Evidence for spin splitting in InxGa

Rashba Spin Splitting in HgCdTe Quantum Wells with Inverted and Normal Band Structures

In quantum wells (QWs) formed in HgCdTe/CdHgTe heterosystems with a variable composition of Cd(Hg), Shubnikov-de-Haas (SdH) oscillations are investigated to characterize the Rashba-type spin-orbit coupling in QWs with both a normal and inverted band structure. Several methods of extracting the Rashba spin-splitting at zero magnetic field and their magnetic field dependences from the beatings of SdH oscillations are used for greater reliability. The large and similar Rashba splitting (25–27 meV) is found for different kinds of spectrum, explained by a significant fraction of the p-type wave functions, in both the E1 subband of the sample with a normal spectrum and the H1 subband for the sample with an inverted one.

Signatures of bosonic Landau levels in a finite-momentum superconductor

Charged particles subjected to magnetic fields form Landau levels (LLs). Originally studied in the context of electrons in metals¹, fermionic LLs continue to attract interest as hosts of exotic electronic phenomena^2,3. Bosonic LLs are also expected to realize novel quantum phenomena^4,5, but, apart from recent advances in synthetic systems^6,7, they remain relatively unexplored. Cooper pairs in superconductors-composite bosons formed by electrons-represent a potential condensed-matter platform for bosonic LLs. Under certain conditions, an applied magnetic field is expected to stabilize an unusual superconductor with finite-momentum Cooper pairs^8,9 and exert control over bosonic LLs^10-13. Here we report thermodynamic signatures, observed by torque magnetometry, of bosonic LL transitions in the layered superconductor Ba₆Nb₁₁S₂₈. By applying an in-plane magnetic field, we observe an abrupt, partial suppression of diamagnetism below the upper critical magnetic field, which is suggestive of an emergent phase within the superconducting state. With increasing out-of-plane magnetic field, we observe a series of sharp modulations in the upper critical magnetic field that are indicative of distinct vortex states and with a structure that agrees with predictions for Cooper pair LL transitions in a finite-momentum superconductor^10-14. By applying Onsager's quantization rule¹⁵, we extract the momentum. Furthermore, study of the fermionic LLs shows evidence for a non-zero Berry phase. This suggests opportunities to study bosonic LLs, topological superconductivity, and their interplay via transport¹⁶, scattering¹⁷, scanning probe¹⁸ and exfoliation techniques¹⁹.

Marginal metallic state at a fractional filling of '8/5' and '4/3' of Landau levels in the GaAs/AlGaAs 2D electron system

A metallic state with a vanishing activation gap, at a filling factor [Formula: see text] in the untilted specimen with [Formula: see text], and at [Formula: see text] at [Formula: see text] under a [Formula: see text] tilted magnetic field, is examined through a microwave photo-excited transport study of the GaAs/AlGaAs 2 dimensional electron system (2DES). The results presented here suggest, remarkably, that at the possible degeneracy point of states with different spin polarization, where the 8/5 or 4/3 FQHE vanish, there occurs a peculiar marginal metallic state that differs qualitatively from a quantum Hall insulating state and the usual quantum Hall metallic state. Such a marginal metallic state occurs most prominently at [Formula: see text], and at [Formula: see text] under tilt as mentioned above, over the interval [Formula: see text], that also includes the [Formula: see text] state, which appears perceptibly gapped in the first instance.

Nonzero Berry phase in quantum oscillations from giant Rashba-type spin splitting in LaTiO3/SrTiO3 heterostructures

The manipulation of the spin degrees of freedom in a solid has been of fundamental and technological interest recently for developing high-speed, low-power computational devices. There has been much work focused on developing highly spin-polarized materials and understanding their behavior when incorporated into so-called spintronic devices. These devices usually require spin splitting with magnetic fields. However, there is another promising strategy to achieve spin splitting using spatial symmetry breaking without the use of a magnetic field, known as Rashba-type splitting. Here we report evidence for a giant Rashba-type splitting at the interface of LaTiO₃ and SrTiO₃. Analysis of the magnetotransport reveals anisotropic magnetoresistance, weak anti-localization and quantum oscillation behavior consistent with a large Rashba-type splitting. It is surprising to find a large Rashba-type splitting in 3d transition metal oxide-based systems such as the LaTiO₃/SrTiO₃ interface, but it is promising for the development of a new kind of oxide-based spintronics.

Rashba-type splitting is an effective way to manipulate the spin degrees of freedom in a solid without external magnetic field. Here, the authors demonstrate a strong Rashba-type splitting at the interface of LaTiO₃ and SrTiO₃ which is promising for the development of oxide-based spintronics.

