Ideal two-dimensional electron systems with a giant Rashba-type spin splitting in real materials: surfaces of bismuth tellurohalides

Screening of Polar Electron-Phonon Interactions near the Surface of the Rashba Semiconductor BiTeCl

Understanding electron-phonon coupling in noncentrosymmetric materials is critical for controlling the internal fields which give rise to Rashba interactions. We apply time- and angle-resolved photoemission spectroscopy (trARPES) to study coherent phonons in the surface and bulk regions of the polar semiconductor BiTeCl. Aided by ab initio calculations, our measurements reveal the coupling of out-of-plane A_{1} modes and an in-plane E_{2} mode. By considering how these modes modulate the electric dipole moment in each unit cell, we show that the polar A_{1} modes are more effectively screened in the metallic surface region, while the nonpolar E_{2} mode couples in both regions. In addition to informing strategies to optically manipulate Rashba interactions, this Letter has broader implications for the behavior of electron-phonon coupling in systems characterized by inhomogeneous dielectric environments.

Strong Sliding Ferroelectricity and Interlayer Sliding Controllable Spintronic Effect in Two-Dimensional HgI2 Layers

Exploration of two-dimensional (2D) sliding ferroelectric (FE) materials with experimentally detectable ferroelectricity and value-added novel functionalities is highly sought for the development of 2D "slidetronics". Herein, based on first-principles calculations, we identify the synthesizable van der Waals (vdW) layered crystals HgX2 (X = Br and I) as a new class of 2D sliding ferroelectrics. Both HgBr2 and HgI2 in 2D multilayered forms adopt the preferential stacking sequence, leading to room temperature stable out-of-plane (vertical) ferroelectricity that can be reversed via the sliding of adjacent monolayers. Owing to strong interlayer coupling and interfacial charge rearrangement, 2D HgI2 layers possess strong sliding ferroelectricity up to 0.16 μC/cm2, readily detectable in experiment. Moreover, robust sliding ferroelectricity and interlayer sliding controllable Rashba spin texture of FE-HgI2 layers enable potential applications as 2D spintronic devices such that the electric control of electron spin detection can be realized at the 2D regime.

Nonlinear transport and radio frequency rectification in BiTeBr at room temperature

Materials showing second-order nonlinear transport under time reversal symmetry can be used for Radio Frequency (RF) rectification, but practical application demands room temperature operation and sensitivity to microwatts level RF signals in the ambient. In this study, we demonstrate that BiTeBr exhibits a giant nonlinear response which persists up to 350 K. Through scaling and symmetry analysis, we show that skew scattering is the dominant mechanism. Additionally, the sign of the nonlinear response can be electrically switched by tuning the Fermi energy. Theoretical analysis suggests that the large Rashba spin-orbit interactions (SOI), which gives rise to the chirality of the Bloch electrons, provide the microscopic origin of the observed nonlinear response. Our BiTeBr rectifier is capable of rectifying radiation within the frequency range of 0.2 to 6 gigahertz at room temperature, even at extremely low power levels of -15 dBm, and without the need for external biasing. Our work highlights that materials exhibiting large Rashba SOI have the potential to exhibit nonlinear responses at room temperature, making them promising candidates for harvesting high-frequency and low-power ambient electromagnetic energy.

Advantages of Ferroelectrics as a Component of Heterostructures for Electronic Purposes: A DFT Insight

The main advantage of using ferroelectric materials as a component of complex heterostructures is the ability to tune various properties of the whole system by means of an external electric field. In particular, the electric field may change the polarization direction within the ferroelectric material and consequently affect the structural properties, which in turn affects the electronic and magnetic properties of the neighboring material. In addition, ferroelectrics allow the electrostriction phenomenon to proceed, which is promising and can be used to affect the magnetic states of the interface state in the heterostructure through a magnetic component. The interfacial phenomena are of great interest, as they provide extended functionality useful for next-generation electronic devices. Following the idea of utilizing ferroelectrics in heterostructural components in the present works, we consider 2DEG, the Rashba effect, the effect of magnetoelectric coupling, and magnetostriction in order to emphasize the advantages of such heterostructures as components of devices. For this purpose, model systems of LaMnO3/BaTiO3, La2CuO4/BaTiO3, Bi/BaTiO3, and Bi/PbTiO3, Fe/BaTiO3 heterostructures are investigated using density functional theory calculations.

