Weak antilocalization and spin precession in quantum wells

Rashba splitting in polar-nonpolar sandwich heterostructure: a DFT study

In this study, we employ density functional theory based first-principles calculations to investigate the spin-orbit effects in the electronic structure of a polar-nonpolar sandwich heterostructure namelyLaAlO3/SrTiO3/LaAlO3. Our focus on theTi-3dbands reveals an inverted ordering of theSrTiO3-t2gorbital near the n-type interface, which is consistent with earlier experimental work. In contrast, toward the p-type interface, the orbital ordering aligns with the natural ordering ofSrTiO3orbitals, influenced by crystal field splitting. In the presence of SOC, a notable inter-orbital coupling betweent2gandegorbitals is observed within the tetragonal slab, a phenomenon not reported before in theSrTiO3-based 2D systems. Additionally, our observations highlight that the cubic Rashba splitting in this system surpasses the linear Rashba splitting, contrary to experimental findings. This comprehensive analysis contributes to a refined understanding of the role of orbital mixing in Rashba splitting in the sandwich oxide heterostructures.

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.

Weak Antilocalization in Polycrystalline SnTe Films Deposited by Magnetron Sputtering

Previous works on weak antilocalization (WAL) of SnTe were mostly carried out in MBE-grown films, where the signals of WAL usually coexist with a large parabolic background of classical magnetoresistance. In this article, we present our study on WAL in polycrystalline SnTe films deposited by magnetron sputtering. Due to the polycrystalline nature and the relatively low mobility of the films, the background of conventional magnetoresistance was greatly suppressed, and clean WAL signals, which are well described by the Hikami–Larkin–Nagaoka equation, were obtained at low temperatures. A close analysis of the WAL data shows that the number of transport channels contributing to WAL increases monotonously with decreasing temperatures, reaching N=2.8 at T=1.6 K in one of the devices, which indicates the decoupling of Dirac cones at low temperatures. Meanwhile, as the temperature decreases, the temperature dependence of phase coherence length gradually changes from lϕ∼T−1 to lϕ∼T−0.5, suggesting that the dominant mechanism of phase decoherence switches from electron–phonon scattering to electron–electron scattering. Our results are helpful for understanding the quantum transport properties of SnTe.

InSbAs Two-Dimensional Electron Gases as a Platform for Topological Superconductivity

Topological superconductivity can be engineered in semiconductors with strong spin-orbit interaction coupled to a superconductor. Experimental advances in this field have often been triggered by the development of new hybrid material systems. Among these, two-dimensional electron gases (2DEGs) are of particular interest due to their inherent design flexibility and scalability. Here, we discuss results on a 2D platform based on a ternary 2DEG (InSbAs) coupled to in situ grown aluminum. The spin-orbit coupling in these 2DEGs can be tuned with the As concentration, reaching values up to 400 meV Å, thus exceeding typical values measured in its binary constituents. In addition to a large Landé g-factor of ∼55 (comparable to that of InSb), we show that the clean superconductor-semiconductor interface leads to a hard induced superconducting gap. Using this new platform, we demonstrate the basic operation of phase-controllable Josephson junctions, superconducting islands, and quasi-1D systems, prototypical device geometries used to study Majorana zero modes.

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.

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.

Interface-based tuning of Rashba spin-orbit interaction in asymmetric oxide heterostructures with 3d electrons

The Rashba effect plays important roles in emerging quantum materials physics and potential spintronic applications, entailing both the spin orbit interaction (SOI) and broken inversion symmetry. In this work, we devise asymmetric oxide heterostructures of LaAlO₃//SrTiO₃/LaAlO₃ (LAO//STO/LAO) to study the Rashba effect in STO with an initial centrosymmetric structure, and broken inversion symmetry is created by the inequivalent bottom and top interfaces due to their opposite polar discontinuities. Furthermore, we report the observation of a transition from the cubic Rashba effect to the coexistence of linear and cubic Rashba effects in the oxide heterostructures, which is controlled by the filling of Ti orbitals. Such asymmetric oxide heterostructures with initially centrosymmetric materials provide a general strategy for tuning the Rashba SOI in artificial quantum materials.