Electrical and thermoelectric transport properties of two-dimensional fermionic systems with k-cubic spin-orbit coupling

We investigate the effect of k-cubic spin-orbit interaction on the electrical and thermoelectric transport properties of two-dimensional fermionic systems. We obtain exact analytical expressions of the inverse relaxation time (IRT) and the Drude conductivity for long-range Coulomb and short-range delta scattering potentials. The IRT reveals that the scattering is completely suppressed along the three directions [Formula: see text] with [Formula: see text]. We also obtain analytical results of the thermopower and thermal conductivity at low temperature. The thermoelectric transport coefficients obey the Wiedemann-Franz law, even in the presence of k-cubic Rashba spin-orbit interaction (RSOI) at low temperature. In the presence of a quantizing magnetic field, the signature of the RSOI is revealed through the appearance of the beating pattern in the Shubnikov-de Haas (SdH) oscillations of thermopower and thermal conductivity in the low magnetic field regime. The empirical formulae for the SdH oscillation frequencies accurately describe the locations of the beating nodes. The beating pattern in magnetothermoelectric measurement can be used to extract the spin-orbit coupling constant.

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

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

Radiation-induced resistance oscillations in 2D electron systems with strong Rashba coupling

We present a theoretical study on the effect of radiation on the mangetoresistance of two-dimensional electron systems with strong Rashba spint-orbit coupling. We want to study the interplay between two well-known effects in these electron systems: the radiation-induced resistance oscillations and the typical beating pattern of systems with intense Rashba interaction. We analytically derive an exact solution for the electron wave function corresponding to a total Hamiltonian with Rashba and radiation terms. We consider a perturbation treatment for elastic scattering due to charged impurities to finally obtain the magnetoresistance of the system. Without radiation we recover a beating pattern in the amplitude of the Shubnikov de Hass oscillations: a set of nodes and antinodes in the magnetoresistance. In the presence of radiation this beating pattern is strongly modified following the profile of radiation-induced magnetoresistance oscillations. We study their dependence on intensity and frequency of radiation, including the teraherzt regime. The obtained results could be of interest for magnetotransport of nonideal Dirac fermions in 3D topological insulators subjected to radiation.

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.

Giant Spin-Orbit Splitting in Inverted InAs/GaSb Double Quantum Wells

Transport measurements in inverted InAs/GaSb quantum wells reveal a giant spin-orbit splitting of the energy bands close to the hybridization gap. The splitting results from the interplay of electron-hole mixing and spin-orbit coupling, and can exceed the hybridization gap. We experimentally investigate the band splitting as a function of top gate voltage for both electronlike and holelike states. Unlike conventional, noninverted two-dimensional electron gases, the Fermi energy in InAs/GaSb can cross a single spin-resolved band, resulting in full spin-orbit polarization. In the fully polarized regime we observe exotic transport phenomena such as quantum Hall plateaus evolving in e^{2}/h steps and a nontrivial Berry phase.

Optical conductivity of a 2DEG with anisotropic Rashba interaction at the interface of LaAlO3/SrTiO3

We study optical conductivity of a two-dimensional electron gas with anisotropic k-cubic Rashba spin-orbit interaction formed at the LaAlO3/SrTiO3 interface. The anisotropic spin splitting energy gives rise to different features of the optical conductivity in comparison to the isotropic k-cubic Rashba spin-orbit interaction. For large carrier density and strong spin-orbit couplings, the density dependence of Drude weight deviates from the linear behavior. The charge and optical conductivities remain isotropic despite anisotropic nature of the Fermi contours. An infinitesimally small photon energy would suffice to initiate inter-band optical transitions due to degeneracy along certain directions in momentum space. The optical conductivity shows a single peak at a given photon energy depending on the system parameters and then falls off to zero at higher photon energy. These features are lacking for systems with isotropic k-cubic Rashba spin-orbit coupling. These striking features can be used to extract the information about nature of the spin-orbit interaction experimentally and illuminate some light on the orbital origin of the two-dimensional electron gas.

Emergent surface superconductivity in the topological insulator Sb2Te3

Surfaces of three-dimensional topological insulators have emerged as one of the most remarkable states of condensed quantum matter where exotic electronic phases of Dirac particles should arise. Here we report on superconductivity in the topological insulator Sb2Te3 with transition to zero resistance induced through a minor tuning of growth chemistry that depletes bulk conduction channels. The depletion shifts Fermi energy towards the Dirac point as witnessed by a factor of 300 reduction of bulk carrier density and by the largest carrier mobility (≳25,000 cm(2) V(-1) s(-1)) found in any topological material. Direct evidence from transport, the unprecedentedly large diamagnetic screening, and the presence of ∼25 meV gaps detected by scanning tunnelling spectroscopy reveal the superconducting condensate to emerge first in surface puddles, with the onset of global phase coherence at ∼9 K. The rich structure of this state lends itself to manipulation via growth conditions and the material parameters such as Fermi velocity and mean free path.

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.