Liquid-Phase Exfoliation of Bismuth Telluride Iodide (BiTeI): Structural and Optical Properties of Single-/Few-Layer Flakes

Bismuth telluride halides (BiTeX) are Rashba-type crystals with several potential applications ranging from spintronics and nonlinear optics to energy. Their layered structures and low cleavage energies allow their production in a two-dimensional form, opening the path to miniaturized device concepts. The possibility to exfoliate bulk BiTeX crystals in the liquid represents a useful tool to formulate a large variety of functional inks for large-scale and cost-effective device manufacturing. Nevertheless, the exfoliation of BiTeI by means of mechanical and electrochemical exfoliation proved to be challenging. In this work, we report the first ultrasonication-assisted liquid-phase exfoliation (LPE) of BiTeI crystals. By screening solvents with different surface tension and Hildebrandt parameters, we maximize the exfoliation efficiency by minimizing the Gibbs free energy of the mixture solvent/BiTeI crystal. The most effective solvents for the BiTeI exfoliation have a surface tension close to 28 mN m^-1 and a Hildebrandt parameter between 19 and 25 MPa^0.5. The morphological, structural, and chemical properties of the LPE-produced single-/few-layer BiTeI flakes (average thickness of ∼3 nm) are evaluated through microscopic and optical characterizations, confirming their crystallinity. Second-harmonic generation measurements confirm the non-centrosymmetric structure of both bulk and exfoliated materials, revealing a large nonlinear optical response of BiTeI flakes due to the presence of strong quantum confinement effects and the absence of typical phase-matching requirements encountered in bulk nonlinear crystals. We estimated a second-order nonlinearity at 0.8 eV of |χ⁽²⁾| ∼ 1 nm V^-1, which is 10 times larger than in bulk BiTeI crystals and is of the same order of magnitude as in other semiconducting monolayers (e.g., MoS₂).

Hot carrier dynamics of BiTeI with large Rashba spin splitting

We present a time-resolved ultrafast optical spectroscopy study on BiTeI, a noncentrosymmetric semiconductor with large spin–orbit splitting.

Non-monotonic variation of the Kramers point band gap with increasing magnetic doping in BiTeI

Polar Rashba-type semiconductor BiTeI doped with magnetic elements constitutes one of the most promising platforms for the future development of spintronics and quantum computing thanks to the combination of strong spin-orbit coupling and internal ferromagnetic ordering. The latter originates from magnetic impurities and is able to open an energy gap at the Kramers point (KP gap) of the Rashba bands. In the current work using angle-resolved photoemission spectroscopy (ARPES) we show that the KP gap depends non-monotonically on the doping level in case of V-doped BiTeI. We observe that the gap increases with V concentration until it reaches 3% and then starts to mitigate. Moreover, we find that the saturation magnetisation of samples under applied magnetic field studied by superconducting quantum interference device (SQUID) magnetometer has a similar behaviour with the doping level. Theoretical analysis shows that the non-monotonic behavior can be explained by the increase of antiferromagnetic coupled atoms of magnetic impurity above a certain doping level. This leads to the reduction of the total magnetic moment in the domains and thus to the mitigation of the KP gap as observed in the experiment. These findings provide further insight in the creation of internal magnetic ordering and consequent KP gap opening in magnetically-doped Rashba-type semiconductors.

Berry curvature induced magnetotransport in 3D noncentrosymmetric metals

We study the magnetoelectric and magnetothermal transport properties of noncentrosymmetric metals using semiclassical Boltzmann transport formalism by incorporating the effects of Berry curvature (BC) and orbital magnetic moment (OMM). These effects impart quadratic-Bdependence to the magnetoelectric and magnetothermal conductivities, leading to intriguing phenomena such as planar Hall effect, negative magnetoresistance (MR), planar Nernst effect and negative Seebeck effect. The transport coefficients associated with these effects show the usual oscillatory behavior with respect to the angle between the applied electric field and magnetic field. The bands of noncentrosymmetric metals are split by Rashba spin-orbit coupling except at a band touching point (BTP). For Fermi energy below (above) the BTP, giant (diminished) negative MR is observed. This difference in the nature of MR is related to the magnitudes of the velocities, BC and OMM on the respective Fermi surfaces, where the OMM plays the dominant role. The absolute MR and planar Hall conductivity show a decreasing (increasing) trend with Rashba coupling parameter for Fermi energy below (above) the BTP.

Prediction of giant and ideal Rashba-type splitting in ordered alloy monolayers grown on a polar surface

A large and ideal Rashba-type spin-orbit splitting is desired for the applications of materials in spintronic devices and the detection of Majorana fermions in solids. Here, we propose an approach to achieve giant and ideal spin-orbit splittings through a combination of ordered surface alloying and interface engineering, that is, growing alloy monolayers on an insulating polar surface. We illustrate this unique strategy by means of first-principle calculations of buckled hexagonal monolayers of SbBi and PbBi supported on Al₂O₃(0001). Both systems display ideal Rashba-type states with giant spin-orbit splittings, characterized with energy offsets over 600 meV and momentum offsets over 0.3 Å⁻¹, respectively. Our study thus points to an effective way of tuning spin-orbit splitting in low-dimensional materials to draw immediate experimental interest.

