometer and derive a map, in parameter space, that determines perfect spin filtering conditions. We find two broad spin filtering regimes: one where filtering is achieved in the original incoming quantization basis, that takes advantage of the purely non-Abelian nature of the spin rotations; and another where one needs a tilted preferential axis in order to observe the polarized output spinor. Both solutions apply for arbitrary incoming electron polarization and energy, and are only limited in output amplitude by the randomness of the incoming spinor state. Including a full account of the beam splitter and mirror effects on spin yields solutions only for the tilted basis, but encompasses a broad range of filtering conditions.

Transition between electron localization and antilocalization in graphene

We show that quantum interference in graphene can result in antilocalization of charge carriers--an increase of the conductance, which is detected by a negative magnetoconductance. We demonstrate that depending on experimental conditions one can observe either weak localization or antilocalization of carriers in graphene. A transition from localization to antilocalization occurs when the carrier density is decreased and the temperature is increased. We show that quantum interference in graphene can survive at high temperatures, up to T approximately 200 K, due to weak electron-phonon scattering.

Modeling the decay of entanglement for electron spin qubits in quantum dots

We investigate the time evolution of entanglement under various models of decoherence: a general heuristic model based on local relaxation and dephasing times, and two microscopic models describing decoherence of electron spin qubits in quantum dots due to the hyperfine interaction with the nuclei. For each of the decoherence models, we investigate and compare how long the entanglement can be detected. We also introduce filtered witness operators, which extend the available detection time and investigate this detection time for various multipartite entangled states. By comparing the time required for detection with the time required for generation and manipulation of entanglement, we estimate for a range of different entangled states how many qubits can be entangled in a one-dimensional array of electron spin qubits.

Crystallographic plane tuning of charge and spin transport in semiconductor quantum wires

We investigate theoretically the charge and spin transport in quantum wires grown along different crystallographic planes in the presence of the Rashba spin-orbit interaction (RSOI) and the Dresselhaus spin-orbit interaction (DSOI). We find that changing the crystallographic planes leads to a variation of the anisotropy of the conductance due to a different interplay between the RSOI and DSOI, since the DSOI is induced by bulk inversion asymmetry, which is determined by crystallographic plane. This interplay depends sensitively on the crystallographic planes, and consequently leads to the anisotropic charge and spin transport in quantum wires embedded in different crystallographic planes.

Electrical measurement of a two-electron spin state in a double quantum dot

We propose a scheme for electrical measurement of two-electron spin states in a semiconductor double quantum dot. We calculated the adiabatic charge transfer when surface gates are modulated in time. Because of spin-orbit coupling in the semiconductor, spatial displacement of the electrons causes a total spin rotation. It follows that the expectation value of the transferred charge reflects the relative phase as well as the total spin population of a prepared singlet-triplet superposition state. The precise detection of the charge transfer serves to identify the quantum superposition.

Gate-controlled spin-orbit interaction in a parabolic GaAs/AlGaAs quantum well

We study the tunability of the spin-orbit interaction in a two-dimensional electron gas with a front and a back gate electrode by monitoring the spin precession frequency of drifting electrons using time-resolved Kerr rotation. The Rashba spin splitting can be tuned by the gate biases, while we find a small Dresselhaus splitting that depends only weakly on the gating. We determine the absolute values and signs of the two components and show that for zero Rashba spin splitting the anisotropy of the spin-dephasing rate vanishes.

Electrical generation of pure spin currents in a two-dimensional electron gas

Pure spin currents are generated and detected in micron-wide channels of a GaAs two-dimensional electron gas, using quantum point contacts in an in-plane magnetic field as injectors and detectors. The enhanced sensitivity to spin transport offered by a nonlocal measurement geometry enables accurate spin current measurements in this widely studied physical system. The polarization of the contacts is used to extract the quantum point contact g factor and provides a test for spontaneous polarization at 0.7 structure. The spin relaxation length in the channel is 30-50 microm over the magnetic field range 3-10 T, much longer than has been reported in GaAs two-dimensional electron gases but shorter than that expected from Dyakonov-Perel relaxation.

