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Metal halide perovskites (MHPs) are characterized as strongly anharmonic and dynamic lattices. While there is a consensus on the solvation-like polarization effect in these materials, whether static polarization, that is, ferroelectricity, exists or not in 3D MHPs remains controversial. In this Review, we resolve this controversy by analysing the stereochemical expression (SE) of the ns2 electron pair (NSEP) on group IV metal cations. The SE-NSEP is key to lattice instability, which governs the breaking of inversion symmetry and induces ferroelectricity. The SE-NSEP is diminishingly small in commonly studied 3D lead iodide or bromide perovskites, indicating an absence of ferroelectricity. In contrast, 2D MHPs promote the SE-NSEP and produce unambiguous ferroelectricity or antiferroelectricity. Irrespective of ferroelectricity, the dynamic manifestation of the SE-NSEP provides the missing link to understanding polar fluctuations and efficient dielectric screening in MHPs, thus, contributing to the long carrier lifetimes and diffusion lengths. This Review establishes a unifying structure–property relationship among chemical composition, centrosymmetry breaking, lattice anharmonicity, ferroelectricity, dielectric screening and the Rashba effect in metal halide perovskites from the perspective of stereochemical expression of ns2 electron pairs on group IV metal cations.

The transverse Rashba effect in a centrosymmetric antiferromagnet materialized by double-Gd-adsorbed graphene nanoribbon is investigated via the first-principle calculations. The Rashba effect is associated with not only the local transverse dipole fields induced by the off-center adsorption of the Gd adatoms but also the local magnetic moments. It is perfectly realized that the transverse Rashba effect (Rashba parameter αx reaches to 2.205 eV A) and strong perpendicular magnetocrystalline anisotropy energy (MAE) coexist in antiferromagnetic (AFM) ground-state structure. However, the global Rashba effect disappears in ferromagnetic structure. The origin of the strong MAE is elaborated in k − space. It is intriguing that the first-order perturbation of the orbit and spin angular momentum coupling is the major source of the MAE due to the specific one-dimensional band structure. The transverse Rashba effect and the strong perpendicular magnetization hosted simultaneously by the proposed centrosymmetric antiferromagnet lock the up- (or down-) spin quantization direction (SQD) to the backward (or forward) movement, and the SQD is related to the chirality of the AFM structure. This finding offers a magnetic approach to a high coherency spin propagation in one-dimensionality, and open a new door to manipulating spin transportation in graphene nanoribbon-based spintronics.

2D hybrid perovskites with strong spin–orbit coupling (SOC) and structural asymmetry represent a new class of quantum materials that can potentially display coexisting ferroelectricity and Rashba spin splitting. Studies on these systems provide insight into the coupling between strain, spin, and electronic degrees of freedom, as well as symmetry and order parameters in the bulk and at the interfaces. We review design principles for ferroelectric hybrid perovskites with tunable band gaps, Rashba spin-split properties, and multiple polar axes. Different from traditional inorganic semiconductors, the composition and chirality of the organic cation, along with the strength of the coupling between the organic and inorganic components, play key roles in deciding the structural asymmetry that drives ferroelectricity and the spin orbit field.

We quantified the bulk Rashba splitting and suppression in polymorphs of MA(Pb, Sn, Ge, or Si)I3 perovskites. The low-computational-cost DFT-1/2 quasiparticle correction was performed for all structures, combined with the inclusion of spin-orbit coupling (SOC) effects. The presence of SOC and symmetry breaking from the metal off-centering octahedral distortion are indispensable and essential conditions for Rashba splitting, whose magnitude emerges from the Pb → Si sequence. Additionally, the quasiparticle correction provides energy bandgaps for MAPbI3 (cubic, tetragonal, and orthorhombic), MASnI3 (cubic and tetragonal), and MAGeI3 (cubic) that are in outstanding agreement with experimental results. However, while gap energies are yielded collaboratively from the metal off-centering and relative octahedral tiltings, the bulk Rashba suppression is reached for metal on-centering (octahedral platonic-like) configurations that are thermodynamically stable even when the charge polarization is kept invariant among metal-I bonds in the polymorphs.