Quantum spin Hall insulators and topological Rashba-splitting edge states in two-dimensional CX3 (X = Sb, Bi)

Two-dimensional topological materials attracted intense interest in condensed matter physics due to their topologically protected edge states and potential applications in electronic devices. Here, based on first-principles calculations, we found that a two-dimensional CX3 (X = Sb, Bi) monolayer is a quantum spin Hall insulator with a large band gap. With the strong spin-orbit coupling effect, CX3 exhibits noticeable bulk band gaps up to 470 meV, sufficiently large for realizing the quantum spin Hall effect at room temperature. The topological characteristic is confirmed by the Z2 invariant since the system preserves time-reversal symmetry. Particularly, the CSb3 monolayer displays unique topologically entangled Rashba-splitting edge states, resembling nearly free-electron quadratic dispersion. Such topologically entangled Rashba-like edge states derive from the spin-orbit coupling effect and inversion symmetry breaking on the edges. Moreover, we demonstrate that the topological properties are perfectly preserved in the CX3 monolayer even with a h-BN substrate. The nontrivial quantum spin Hall state in the CX3 monolayer will provide possibilities for studying a novel phenomenon of edge states and potential applications in low-dissipation electronic devices.

Epitaxial Synthesis of Highly Oriented 2D Janus Rashba Semiconductor BiTeCl and BiTeBr Layers

The family of layered BiTeX (X = Cl, Br, I) compounds are intrinsic Janus semiconductors with giant Rashba-splitting and many exotic surface and bulk physical properties. To date, studies on these materials required mechanical exfoliation from bulk crystals which yielded thick sheets in nonscalable sizes. Here, we report epitaxial synthesis of Janus BiTeCl and BiTeBr sheets through a nanoconversion technique that can produce few triple layers of Rashba semiconductors (<10 nm) on sapphire substrates. The process starts with van der Waals epitaxy of Bi₂Te₃ sheets on sapphire and converts these sheets to BiTeCl or BiTeBr layers at high temperatures in the presence of chemically reactive BiCl₃/BiBr₃ inorganic vapor. Systematic Raman, XRD, SEM, EDX, and other studies show that highly crystalline BiTeCl and BiTeBr sheets can be produced on demand. Atomic level growth mechanism is also proposed and discussed to offer further insights into growth process steps. Overall, this work marks the direct deposition of 2D Janus Rashba materials and offers pathways to synthesize other Janus compounds belonging to MXY family members.

Orbital-Driven Rashba Effect in a Binary Honeycomb Monolayer AgTe

The Rashba effect is fundamental to the physics of two-dimensional electron systems and underlies a variety of spintronic phenomena. It has been proposed that the formation of Rashba-type spin splittings originates microscopically from the existence of orbital angular momentum (OAM) in the Bloch wave functions. Here, we present detailed experimental evidence for this OAM-based origin of the Rashba effect by angle-resolved photoemission (ARPES) and two-photon photoemission experiments for a monolayer AgTe on Ag(111). Using quantitative low-energy electron diffraction analysis, we determine the structural parameters and the stacking of the honeycomb overlayer with picometer precision. Based on an orbital-symmetry analysis in ARPES and supported by first-principles calculations, we unequivocally relate the presence and absence of Rashba-type spin splittings in different bands of AgTe to the existence of OAM.

Rashba-like spin splitting along three momentum directions in trigonal layered PtBi2

Spin-orbit coupling (SOC) has gained much attention for its rich physical phenomena and highly promising applications in spintronic devices. The Rashba-type SOC in systems with inversion symmetry breaking is particularly attractive for spintronics applications since it allows for flexible manipulation of spin current by external electric fields. Here, we report the discovery of a giant anisotropic Rashba-like spin splitting along three momentum directions (3D Rashba-like spin splitting) with a helical spin polarization around the M points in the Brillouin zone of trigonal layered PtBi₂. Due to its inversion asymmetry and reduced symmetry at the M point, Rashba-type as well as Dresselhaus-type SOC cooperatively yield a 3D spin splitting with α_R ≈ 4.36 eV Å in PtBi₂. The experimental realization of 3D Rashba-like spin splitting not only has fundamental interests but also paves the way to the future exploration of a new class of material with unprecedented functionalities for spintronics applications.

Rashba type spin splitting – relevant for spintronics applications - is driven by inversion symmetry breaking but could so far not be realized in all momentum directions in a crystal. Here, the authors report on PtBi₂ that exhibits Rashba spin splitting in all three momentum directions.

Spin-orbit split two-dimensional states of BiTeI/Au(1 1 1) interfaces

We present an ab initio study of interfaces formed by placing a single trilayer of BiTeI on the Au(1 1 1) surface. We consider two possible interfaces with the parallel and antiparallel orientation of the trilayer dipole moment with respect to the surface normal, i.e. Te-Bi-I/Au(1 1 1) and I-Bi-Te/Au(1 1 1). We show that the resulting interface state that originates from the modified spin-orbit split surface state of the clean Au(1 1 1) surface resides at high energy above the Fermi level and acquires a large spin-splitting and reversal helicity as compared with the original surface state. The former lowest conduction state of the trilayer, which is one of the hitherto known giant Rashba spin-split states of few-atomic-layer structures, becomes partly occupied. In the I-Bi-Te/Au(1 1 1) interface, this state represents a Rashba system with strong spin-orbit interaction, where the outer branch of the spin-split state is mostly populated.