The two-dimensional electron gases that form at LaAlO₃/SrTiO₃ heterostructure interfaces feature strong spin-orbit interactions, leading to proposed spintronic applications. Lin et al. show that the design of asymmetric heterostructures enables the Rashba spin-orbit interaction to be tuned between two regimes.

Closed-Form Weak Localization Magnetoconductivity in Quantum Wells with Arbitrary Rashba and Dresselhaus Spin-Orbit Interactions

We derive a closed-form expression for the weak localization (WL) corrections to the magnetoconductivity of a 2D electron system with arbitrary Rashba α and Dresselhaus β (linear) and β_{3} (cubic) spin-orbit interaction couplings, in a perpendicular magnetic field geometry. In a system of reference with an in-plane z[over ^] axis chosen as the high spin-symmetry direction at α=β, we formulate a new algorithm to calculate the three independent contributions that lead to WL. The antilocalization is counterbalanced by the term associated with the spin relaxation along z[over ^], dependent only on α-β. The other term is generated by two identical scattering modes characterized by spin-relaxation rates which are explicit functions of the orientation of the scattered momentum. Excellent agreement is found with data from GaAs quantum wells, where, in particular, our theory correctly captures the shift of the minima of the WL curves as a function of α/β. This suggests that the anisotropy of the effective spin-relaxation rates is fundamental to understanding the effect of the spin-orbit coupling in transport.

Quantum contributions to the magnetoconductivity of critically disordered superconducting TiN films

The onset of superconductivity in the presence of disorder is a fundamental problem of condensed matter physics. Here we investigate the magnetoconductance of disordered ([Formula: see text]) superconducting TiN films above the critical temperature T _c. We show that the magnetoconductivity of moderately disordered films with [Formula: see text] is in full agreement with the perturbative theory of quantum contributions to conductivity. We demonstrate that the magnetoconductivity of films with [Formula: see text] is also in agreement with the perturbative theory down to temperatures [Formula: see text]. The quantitative discrepancy between experiment and theory develops only below temperatures [Formula: see text] for films with [Formula: see text]. This discrepancy can be eliminated if we assume steeper temperature dependence of the Larkin's electron-electron attraction strength, [Formula: see text]. The obtained temperature dependence of electron phase breaking time [Formula: see text] is in agreement with theoretical predictions for all samples.

Kondo effect with tunable spin-orbit interaction in LaTiO3/CeTiO3/SrTiO3 heterostructure

We have fabricated epitaxial films of CeTiO₃ (CTO) on (0 0 1) oriented SrTiO₃ (STO) substrates, which exhibit highly insulating and diamagnetic properties. X-ray photoelectron spectroscopy was used to establish the 3+  valence state of the Ce and Ti ions. Furthermore, we have also fabricated δ (CTO) doped LaTiO₃ (LTO)/SrTiO₃ thin films which exhibit variety of interesting properties including Kondo effect and spin-orbit interaction (SOI) at low temperatures. The SOI shows a non-monotonic behaviour as the thickness of the CTO layer is increased and is reflected in the value of characteristic SOI field ([Formula: see text]) obtained from weak anti-localization fitting. The maximum value of [Formula: see text] is 1.00 T for δ layer thickness of 6 u.c. This non-monotonic behaviour of SOI is attributed to the strong screening of the confining potential at the interface. The screening effect is enhanced by the CTO layer thickness and the dielectric constant of STO which increases at low temperatures. Due to the strong screening, electrons confined at the interface are spread deeper into the STO bulk where it starts to populate the Ti [Formula: see text] subbands; consequently the Fermi level crosses over from [Formula: see text] to the [Formula: see text] subbands. At the crossover region of [Formula: see text] where there is orbital mixing, SOI goes through a maximum.

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.