Beating pattern in quantum magnetotransport coefficients of spin-orbit coupled Dirac fermions in gated silicene

We report a theoretical study of magnetotransport coefficients of spin-orbit coupled gated silicene in the presence and absence of spatial periodic modulation. The combined effect of spin-orbit coupling and perpendicular electric field manifests through the formation of a regular beating pattern in Weiss and SdH oscillations. Analytical results, in addition to the numerical results, of the beating pattern formation are provided. The analytical results yield a beating condition which will be useful to determine the spin-orbit coupling constant by simply counting the number of oscillation between any two successive nodes. Moreover, the numerical results of modulation effect on collisional and Hall conductivities are presented.

Giant collective spin-orbit field in a quantum well: fine structure of spin plasmons

We employ inelastic light scattering with magnetic fields to study intersubband spin plasmons in a quantum well. We demonstrate the existence of a giant collective spin-orbit (SO) field that splits the spin-plasmon spectrum into a triplet. The effect is remarkable as each individual electron would be expected to precess in its own momentum-dependent SO field, leading to D'yakonov-Perel' dephasing. Instead, many-body effects lead to a striking organization of the SO fields at the collective level. The macroscopic spin moment is quantized by a uniform collective SO field, five times higher than the individual SO field. We provide a momentum-space cartography of this field.

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

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

Thermoelectric probe for the Rashba spin-orbit interaction strength in a two dimensional electron gas

The thermoelectric coefficients of a two dimensional electron gas (2DEG) with the Rashba spin-orbit interaction (SOI) are presented here. In the absence of a magnetic field, thermoelectric coefficients are enhanced due to the Rashba SOI. In the presence of a magnetic field, the thermoelectric coefficients of spin-up and spin-down electrons oscillate with different frequencies and produces beating patterns in the components of the total thermoelectric power and the total thermal conductivity. We also provide analytical expressions for the thermoelectric coefficients to explain the formation of the beating pattern. We obtain a simple relation which determines the strength of the Rashba SOI if the magnetic fields corresponding to any two successive beat nodes are known from the experiment.

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

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

Zero-field spin splitting in a two-dimensional electron gas with the spin-orbit interaction revisited

We consider a two-dimensional electron gas (2DEG) with the Rashba spin-orbit interaction (SOI) in the presence of a perpendicular magnetic field. We derive analytical expressions of the density of states (DOS) of a 2DEG with the Rashba SOI in the presence of a magnetic field by using the Green's function technique. The DOS allows us to obtain the analytical expressions of the magnetoconductivities for spin-up and spin-down electrons. The conductivities for spin-up and spin-down electrons oscillate with different frequencies and give rise to the beating patterns in the amplitude of the Shubnikov-de Haas (SdH) oscillations. We find a simple equation which determines the zero-field spin splitting energy if the magnetic field corresponding to any beat node is known from the experiment. Our analytical results reproduce well the experimentally observed non-periodic beating patterns, number of oscillations between two successive nodes and the measured zero-field spin splitting energy.

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.

Suppression of spin relaxation in submicron InGaAs wires

We investigate electron-spin dynamics in narrow two-dimensional n-InGaAs channels as a function of the channel width. The spin relaxation times increase with decreasing channel width, in accordance with recent theoretical predictions based on the dimensionally constrained D'yakonov-Perel' mechanism. Surprisingly, the suppression of the relaxation rate, which is anticipated for the one-dimensional limit, is observed for widths that are an order of magnitude larger than the electron mean free path. We find the spin precession length and the channel width to be the relevant length scales for interpreting these results.

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.

Possible evidence of a spontaneous spin polarization in mesoscopic two-dimensional electron systems

We have experimentally studied the nonequilibrium transport in low-density clean two-dimensional (2D) electron systems at mesoscopic length scales. At zero magnetic field (B), a double-peak structure in the nonlinear conductance was observed close to the Fermi energy in the localized regime. From the behavior of these peaks at nonzero B, we could associate them with the opposite spin states of the system, indicating a spontaneous spin polarization at B=0. Detailed temperature and disorder dependence of the structure shows that such a splitting is a ground-state property of low-density 2D systems.

Two-component interference effect: model of a spin-polarized transport

The effect of spin-involved interaction on the transport properties of disordered two-dimensional electron systems with ferromagnetic contacts is described using a two-component model. Components representing spin-up and spin-down states are supposed to be coupled at a discrete set of points. We have found that due to the additional interference arising in two-component systems the difference between conductances for the parallel and antiparallel orientations of the contact magnetization changes its sign as a function of the length of the conducting channel.

The effect of spin splitting on the metallic behavior of a two-dimensional system

Experiments on a constant-density two-dimensional hole system in a gallium arsenide quantum well revealed that the metallic behavior observed in the zero-magnetic-field temperature dependence of the resistivity depends on the symmetry of the confinement potential and the resulting spin splitting of the valence band.