Ubiquitous Spin-Orbit Coupling in a Screw Dislocation with High Spin Coherency

We theoretically demonstrate that screw dislocation (SD), a 1D topological defect widely present in semiconductors, exhibits ubiquitously a new form of spin-orbit coupling (SOC) effect. Differing from the widely known conventional 2D Rashba-Dresselhaus (RD) SOC effect that typically exists at surfaces or interfaces, the deep-level nature of SD-SOC states in semiconductors readily makes it an ideal SOC. Remarkably, the spin texture of 1D SD-SOC, pertaining to the inherent symmetry of SD, exhibits a significantly higher degree of spin coherency than the 2D RD-SOC. Moreover, the 1D SD-SOC can be tuned by ionicity in compound semiconductors to ideally suppress spin relaxation, as demonstrated by comparative first-principles calculations of SDs in Si/Ge, GaAs, and SiC. Our findings therefore open a new door to manipulating spin transport in semiconductors by taking advantage of an otherwise detrimental topological defect.

Inherent orbital spin textures in Rashba effect and their implications in spin-orbitronics

The Rashba effect gives rise to the key feature of chiral spin texture. Recently it was demonstrated that the orbital angular momentum (OAM) texture forms the underlying basis for Rashba spin texture. Here we solve a model Hamiltonian of a generic p-orbital system in the presence of crystal field, internal spin-orbit coupling (SOC) and inversion symmetry breaking (ISB), and demonstrate, in addition to OAM and spin texture, the existence of orbital projection (OP) of the spin texture in a general Rashba system. The unique form of the OP pattern follows from the same condition for the existence of chirality of the spin texture. From the analytical results, we obtained the spin polarization as a function of parameters such as the SOC strength, crystal field splitting and degree of ISB, and compare them with those from numerical solutions and ab initio calculations. All three methods yield highly consistent results. Our results suggest means of external modulation, and elucidate the multi-orbital nature of the Rashba effect and the underlying OP of the spin texture. The understanding has potential applications in fields such as spin-orbitronics that requires delicate control between orbital occupancy and spin momentum.

Chemically driven surface effects in polar intermetallic topological insulators A3Bi

Surface electronic spectra, surface and bulk properties as well as the underlying chemical bonding characteristics in topological insulators with complex bonding patterns are considered for the example of cubic, polar intermetallics KNa₂Bi, K₃Bi and Rb₃Bi (with the general formula A₃Bi, A – alkali metal).

Covariant Conservation Laws and the Spin Hall Effect in Dirac-Rashba Systems

We present a theoretical analysis of two-dimensional Dirac-Rashba systems in the presence of disorder and external perturbations. We unveil a set of exact symmetry relations (Ward identities) that impose strong constraints on the spin dynamics of Dirac fermions subject to proximity-induced interactions. This allows us to demonstrate that an arbitrary dilute concentration of scalar impurities results in the total suppression of nonequilibrium spin Hall currents when only Rashba spin-orbit coupling is present. Remarkably, a finite spin Hall conductivity is restored when the minimal Dirac-Rashba model is supplemented with a spin-valley interaction. The Ward identities provide a systematic way to predict the emergence of the spin Hall effect in a wider class of Dirac-Rashba systems of experimental relevance and represent an important benchmark for testing the validity of numerical methodologies.

Bulk Rashba Semiconductors and Related Quantum Phenomena

Bithmuth tellurohalides BiTeX (X = Cl, Br and I) are model examples of bulk Rashba semiconductors, exhibiting a giant Rashba-type spin splitting among their both valence and conduction bands. Extensive spectroscopic and transport experiments combined with the state-of-the-art first-principles calculations have revealed many unique quantum phenomena emerging from the bulk Rashba effect in these systems. The novel features such as the exotic inter- and intra-band optical transitions, enhanced magneto-optical response, divergent orbital dia-/para-magnetic susceptibility and helical spin textures with a nontrivial Berry's phase in the momentum space are among the salient discoveries, all arising from this effect. Also, it is theoretically proposed and indications have been experimentally reported that bulk Rashba semiconductors such as BiTeI have the capability of becoming a topological insulator under the application of a hydrostatic pressure. Here, we overview these studies and show that BiTeX are an ideal platform to explore the next aspects of quantum matter, which could ultimately be utilized to create spintronic devices with novel functionalities.

Giant Magnetic Band Gap in the Rashba-Split Surface State of Vanadium-Doped BiTeI: A Combined Photoemission and Ab Initio Study

One of the most promising platforms for spintronics and topological quantum computation is the two-dimensional electron gas (2DEG) with strong spin-orbit interaction and out-of-plane ferromagnetism. In proximity to an s-wave superconductor, such 2DEG may be driven into a topologically non-trivial superconducting phase, predicted to support zero-energy Majorana fermion modes. Using angle-resolved photoemission spectroscopy and ab initio calculations, we study the 2DEG at the surface of the vanadium-doped polar semiconductor with a giant Rashba-type splitting, BiTeI. We show that the vanadium-induced magnetization in the 2DEG breaks time-reversal symmetry, lifting Kramers degeneracy of the Rashba-split surface state at the Brillouin zone center via formation of a huge gap of about 90 meV. As a result, the constant energy contour inside the gap consists of only one circle with spin-momentum locking. These findings reveal a great potential of the magnetically-doped semiconductors with a giant Rashba-type splitting for realization of novel states of matter.