We discuss the current state of a promising area of modern physics, the study of the physical properties of metal nanowires and atomic chains. One-dimensional nanostructures are attractive because of both the promise of their practical applications and the possibility of using them to test various theoretical models and approaches by comparing theoretical results with experimental data. We describe experimental conditions under which metal nanowires form on metal and semiconductor surfaces. We give special attention to theoretical models describing the scenario of nanowire growth on various surfaces. We analyze the main experimentally determined factors that affect the distribution of nanowire lengths. We show that the distribution of nanowire lengths on metal and semiconductor surfaces depends not only on external parameters but also on the formation time. We consider the magnetic properties of finite-length atomic chains located on the surfaces of metal and semiconductor crystals. We demonstrate a correlation among the structural, electronic, and magnetic properties of nanowires. We elucidate the effect that nanowires exert on the electronic properties of the surface on which they form. The nature of edge states is explained. The electron states of nanowire atoms are shown to be sensitive to the nanowire length. We discuss the Rashba effect for metal nanowires on a semiconductor surface and analyze how the exchange energy between atoms and the magnetic anisotropy energy affect the macroscopic characteristics of nanowires, such as their critical temperature and the time of spontaneous magnetization reversal.

Indirect absorption extended below the direct transition edge and increase in carrier lifetime derived from Rashba spin–orbit coupling may advance theoptoelectronicapplications of metalhalideperovskites. Spin-orbit coupling in halide perovskites is due to the presence of heavy elements in their structure. However, when these materials lack an inversion symmetry, for example by the application of strain, spin–orbit coupling becomes odd in the electron’s momentum giving rise to a splitting in the electronic energy bands. Here we report on the observation of a large Rashba splitting of 117 meV at room temperature, as predicted by relativistic first-principles calculations, in halide perovskitesingle crystalsthrough a facile compositional engineering approach. Partial substitution oforganic cationsbyrubidiumin single crystals induces significant indirect absorption and dual peakphotoluminescenceas a result of a large Rashba splitting. We measured circularly polarized photoluminescence and magneto-photoluminescence in perovskite films printed by single crystals as well as magneto-electroluminescence and magneto-photocurrent in spin-LEDs based on perovskite single crystals. They indicated significant spin-momentum locking due to the large Rashba effect. A hybrid perovskite single crystalphotodetectorachieved record figures of merit, including detectivity of more than 1.3 × 1018Jones which represents a three orders of magnitude improvement compared to the to date record. These findings show that facile compositional engineering of perovskite single crystals holds great promise for further advancing the optoelectronic properties of existing materials.

The detection of spin current injected from the ferromagnet source to the semiconductor channel is very challenging due to the low injection efficiency at the interface. Especially, it is difficult to detect the spin precession signal in a strong Rashba system without a signal decay. In a semiconductor system, the spin Hall angle is much larger than the spin injection efficiency, so the spin Hall effect is utilized for room temperature operation of the semiconductor-based Rashba devices. To realize spin transport device induce by the spin-charge and charge-spin conversions, the direct spin Hall effect (DSHE) and the inverse spin Hall effect (ISHE) are adopted, respectively. The spin current is clearly detected up to room temperature and the spin transport signal agrees to the temperature dependence of the Rashba effect. From these spin transport signals, we suggest another option to extract Rashba parameters from cryogenic temperature to room temperature. The both signals of DSHE and ISHE also confirm the Onsager Reciprocity in a Rashba system.

Rashba spin current generation emerges in heterostructures of ferromagnets and transition metal dichalcogenides (TMDs) due to an interface polarization and associated inversion symmetry breaking. Recent work exploring the synthesis and transfer of epitaxial films on the top of low layer count 2D materials reveals that atomic potentials from the underlying substrate interface are not completely screened. The extension of this transparency effect to other interfacial phenomena, such as the Rashba effect and associated spin torques, has not yet been demonstrated. Here, we report enhanced spin transfer torques from the Rashba spin current in heterostructures of permalloy (Py) and WSe2. We show that insertion of up to two monolayers of WSe2 enhances the spin transfer torques in a Rashba system by up to 3×, without changing the fieldlike Rashba spin-orbit torque (SOT), a measure of interface polarization. Our results indicate that low layer count TMD films can be used as an interfacial "scattering promoter" in heterostructure interfaces without quenching the original polarization.