Optical Manipulation of Rashba Spin-Orbit Coupling at SrTiO3-Based Oxide Interfaces

Spin-orbit coupling (SOC) plays a crucial role for spintronics applications. Here we present the first demonstration that the Rashba SOC at the SrTiO₃-based interfaces is highly tunable by photoinduced charge doping, that is, optical gating. Such optical manipulation is nonvolatile after the removal of the illumination in contrast to conventional electrostatic gating and also erasable via a warming-cooling cycle. Moreover, the SOC evolutions tuned by illuminations with different wavelengths at various gate voltages coincide with each other in different doping regions and collectively form an upward-downward trend curve: In response to the increase of conductivity, the SOC strength first increases and then decreases, which can be attributed to the orbital hybridization of Ti 3d subbands. More strikingly, the optical manipulation is effective enough to tune the interferences of Bloch wave functions from constructive to destructive and therefore to realize a transition from weak localization to weak antilocalization. The present findings pave a way toward the exploration of photoinduced nontrivial quantum states and the design of optically controlled spintronic devices.

Spin-relaxation time in materials with broken inversion symmetry and large spin-orbit coupling

We study the spin-relaxation time in materials where a large spin-orbit coupling (SOC) is present which breaks the spatial inversion symmetry. Such a spin-orbit coupling is realized in zincblende structures and heterostructures with a transversal electric field and the spin relaxation is usually described by the so-called D'yakonov-Perel' (DP) mechanism. We combine a Monte Carlo method and diagrammatic calculation based approaches in our study; the former tracks the time evolution of electron spins in a quasiparticle dynamics simulation in the presence of the built-in spin-orbit magnetic fields and the latter builds on the spin-diffusion propagator by Burkov and Balents. Remarkably, we find a parameter free quantitative agreement between the two approaches and it also returns the conventional result of the DP mechanism in the appropriate limit. We discuss the full phase space of spin relaxation as a function of SOC strength, its distribution, and the magnitude of the momentum relaxation rate. This allows us to identify two novel spin-relaxation regimes; where spin relaxation is strongly non-exponential and the spin relaxation equals the momentum relaxation. A compelling analogy between the spin-relaxation theory and the NMR motional narrowing is highlighted.

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.

Control of Spin Helix Symmetry in Semiconductor Quantum Wells by Crystal Orientation

We investigate the possibility of spin-preserving symmetries due to the interplay of Rashba and Dresselhaus spin-orbit coupling in n-doped zinc-blende semiconductor quantum wells of general crystal orientation. It is shown that a conserved spin operator can be realized if and only if at least two growth direction Miller indices agree in modulus. The according spin-orbit field has in general both in-plane and out-of-plane components and is always perpendicular to the shift vector of the corresponding persistent spin helix. We also analyze higher-order effects arising from the Dresselhaus term, and the impact of our results on weak (anti)localization corrections.

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.

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.

Enhanced spin-orbit coupling and charge carrier density suppression in LaAl1-xCrxO3/SrTiO3 hetero-interfaces

We report a gradual suppression of the two-dimensional electron gas (2DEG) at the LaAlO(3)/SrTiO(3) interface on substitution of chromium at the Al sites. The sheet carrier density at the interface (n□) drops monotonically from ∼2.2 × 10(14) cm(-2) to ∼2.5 × 10(13) cm(-2) on replacing ≈60% of the Al sites by Cr and the sheet resistance (R□) exceeds the quantum limit for localization (h/2e(2)) in the concentrating range 40-60% of Cr. The samples with Cr ⩽40% show a distinct minimum (T(m)) in metallic R□(T) whose position shifts to higher temperatures on increasing the substitution. Distinct signatures of Rashba spin-orbit interaction (SOI) induced magnetoresistance (MR) are seen in R□ measured in out of plane field (H⊥) geometry at T ⩽ 8 K. Analysis of these data in the framework of Maekawa-Fukuyama theory allows extraction of the SOI critical field (H(SO)) and time scale (τ(SO)) whose evolution with Cr concentration is similar as with the increasing negative gate voltage in LAO/STO interface. The MR in the temperature range 8 K ⩽ T ⩽ T(m) is quadratic in the field with a +ve sign for H⊥ and -ve sign for H∥. The behaviour of H∥ MR is consistent with Kondo theory which in the present case is renormalized by the strong Rashba SOI at T < 8 K.

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.