Orbital angular momentum analysis for giant spin splitting in solids and nanostructures

Giant spin splitting (GSS) of electronic bands, which is several orders of magnitude greater than the standard Rashba effect has been observed in various systems including noble-metal surfaces and thin films of transition-metal dichalcogenides. Previous studies reported that orbital angular momentum (OAM) is not quenched in some GSS materials and that the atomic spin-orbit interaction (SOI) generates spin splitting in some solid states via the interorbital hopping. Although the unquenched OAM may be closely related to the interorbital hopping, their relationship is hardly studied in the aspect of using the unquenched OAM as a control parameter of GSS. Here, we analyze OAM in GSS materials by using the interorbital-hopping mechanism and first-principles calculations. We report that the interatomic hopping between different-parity orbitals, which is generated by specific broken mirror symmetry, produces k-dependent OAM, resulting in valley-dependent GSS in WSe₂ monolayer, Rashba-type GSS in Au (111) surface, and Dresselhaus-type GSS in bulk HgTe. We also demonstrate systematic control of OAM by pressure, external fields, and substrates, thereby controlling the spin splitting, and discuss the temperature dependence of OAM. Our results provide a simplified picture for systematic design and control of GSS materials.

Quantum spin Hall insulators in centrosymmetric thin films composed from topologically trivial BiTeI trilayers

The quantum spin Hall insulators predicted ten years ago and now experimentally observed are instrumental for a break- through in nanoelectronics due to non-dissipative spin-polarized electron transport through their edges. For this transport to persist at normal conditions, the insulators should possess a sufficiently large band gap in a stable topological phase. Here, we theoretically show that quantum spin Hall insulators can be realized in ultra-thin films constructed from a trivial band insulator with strong spin-orbit coupling. The thinnest film with an inverted gap large enough for practical applications is a centrosymmetric sextuple layer built out of two inversely stacked non-centrosymmetric BiTeI trilayers. This nontrivial sextuple layer turns out to be the structure element of an artificially designed strong three-dimensional topological insulator Bi2Te2I2. We reveal general principles of how a topological insulator can be composed from the structure elements of the BiTeX family (X = I, Br, Cl), which opens new perspectives towards engineering of topological phases.

Spin Orientation of Two-Dimensional Electrons Driven by Temperature-Tunable Competition of Spin-Orbit and Exchange-Magnetic Interactions

Finding ways to create and control the spin-dependent properties of two-dimensional electron states (2DESs) is a major challenge for the elaboration of novel spin-based devices. Spin-orbit and exchange-magnetic interactions (SOI and EMI) are two fundamental mechanisms that enable access to the tunability of spin-dependent properties of carriers. The silicon surface of HoRh₂Si₂ appears to be a unique model system, where concurrent SOI and EMI can be visualized and controlled by varying the temperature. The beauty and simplicity of this system lie in the 4f moments, which act as a multiple tuning instrument on the 2DESs, as the 4f projections parallel and perpendicular to the surface order at essentially different temperatures. Here we show that the SOI locks the spins of the 2DESs exclusively in the surface plane when the 4f moments are disordered: the Rashba-Bychkov effect. When the temperature is gradually lowered and the system experiences magnetic order, the rising EMI progressively competes with the SOI leading to a fundamental change in the spin-dependent properties of the 2DESs. The spins rotate and reorient toward the out-of-plane Ho 4f moments. Our findings show that the direction of the spins and the spin-splitting of the two-dimensional electrons at the surface can be manipulated in a controlled way by using only one parameter: the temperature.

Topological Phases in InAs_{1-x}Sb_{x}: From Novel Topological Semimetal to Majorana Wire

Superconductor proximitized one-dimensional semiconductor nanowires with strong spin-orbit interaction (SOI) are, at this time, the most promising candidates for the realization of topological quantum information processing. In current experiments the SOI originates predominantly from extrinsic fields, induced by finite size effects and applied gate voltages. The dependence of the topological transition in these devices on microscopic details makes scaling to a large number of devices difficult unless a material with dominant intrinsic bulk SOI is used. Here, we show that wires made of certain ordered alloys InAs_{1-x}Sb_{x} have spin splittings up to 20 times larger than those reached in pristine InSb wires. In particular, we show this for a stable ordered CuPt structure at x=0.5, which has an inverted band ordering and realizes a novel type of a topological semimetal with triple degeneracy points in the bulk spectrum that produce topological surface Fermi arcs. Experimentally achievable strains can either drive this compound into a topological insulator phase or restore the normal band ordering, making the CuPt-ordered InAs_{0.5}Sb_{0.5} a semiconductor with a large intrinsic linear in k bulk spin splitting.