Rashba spin-orbit coupling enables electric control of spin states, promising enormous advances from conventional charge-based computing. Until now, a general scheme or a descriptor to find an optimal system with isolated spin states with large tunable splitting is still lacking. Here, based on first-principles calculations, we explore the microscopic physicochemical mechanism responsible for the Rashba effect in 2D van der Waals heterobilayers. We find that the difference in the Born effective charge of atoms at the interface can be used as a single-layer descriptor to predict heteropairs with large Rashba splitting, thus reducing the scaling factor in materials search. Moreover, we discover that for most 2D materials, the routinely used Rashba parameter αR is not a good gauge of the effect's strength. From our general scheme, MoTe2|Tl2O and MoTe2|PtS2, with spin splitting above 120 meV, Rashba energy ER = 94 meV, and wavenumber difference 2k0 = 0.36 A-1 ("effective" αR > 1 eVA), emerge as the best candidates for spin transistors at room temperature.

The Rashba effect has been proposed to give rise to a bright exciton ground state in halide perovskite nanocrystals (NCs), resulting in very fast radiative recombination at room temperature and extremely fast radiative recombination at low temperature. In this paper we find the dispersion of the “Rashba exciton”, i.e., the exciton whose bulk dispersion reflects large spin–orbit Rashba terms in the conduction and valence bands and thus has minima at non-zero quasi-momenta. Placing Rashba excitonsin quasi-2D cylindrical quantum dots, we calculate size-dependent levels of confined excitons and their oscillator transition strengths. We consider the implications of this model for two-dimensional hybrid organic–inorganic perovskites, discuss generalizations of this model to 3D NCs, and establish criteria under which a bright ground exciton state could be realized.

Achieving a large and tunable Rashba effect is of great significance for advancing both the understanding and applications of spintronics. Two-dimensional nanostructures that are expected to sustain large mechanical deformation provide a great platform to study the strain effect on the tunability of the Rashba effect. Using first-principles density functional theory simulations, we investigate the mechanical stability and the effect of biaxial tensile strain on the Rashba parameters of the two-dimensional BiTeBr monolayer sheet. The mechanical stability is computed taking into account both elastic and dynamical aspects. The simulated stress-strain curve shows that the BiTeBr monolayer sheet can withstand a biaxial loading stress up to 4.36 GPa with a critical strain of 17%. Further phonon dispersion calculations indicate that the structure becomes unstable due to the existence of imaginary frequencies for strains beyond 7% limiting the maximum stress to 2.79 GPa. Moreover, the electronic structures and Rashba parameters are calculated as a function of strain from 0% to 7%. The band gaps remain indirect and exhibit a linear dependence on the strain. The decrease in band gaps with increasing strains can be attributed to the different bonding characters of near-gap states that the conduction band minimum is of anti-bonding nature while the valence band maximum is mainly non-bonding. The Rashba parameters can be tuned by 33.6% from 1.28 to 1.71 eV Å following a linear dependence on strain. This enhancement can be understood from the perspectives of enhanced charge transfer and charge distribution inhomogeneity induced by strain. The intuitive understanding could be used to understand and motivate the application of various methods that can lead to charge redistribution to tune the electronic properties of Rashba materials.

GeTe has become a high-performance thermoelectric material with a figure of merit (ZT) over two through alloying and band engineering strategies. Yet, the question on how to effectively engineer the electronic band structure of GeTe toward achieving a better thermoelectric performance still cannot be clearly answered, and its underlying physics has not been well understood. Here, we manipulate the lattice structure of GeTe via modifying the lattice parameters, interaxial angles and reciprocal displacements, and investigate their influence on the electronic band structure and thermoelectric properties using first-principles calculations. The calculation results show that the reciprocal displacement directly manipulates the energy level of the L-band and the Z-band, resulting in an indirect–direct transition of the band gap and a strong Rashba effect. Modifications of lattice parameters and interaxial angles can affect band gaps, band convergence and density of states, which are crucial to determining thermoelectric performance. This work performs a systematic study on how the lattice structure manipulation influences the electronic band structure and thermoelectric properties of GeTe, and can provide a clear route to further enhance its ZT.