All-electrical detection of the relative strength of Rashba and Dresselhaus spin-orbit interaction in quantum wires

We propose a method to determine the relative strength of Rashba and Dresselhaus spin-orbit interaction from transport measurements without the need of fitting parameters. To this end, we make use of the conductance anisotropy in narrow quantum wires with respect to the directions of an in-plane magnetic field, the quantum wire, and the crystal orientation. We support our proposal by numerical calculations of the conductance of quantum wires based on the Landauer formalism which show the applicability of the method to a wide range of parameters.

Mesoscopic fluctuations in the spin-electric susceptibility due to Rashba spin-orbit interaction

We investigate mesoscopic fluctuations in the spin polarization generated by a static electric field and by Rashba spin-orbit interaction in a disordered 2D electron gas. In a diagrammatic approach we find that the out-of-plane polarization--while being zero for self-averaging systems--exhibits large sample-to-sample fluctuations which are shown to be well within experimental reach. We evaluate the disorder-averaged variance of the susceptibility and find its dependence on magnetic field, spin-orbit interaction, dephasing, and chemical potential difference.

Semiconductor spintronics

Spintronics refers commonly to phenomena in which the spin of electrons in a solid state environment plays the determining role. In a more narrow sense spintronics is an emerging research field of electronics: spintronics devices are based on a spin control of electronics, or on an electrical and optical control of spin or magnetism. While metal spintronics has already found its niche in the computer industry—giant magnetoresistance systems are used as hard disk read heads—semiconductor spintronics is yet to demonstrate its full potential. This review presents selected themes of semiconductor spintronics, introducing important concepts in spin transport, spin injection, Silsbee-Johnson spin-charge coupling, and spin-dependent tunneling, as well as spin relaxation and spin dynamics. The most fundamental spin-dependent interaction in nonmagnetic semiconductors is spin-orbit coupling. Depending on the crystal symmetries of the material, as well as on the structural properties of semiconductor based heterostructures, the spin-orbit coupling takes on different functional forms, giving a nice playground of effective spin-orbit Hamiltonians. The effective Hamiltonians for the most relevant classes of materials and heterostructures are derived here from realistic electronic band structure descriptions. Most semiconductor device systems are still theoretical concepts, waiting for experimental demonstrations. A review of selected proposed, and a few demonstrated devices is presented, with detailed description of two important classes: magnetic resonant tunnel structures and bipolar magnetic diodes and transistors. In view of the importance of ferromagnetic semiconductor materials, a brief discussion of diluted magnetic semiconductors is included. In most cases the presentation is of tutorial style, introducing the essential theoretical formalism at an accessible level, with case-study-like illustrations of actual experimental results, as well as with brief reviews of relevant recent achievements in the field.

Cubic Dresselhaus spin-orbit coupling in 2D electron quantum dots

We study effects of the oft-neglected cubic Dresselhaus spin-orbit coupling (i.e., directly proportional p3) in GaAs/AlGaAs quantum dots. Using a semiclassical billiard model, we estimate the magnitude of the spin-orbit induced avoided crossings in a closed quantum dot in a Zeeman field. Using previous analyses based on random matrix theory, we calculate corresponding effects on the conductance through an open quantum dot. Combining our results with an experiment on an 8 microm2 quantum dot [D. M. Zumbühl, Phys. Rev. B 72, 081305 (2005)10.1103/PhysRevB.72.081305] suggests that (1) the GaAs Dresselhaus coupling constant gamma is approximately 9 eV A3, significantly less than the commonly cited value of 27.5 eV A3, and (2) the majority of the spin-flip effects can come from the cubic Dresselhaus term.

Theory of phonon-induced spin relaxation in laterally coupled quantum dots

Phonon-induced spin relaxation in coupled lateral quantum dots in the presence of spin-orbit coupling is calculated. The calculation for single dots is consistent with experiment. Spin relaxation in double dots at useful interdot couplings is dominated by spin-hot spots that are strongly anisotropic. Spin-hot spots are ineffective for a diagonal crystallographic orientation of the dots with a transverse in-plane field. This geometry is proposed for spin-based quantum information processing.

Quantum interference of electrons in a ring: tuning of the geometrical phase

We calculate the oscillations of the dc conductance across a mesoscopic ring, simultaneously tuned by applied magnetic and electric fields orthogonal to the ring. The oscillations depend on the Aharonov-Bohm flux and of the spin-orbit coupling. They result from mixing of the dynamical phase, including the Zeeman spin splitting, and of geometric phases. By changing the applied fields, the geometric phase contribution to the conductance oscillations can be tuned from the adiabatic (Berry) to the nonadiabatic (Ahronov-Anandan) regime. To model a realistic device, we also include nonzero backscattering at the connection between ring and contacts, and a random phase for electron wave function, accounting for dephasing effects.