Intertwined Rashba, Dirac, and Weyl Fermions in Hexagonal Hyperferroelectrics

By means of density functional theory based calculations, we study the role of spin-orbit coupling in the new family of ABC hyperferroelectrics [Garrity, Rabe, and Vanderbilt Phys. Rev. Lett. 112, 127601 (2014)]. We unveil an extremely rich physics strongly linked to ferroelectric properties, ranging from the electric control of bulk Rashba effect to the existence of a three-dimensional topological insulator phase, with concomitant topological surface states even in the ultrathin film limit. Moreover, we predict that the topological transition, as induced by alloying, is followed by a Weyl semimetal phase of finite concentration extension, which is robust against disorder, putting forward hyperferroelectrics as promising candidates for spin-orbitronic applications.

Semiclassical magnetotransport in strongly spin-orbit coupled Rashba two-dimensional electron systems

Semiclassical magnetoelectric and magnetothermoelectric transport in strongly spin-orbit coupled Rashba two-dimensional electron systems is investigated. In the presence of a perpendicular classically weak magnetic field and short-range impurity scattering, we solve the linearized Boltzmann equation self-consistently. Using the solution, it is found that when Fermi energy E F locates below the band crossing point (BCP), the Hall coefficient is a nonmonotonic function of electron density n e and not inversely proportional to n e. While the magnetoresistance (MR) and Nernst coefficient vanish when E F locates above the BCP, non-zero MR and enhanced Nernst coefficient emerge when E F decreases below the BCP. Both of them are nonmonotonic functions of E F below the BCP. The different semiclassical magnetotransport behaviors between the two sides of the BCP can be helpful to experimental identifications of the band valley regime and topological change of Fermi surface in considered systems.

Spin-texture inversion in the giant Rashba semiconductor BiTeI

Semiconductors with strong spin-orbit interaction as the underlying mechanism for the generation of spin-polarized electrons are showing potential for applications in spintronic devices. Unveiling the full spin texture in momentum space for such materials and its relation to the microscopic structure of the electronic wave functions is experimentally challenging and yet essential for exploiting spin-orbit effects for spin manipulation. Here we employ a state-of-the-art photoelectron momentum microscope with a multichannel spin filter to directly image the spin texture of the layered polar semiconductor BiTeI within the full two-dimensional momentum plane. Our experimental results, supported by relativistic ab initio calculations, demonstrate that the valence and conduction band electrons in BiTeI have spin textures of opposite chirality and of pronounced orbital dependence beyond the standard Rashba model, the latter giving rise to strong optical selection-rule effects on the photoelectron spin polarization. These observations open avenues for spin-texture manipulation by atomic-layer and charge carrier control in polar semiconductors.

Unconventional dc Transport in Rashba Electron Gases

We discuss the transport properties of a disordered two-dimensional electron gas with strong Rashba spin-orbit coupling. We show that in the high-density regime where the Fermi energy overcomes the energy associated with spin-orbit coupling, dc transport is accurately described by a standard Drude's law, due to a nontrivial compensation between the suppression of backscattering and the relativistic correction to the quasiparticle velocity. On the contrary, when the system enters the opposite dominant spin-orbit regime, Drude's paradigm breaks down and the dc conductivity becomes strongly sensitive to the spin-orbit coupling strength, providing a suitable tool to test the entanglement between spin and charge degrees of freedom in these systems.

Multiple Coexisting Dirac Surface States in Three-Dimensional Topological Insulator PbBi₆Te₁₀

By means of angle-resolved photoemission spectroscopy (ARPES) measurements, we unveil the electronic band structure of three-dimensional PbBi6Te10 topological insulator. ARPES investigations evidence multiple coexisting Dirac surface states at the zone-center of the reciprocal space, displaying distinct electronic band dispersion, different constant energy contours, and Dirac point energies. We also provide evidence of Rashba-like split states close to the Fermi level, and deeper M- and V-shaped bands coexisting with the topological surface states. The experimental findings are in agreement with scanning tunneling microscopy measurements revealing different surface terminations according to the crystal structure of PbBi6Te10. Our experimental results are supported by density functional theory calculations predicting multiple topological surface states according to different surface cleavage planes.

Enhanced thermoelectric performance in the Rashba semiconductor BiTeI through band gap engineering

Rashba semiconductors are of great interest in spintronics, superconducting electronics and thermoelectrics. Bulk BiTeI is a new Rashba system with a giant spin-split band structure. 2D-like thermoelectric response has been found in BiTeI. However, as optimizing the carrier concentration, the bipolar effect occurs at elevated temperature and deteriorates the thermoelectric performance of BiTeI. In this paper, band gap engineering in Rashba semiconductor BiTeI through Br-substitution successfully reduces the bipolar effect and improves the thermoelectric properties. By utilizing the optical absorption and Burstein-Moss-effect analysis, we find that the band gap in Rashba semiconductor BiTeI increases upon bromine substitution, which is consistent with theoretical predictions. Bipolar transport is mitigated due to the larger band gap, as the thermally-activated minority carriers diminish. Consequently, the Seebeck coefficient keeps increasing with a corresponding rise in temperature, and thermoelectric performance can thus be enhanced with a ZT  =  0.5 at 570 K for BiTeI0.88Br0.12.