Two-dimensional TaSe2 metallic crystals: spin-orbit scattering length and breakdown current density

We have determined the spin-orbit scattering length of two-dimensional layered 2H-TaSe2 metallic crystals by detailed characterization of the weak antilocalization phenomena in this strong spin-orbit interaction material. By fitting the observed magneto-conductivity, the spin-orbit scattering length for 2H-TaSe2 is determined to be 17 nm in the few-layer films. This small spin-orbit scattering length is comparable to that of Pt, which is widely used to study the spin Hall effect, and indicates the potential of TaSe2 for use in spin Hall effect devices. A material must also support large charge currents in addition to strong spin-orbit coupling to achieve spin-transfer-torque via the spin Hall effect. Therefore, we have characterized the room temperature breakdown current density of TaSe2 in air, where the best breakdown current density reaches 3.7 × 10(7) A/cm(2). This large breakdown current further indicates the potential of TaSe2 for use in spin-torque devices and two-dimensional device interconnect applications.

Magneto-transport in MoS2: phase coherence, spin-orbit scattering, and the hall factor

We have characterized phase coherence length, spin-orbit scattering length, and the Hall factor in n-type MoS2 2D crystals via weak localization measurements and Hall-effect measurements. Weak localization measurements reveal a phase coherence length of ~50 nm at T = 400 mK for a few-layer MoS2 film, decreasing as T(-1/2) with increased temperatures. Weak localization measurements also allow us, for the first time without optical techniques, to estimate the spin-orbit scattering length to be 430 nm, pointing to the potential of MoS2 for spintronics applications. Via Hall-effect measurements, we observe a low-temperature Hall mobility of 311 cm(2)/(V s) at T = 1 K, which decreases as a power law with a characteristic exponent γ = 1.5 from 10 to 60 K. At room temperature, we observe Hall mobility of 24 cm(2)/(V s). By determining the Hall factor for MoS2 to be 1.35 at T = 1 K and 2.4 at room temperature, we observe drift mobility of 420 and 56 cm(2)/(V s) at T = 1 K and room temperature, respectively.

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.

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.

Spin relaxation near the metal-insulator transition: dominance of the Dresselhaus spin-orbit coupling

We identify the Dresselhaus spin-orbit coupling as the source of the dominant spin-relaxation mechanism in the impurity band of a wide class of n-doped zinc blende semiconductors. The Dresselhaus hopping terms are derived and incorporated into a tight-binding model of impurity sites, and they are shown to unexpectedly dominate the spin relaxation, leading to spin-relaxation times in good agreement with experimental values. This conclusion is drawn from two complementary approaches: an analytical diffusive-evolution calculation and a numerical finite-size scaling study of the spin-relaxation time.

ANTILOCALIZATION IN GATED 2D QUANTUM WELL STRUCTURES WITH COMPOSITION GRADIENT

Low-field magnetoconductivity caused by the quantum interference is studied in the gated 2D quantum well structures with the composition gradient. It is shown that the Dresselhaus mechanism describes well an antilocalization minimum on the conductivity-magnetic field curve.

Gate-voltage control of chemical potential and weak antilocalization in Bi₂Se₃

We report that Bi₂Se₃ thin films can be epitaxially grown on SrTiO₃ substrates, which allow for very large tunablity in carrier density with a back gate. The observed low field magnetoconductivity due to weak antilocalization (WAL) has a very weak gate-voltage dependence unless the electron density is reduced to very low values. Such a transition in WAL is correlated with unusual changes in longitudinal and Hall resistivities. Our results suggest a much suppressed bulk conductivity at large negative gate voltages and a possible role of surface states in the WAL phenomena.

The fine structure of two-electron states in single and double quantum dots

The energy spectrum fine structure of triplet two-electron states in nanostructures is investigated theoretically. Spin-orbit interaction-induced terms in the effective Hamiltonian of the electron-electron interaction are derived for zinc blende lattice semiconductor systems: quantum wells and quantum dots. The effects of bulk and structural inversion asymmetry are taken into account. Simple analytical expressions describing the splittings of the two-electron states localized in a single quantum dot and in a lateral double quantum dot are derived. The spin degeneracy of triplet states is shown to be completely lifted by the spin-orbit interaction. An interplay of the conduction band spin splitting and the spin-orbit terms in the electron-electron interaction is discussed. The emission spectra of hot trions and of doubly charged excitons are calculated and are shown to reveal the fine structure of two-electron states.