Anisotropy of spin splitting and spin relaxation in lateral quantum dots

Inelastic spin relaxation and spin splitting epsilon(s) in lateral quantum dots are studied in the regime of strong in-plane magnetic field. Because of both the g-factor energy dependence and spin-orbit coupling, epsilon(s) demonstrates a substantial nonlinear magnetic field dependence similar to that observed by Hanson et al. [Phys. Rev. Lett. 91, 196802 (2003)]. It also varies with the in-plane orientation of the magnetic field due to crystalline anisotropy of the spin-orbit coupling. The spin relaxation rate is also anisotropic, the anisotropy increasing with the field. When the magnetic length is less than the "thickness" of the GaAs dot, the relaxation can be an order of magnitude faster for B ||[100] than for B || [110].

Spin relaxation and decoherence of holes in quantum dots

We investigate heavy-hole spin relaxation and decoherence in quantum dots in perpendicular magnetic fields. We show that at low temperatures the spin decoherence time is 2 times longer than the spin relaxation time. We find that the spin relaxation time for heavy holes can be comparable to or even longer than that for electrons in strongly two-dimensional quantum dots. We discuss the difference in the magnetic-field dependence of the spin relaxation rate due to Rashba or Dresselhaus spin-orbit coupling for systems with positive (i.e., GaAs quantum dots) or negative (i.e., InAs quantum dots) g factor.

Spin-orbit coupling and anisotropy of spin splitting in quantum dots

In lateral quantum dots, the combined effect of both Dresselhaus and Bychkov-Rashba spin-orbit coupling is equivalent to an effective magnetic field +/- B(SO) which has the opposite sign for s(z)= +/- 1/2 spin electrons. When the external magnetic field is perpendicular to the planar structure, the field B(SO) generates an additional splitting for electron states as compared to the spin splitting in the in-plane field orientation. The anisotropy of spin splitting has been measured and then analyzed in terms of spin-orbit coupling in several AlGaAs/GaAs quantum dots by means of resonant tunneling spectroscopy. From the measured values and sign of the anisotropy we are able to determine the dominating spin-orbit coupling mechanism.

Zitterbewegung of electronic wave packets in III-V zinc-blende semiconductor quantum wells

We study the zitterbewegung of electronic wave packets in III-V zinc-blende semiconductor quantum wells due to spin-orbit coupling. Our results suggest a direct experimental proof of this fundamental effect, confirming a long-standing theoretical prediction. For electron motion in a harmonic quantum wire, we numerically and analytically find a resonance condition maximizing the zitterbewegung.

Role of orbital dynamics in spin relaxation and weak antilocalization in quantum dots

We develop a semiclassical theory for spin-dependent quantum transport to describe weak (anti)localization in quantum dots with spin-orbit coupling. This allows us to distinguish different types of spin relaxation in systems with chaotic, regular, and diffusive orbital classical dynamics. We find, in particular, that for typical Rashba spin-orbit coupling strengths, integrable ballistic systems can exhibit weak localization, while corresponding chaotic systems show weak antilocalization. We further calculate the magnetoconductance and analyze how the weak antilocalization is suppressed with decreasing quantum dot size and increasing additional in-plane magnetic field.

Spin-Hall effect in two-dimensional electron systems with Rashba spin-orbit coupling and disorder

Using the four-terminal Landauer-Bu ttiker formula and Green's function approach, we calculate numerically the spin-Hall conductance in a two-dimensional junction system with the Rashba spin-orbit (SO) coupling and disorder. We find that the spin-Hall conductance can be much greater or smaller than the universal value e/8pi, depending on the magnitude of the SO coupling, the electron Fermi energy, and the disorder strength. The spin-Hall conductance does not vanish with increasing sample size for a wide range of disorder strength. Our numerical calculation reveals that a nonzero SO coupling can induce electron delocalization for disorder strength smaller than a critical value, and the nonvanishing spin-Hall effect appears mainly in the metallic regime.