Mirror-symmetry protected non-TRIM surface state in the weak topological insulator Bi2TeI

Strong topological insulators (TIs) support topological surfaces states on any crystal surface. In contrast, a weak, time-reversal-symmetry-driven TI with at least one non-zero v₁, v₂, v₃ ℤ₂ index should host spin-locked topological surface states on the surfaces that are not parallel to the crystal plane with Miller indices (v₁ v₂ v₃). On the other hand, mirror symmetry can protect an even number of topological states on the surfaces that are perpendicular to a mirror plane. Various symmetries in a bulk material with a band inversion can independently preordain distinct crystal planes for realization of topological states. Here we demonstrate the first instance of coexistence of both phenomena in the weak 3D TI Bi₂TeI which (v₁ v₂ v₃) surface hosts a gapless spin-split surface state protected by the crystal mirror-symmetry. The observed topological state has an even number of crossing points in the directions of the 2D Brillouin zone due to a non-TRIM bulk-band inversion. Our findings shed light on hitherto uncharted features of the electronic structure of weak topological insulators and open up new vistas for applications of these materials in spintronics.

Formation of Ideal Rashba States on Layered Semiconductor Surfaces Steered by Strain Engineering

Spin splitting of Rashba states in two-dimensional electron system provides a promising mechanism of spin manipulation for spintronics applications. However, Rashba states realized experimentally to date are often outnumbered by spin-degenerated substrate states at the same energy range, hindering their practical applications. Here, by density functional theory calculation, we show that Au one monolayer film deposition on a layered semiconductor surface β-InSe(0001) can possess "ideal" Rashba states with large spin splitting, which are completely situated inside the large band gap of the substrate. The position of the Rashba bands can be tuned over a wide range with respect to the substrate band edges by experimentally accessible strain. Furthermore, our nonequilibrium Green's function transport calculation shows that this system may give rise to the long-sought strong current modulation when made into a device of Datta-Das transistor. Similar systems may be identified with other metal ultrathin films and layered semiconductor substrates to realize ideal Rashba states.

Rashba and Dresselhaus Effects in Hybrid Organic-Inorganic Perovskites: From Basics to Devices

We use symmetry analysis, density functional theory calculations, and k·p modeling to scrutinize Rashba and Dresselhaus effects in hybrid organic-inorganic halide perovskites. These perovskites are at the center of a recent revolution in the field of photovoltaics but have also demonstrated potential for optoelectronic applications such as transistors and light emitters. Due to a large spin-orbit coupling of the most frequently used metals, they are also predicted to offer a promising avenue for spin-based applications. With an in-depth inspection of the electronic structures and bulk lattice symmetries of a variety of systems, we analyze the origin of the spin splitting in two- and three-dimensional hybrid perovskites. It is shown that low-dimensional nanostructures made of CH3NH3PbX3 (X = I, Br) lead to spin splittings that can be controlled by an applied electric field. These findings further open the door for a perovskite-based spintronics.

Spin-orbit coupling at surfaces and 2D materials

Spin-orbit interaction gives rise to a splitting of surface states via the Rashba effect, and in topological insulators it leads to the existence of topological surface states. The resulting k(//) momentum separation between states with the opposite spin underlies a wide range of new phenomena at surfaces and interfaces, such as spin transfer, spin accumulation, spin-to-charge current conversion, which are interesting for fundamental science and may become the basis for a breakthrough in the spintronic technology. The present review summarizes recent theoretical and experimental efforts to reveal the microscopic structure and mechanisms of spin-orbit driven phenomena with the focus on angle and spin-resolved photoemission and scanning tunneling microscopy.

Scanning tunneling microscopy study of the possible topological surface states in BiTeCl

Recently, the non-centrosymmetric bismuth tellurohalides such as BiTeCl are being studied as possible candidates for topological insulators. While some photoemission studies showed that BiTeCl is an inversion asymmetric topological insulator, others showed that it is a normal semiconductor with Rashba splitting. Meanwhile, first-principle calculations have failed to confirm the existence of topological surface states in BiTeCl so far. Therefore, the topological nature of BiTeCl requires further investigation. Here we report a low-temperature scanning tunneling microscopy study on the surface states of BiTeCl single crystals. On the tellurium (Te) -terminated surfaces with relatively low defect density, evidence for topological surface states is observed in the quasi-particle interference patterns, both in the anisotropy of the scattering vectors and the fast decay of the interference near the step edges. Meanwhile, on the samples with much higher defect densities, we observed surface states that behave differently. Our results may help to resolve the current controversy on the topological nature of BiTeCl.