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.

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.

2D ANOMALOUS MAGNETORESISTANCE IN THE PRESENCE OF SPIN–ORBIT SCATTERING

The model of weak localization in 2D semiconductor structures in the whole range of classically weak magnetic fields in the presence of the Elliot–Yafet spin relaxation has been developed. It was shown that the spin–orbit interaction influences the value of magnetoresistance in small magnetic fields (within diffusion approximation) and when diffusion approximation is no longer valid.

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.

Giant spin-orbit bowing in GaAs1-xBix

We report a giant bowing of the spin-orbit splitting energy Delta0 in the dilute GaAs1-xBix alloy for Bi concentrations ranging from 0% to 1.8%. This is the first observation of a large relativistic correction to the host electronic band structure induced by just a few percent of isoelectronic doping in a semiconductor material. It opens up the possibility of tailoring the spin-orbit splitting in semiconductors for spintronic applications.

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.

Ab initio prediction of conduction band spin splitting in zinc blende semiconductors

We use a recently developed self-consistent GW approximation to present systematic ab initio calculations of the conduction band spin splitting in III-V and II-VI zinc blende semiconductors. The spin-orbit interaction is taken into account as a perturbation to the scalar relativistic Hamiltonian. These are the first calculations of conduction band spin splittings based on a quasiparticle approach; and because the self-consistent GW scheme accurately reproduces the relevant band parameters, it is expected to be a reliable predictor of spin splittings. The results are compared to the few available experimental data and a previous calculation based on a model one-particle potential. We also briefly address the widely used k x p parametrization in the context of these results.

Spin relaxation in the presence of electron-electron interactions

The D'yakonov-Perel' spin relaxation induced by the spin-orbit interaction is examined in disordered two-dimensional electron gas. It is shown that, because of the electron-electron interactions, substantially different spin relaxation rates may be observed depending on the technique used to extract them. It is demonstrated that the relaxation rate of a spin population is proportional to the spin-diffusion constant D(s), while the spin-orbit scattering rate controlling the weak-localization corrections is proportional to the diffusion constant D, i.e., the conductivity. The two diffusion constants get strongly renormalized by the electron-electron interactions, but in different ways. As a result, the corresponding relaxation rates are different, with the difference between the two being especially strong near a magnetic instability or near the metal-insulator transition.

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-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.

Hanle effect driven by weak localization

The influence of weak localization on the Hanle effect in a two-dimensional system with a spin-split spectrum is considered. We show that weak localization drastically changes the dependence of a stationary spin polarization S on an external magnetic field B. In particular, the nonanalytic dependence of S on B is predicted for III-V-based quantum wells grown in the [110] direction and for the [100]-grown quantum wells having equal strengths of Dresselhaus and Bychkov-Rashba spin-orbit coupling. It is shown that in a weakly localized regime the components of S are discontinuous at B = 0. At low B, the magnetic field-induced rotation of the stationary polarization is determined by quantum interference effects. This implies that the Hanle effect in such systems is totally driven by weak localization.

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

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

Coherent spin manipulation without magnetic fields in strained semiconductors

A consequence of relativity is that in the presence of an electric field, the spin and momentum states of an electron can be coupled; this is known as spin-orbit coupling. Such an interaction opens a pathway to the manipulation of electron spins within non-magnetic semiconductors, in the absence of applied magnetic fields. This interaction has implications for spin-based quantum information processing and spintronics, forming the basis of various device proposals. For example, the concept of spin field-effect transistors is based on spin precession due to the spin-orbit coupling. Most studies, however, focus on non-spin-selective electrical measurements in quantum structures. Here we report the direct measurement of coherent electron spin precession in zero magnetic field as the electrons drift in response to an applied electric field. We use ultrafast optical techniques to spatiotemporally resolve spin dynamics in strained gallium arsenide and indium gallium arsenide epitaxial layers. Unexpectedly, we observe spin splitting in these simple structures arising from strain in the semiconductor films. The observed effect provides a flexible approach for enabling electrical control over electron spins using strain engineering. Moreover, we exploit this strain-induced field to electrically drive spin resonance with Rabi frequencies of up to approximately 30 MHz.