New generation of two-dimensional spintronic systems realized by coupling of Rashba and Dirac fermions

Intriguing phenomena and novel physics predicted for two-dimensional (2D) systems formed by electrons in Dirac or Rashba states motivate an active search for new materials or combinations of the already revealed ones. Being very promising ingredients in themselves, interplaying Dirac and Rashba systems can provide a base for next generation of spintronics devices, to a considerable extent, by mixing their striking properties or by improving technically significant characteristics of each other. Here, we demonstrate that in BiTeI@PbSb₂Te₄ composed of a BiTeI trilayer on top of the topological insulator (TI) PbSb₂Te₄ weakly- and strongly-coupled Dirac-Rashba hybrid systems are realized. The coupling strength depends on both interface hexagonal stacking and trilayer-stacking order. The weakly-coupled system can serve as a prototype to examine, e.g., plasmonic excitations, frictional drag, spin-polarized transport, and charge-spin separation effect in multilayer helical metals. In the strongly-coupled regime, within ~100 meV energy interval of the bulk TI projected bandgap a helical state substituting for the TI surface state appears. This new state is characterized by a larger momentum, similar velocity, and strong localization within BiTeI. We anticipate that our findings pave the way for designing a new type of spintronics devices based on Rashba-Dirac coupled systems.

Spin-helical Dirac states in graphene induced by polar-substrate surfaces with giant spin-orbit interaction: a new platform for spintronics

Spintronics, or spin electronics, is aimed at efficient control and manipulation of spin degrees of freedom in electron systems. To comply with demands of nowaday spintronics, the studies of electron systems hosting giant spin-orbit-split electron states have become one of the most important problems providing us with a basis for desirable spintronics devices. In construction of such devices, it is also tempting to involve graphene, which has attracted great attention because of its unique and remarkable electronic properties and was recognized as a viable replacement for silicon in electronics. In this case, a challenging goal is to lift spin degeneracy of graphene Dirac states. Here, we propose a novel pathway to achieve this goal by means of coupling of graphene and polar-substrate surface states with giant Rashba-type spin-splitting. We theoretically demonstrate it by constructing the graphene@BiTeCl system, which appears to possess spin-helical graphene Dirac states caused by the strong interaction of Dirac and Rashba electrons. We anticipate that our findings will stimulate rapid growth in theoretical and experimental investigations of graphene Dirac states with real spin-momentum locking, which can revolutionize the graphene spintronics and become a reliable base for prospective spintronics applications.

Tunable Rashba effect in two-dimensional LaOBiS2 films: ultrathin candidates for spin field effect transistors

Rashba spin splitting is a two-dimensional (2D) relativistic effect closely related to spintronics. However, so far there is no pristine 2D material to exhibit enough Rashba splitting for the fabrication of ultrathin spintronic devices, such as spin field effect transistors (SFET). On the basis of first-principles calculations, we predict that the stable 2D LaOBiS2 with only 1 nm of thickness can produce remarkable Rashba spin splitting with a magnitude of 100 meV. Because the medium La2O2 layer produces a strong polar field and acts as a blocking barrier, two counter-helical Rashba spin polarizations are localized at different BiS2 layers. The Rashba parameter can be effectively tuned by the intrinsic strain, while the bandgap and the helical direction of spin states sensitively depends on the external electric field. We propose an advanced Datta-Das SFET model that consists of dual gates and 2D LaOBiS2 channels by selecting different Rashba states to achieve the on-off switch via electric fields.

Landau level spectroscopy of Dirac electrons in a polar semiconductor with giant Rashba spin splitting

Optical excitations of BiTeI with large Rashba spin splitting have been studied in an external magnetic field (B) applied parallel to the polar axis. A sequence of transitions between the Landau levels (LLs), whose energies are in proportion to √B were observed, being characteristic of massless Dirac electrons. The large separation energy between the LLs makes it possible to detect the strongest cyclotron resonance even at room temperature in moderate fields. Unlike in 2D Dirac systems, the magnetic field induced rearrangement of the conductivity spectrum is directly observed.

Circular dichroism and superdiffusive transport at the surface of BiTeI

We investigate the electronic states of BiTeI after the optical pumping with circularly polarized photons. Our data show that photoexcited electrons reach an internal thermalization within 300 fs of the arrival of the pump pulse. Instead, the dichroic contrast generated by the circularly polarized light relaxes on a time scale shorter than 80 fs. This result implies that orbital and spin polarization created by the circular pump pulse rapidly decays via manybody interaction. The persistent dichroism at longer delay times is due to the helicity dependence of superdiffussive transport. We ascribe it to the lack of inversion symmetry in an electronic system far from equilibrium conditions.

Strongly spin-orbit coupled two-dimensional electron gas emerging near the surface of polar semiconductors

We investigate the two-dimensional highly spin-polarized electron accumulation layers commonly appearing near the surface of n-type polar semiconductors BiTeX (X=I, Br, and Cl) by angular-resolved photoemission spectroscopy. Because of the polarity and the strong spin-orbit interaction built in the bulk atomic configurations, the quantized conduction-band subbands show giant Rashba-type spin splitting. The characteristic 2D confinement effect is clearly observed also in the valence bands down to the binding energy of 4 eV. The X-dependent Rashba spin-orbit coupling is directly estimated from the observed spin-split subbands, which roughly scales with the inverse of the band-gap size in BiTeX.