Orbital mechanisms of electron-spin manipulation by an electric field

A theory of spin manipulation of quasi-two-dimensional (2D) electrons by a time-dependent gate voltage applied to a quantum well is developed. The Dresselhaus and Rashba spin-orbit coupling mechanisms are shown to be rather efficient for this purpose. The spin response to a perpendicular-to-plane electric field is due to a deviation from the strict 2D limit and is controlled by the ratios of the spin, cyclotron, and confinement frequencies. The dependence of this response on the magnetic field direction is indicative of the strengths of the competing spin-orbit coupling mechanisms.

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

In situ control of spin-orbit coupling in coherent transport using a clean GaAs/AlGaAs two-dimensional electron gas is realized, leading to a gate-tunable crossover from weak localization to antilocalization. The necessary theory of 2D magnetotransport in the presence of spin-orbit coupling beyond the diffusive approximation is developed and used to analyze experimental data. With this theory the Rashba contribution and linear and cubic Dresselhaus contributions to spin-orbit coupling are separately estimated, allowing the angular dependence of spin-orbit precession to be extracted at various gate voltages.

Spin-orbit coupling, antilocalization, and parallel magnetic fields in quantum dots

We investigate antilocalization due to spin-orbit coupling in ballistic GaAs quantum dots. Antilocalization that is prominent in large dots is suppressed in small dots, as anticipated theoretically. Parallel magnetic fields suppress both antilocalization and also, at larger fields, weak localization, consistent with random matrix theory results once orbital coupling of the parallel field is included. In situ control of spin-orbit coupling in dots is demonstrated as a gate-controlled crossover from weak localization to antilocalization.

Zero-field satellites of a zero-bias anomaly

Spin-orbit (SO) splitting, +/-omega(SO), of the electron Fermi surface in two-dimensional systems manifests itself in the interaction-induced corrections to the tunneling density of states, nu(epsilon). Namely, in the case of a smooth disorder, it gives rise to the satellites of a zero-bias anomaly at energies epsilon = +/-2 omega(SO). Zeeman splitting, +/-omega(Z), in a weak parallel magnetic field causes a narrow plateau of a width delta epsilon = 2 omega(Z) at the top of each sharp satellite peak. As omega(Z) exceeds omega(SO), the SO satellites cross over to the conventional narrow maxima at epsilon = +/-2 omega(Z) with SO-induced plateaus delta epsilon = 2 omega(SO) at the tops.

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

We have investigated the values of the Rashba spin-orbit coupling constant alpha in In(0.52)Al(0.48)As/In(0.53)Ga(0.47)As/In(0.52)Al(0.48)As quantum wells using the weak antilocalization (WAL) analysis as a function of the structural inversion asymmetry (SIA) of the quantum wells. We have found that the deduced alpha values have a strong correlation with the degree of SIA of the quantum wells as predicted theoretically. The good agreement between the theoretical and experimental values of alpha suggests that our WAL approach for deducing alpha values provides a useful tool in designing future spintronics devices that utilize the Rashba spin-orbit coupling.

Spin-orbit effects in a GaAs quantum dot in a parallel magnetic field

We analyze the effects of spin-orbit coupling on fluctuations of the conductance of a quantum dot fabricated in a GaAs heterostructure. Counterintuitively we argue that spin-orbit effects may become important in the presence of a large parallel magnetic field B( parallel), even if they are negligible for B( parallel) = 0. This should be manifest in the level repulsion of a closed dot, and in reduced conductance fluctuations in dots with a small number of open channels in each lead, for large B( parallel). Our picture is consistent with the experimental observations of Folk et al.

Analysis of the metallic phase of two-dimensional holes in SiGe in terms of temperature dependent screening

We find that temperature dependent screening can quantitatively explain the metallic behavior of the resistivity on the metallic side of the so-called metal-insulator transition in p-SiGe. Interference and interaction effects exhibit the usual insulating behavior which is expected to overpower the metallic background at sufficiently low temperatures. We find empirically that the concept of a Fermi liquid describes our system with its large interaction parameter r(s) approximately 8.