Recent developments in the synthesis of highly crystalline ultrathin BiTeX (X = Br, Cl) structures [Debarati Hajra et al., ACS Nano 14, 15626 (2020)] have led to the exploration of the atomic structure, dynamical stability, and electronic, optical, and thermoelectric properties of SbXY (X = Se, Te; Y = Br, I) monolayers via density functional calculations. The calculated phonon spectrum, elastic stability conditions, and cohesive energy verified the stability of the studied SbXY monolayers. The mechanical properties reveal that all studied monolayers are stable and brittle. Based on PBE (PBE + SOC) functional calculations, the SbXY monolayers are semiconductors with indirect bandgaps. The calculated bandgaps using HSE (HSE + SOC) for SbSeBr, SbSeI, SbTeBr, and SbTeI monolayers are between 1.45 and 1.91 eV, which are appealing for applications in nanoelectronic devices. The signature of the Rashba effect appears in the SbXY monolayer. The SbXY monolayers are visible-light active. Hole doping can be an efficient way to increase the electricity production of SbXY monolayers from waste heat energy. This study suggests that SbXY (X = Se, Te; Y = Br, I) monolayers represent promising new electronic, optical, and energy conversion systems.

Spin field-effect transistors (SFETs) based on the Rashba effect could manipulate the spin of electrons electrically, while seeking desirable Rashba semiconductors with large Rashba constant and strong electric-field response, to preserve spin coherence remains a key challenge. Herein, we propose a series of 2D Rashba semiconductors with two-atom-thick buckled honeycomb structure (BHS) according to high-throughput first-principles density functional theory calculations. BHS semiconductors show large Rashba constants that are favorable to be integrated into nanodevices superior to conventional bulk materials, and they can be fabricated by mechanical exfoliation or chemical vapor deposition. In particular, 2D AlBi monolayer has the largest Rashba constant (2.77 eVÅ) of all 2D Rashba materials. Furthermore, 2D BiSb monolayer is a promising candidate for SFETs due to its large Rashba constant (1.94 eVÅ) and strong electric field response (0.92 eÅ

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.

Ferroelectric Rashba semiconductors (FERSCs) have recently attracted intensive attention due to their giant bulk Rashba parameter, αR, which results in a locking between the spin degrees of freedom and the switchable electric polarization. However, the integration of FERSCs into microelectronic devices has provoked questions concerning whether the Rashba effect can persist when the material thickness is reduced to several nanometers. Here we find that αR can keep a large value of 2.12 eV A in the 5.0 nm thick GeTe film. The behavior of αR with thickness can be expressed by the scaling law and provides a 3D thickness limit of the bulk Rashba effect, dc = 2.1 ± 0.5 nm. Finally, we find that the thickness can modify the Berry curvature as well, which influences the polarization and consequently alters the αR. Our results give insight into understanding the factors influencing αR in FERSCs and pave a novel route for designing Rashba-type quantum materials.

The spin-resolved transport for monolayer MoS2 through a zigzag nanoribbon superlattice based on the transfer matrix method in the resonant tunneling regime is investigated in the presence of an external perpendicular electric field. The controllable external electric field leads to the so-called Rashba effect, which can modulate the internal spin–orbit coupling. Our investigations show that by controlling the Rashba strength, it is possible to attain 100% spin-polarization and spin-flip, which can be used in designing an optimized spintronic device. In addition, the effects of superlattice specific parameters (D/W), the barrier height (V0), and the number of barriers (N) on the functionality of the system are studied, leading to optimum results for the case of 20 barriers.

Taking into account the interaction of the electron with bulk longitudinal-optical and the Rashba effect brought by the spin–orbit interaction, we have studied the effective mass ( $$ m^{*} $$ ) of the strong coupling polaron in semiconductor weak triangular polar slab. Using the method of Green’s function, $$ m^{*} $$ has been derived as a function of slab thickness $$ L_{z} $$ , the velocity $$ u $$ and the coupling constant $$ \alpha $$ . Numerical results showed that the interactions between the orbit and the spin directions will affect $$ m^{*} $$ .

The simultaneous occurrence of gigantic piezoelectricity and Rashba effect in two-dimensional materials are unusually scarce. Inversion symmetry occurring in MX3 (M= Ti, Zr, Hf; X= S, Se) monolayer...

Summary Advances in thermoelectrics are motivated by the innovation of thermoelectric theories. The Rashba effect, spin-dependent band splitting, paves a new path to enhance thermoelectric performance. Herein, we investigate the Rashba effect in GeTe, in which the rhombohedral distortion provides a unique handle to examine the mechanism of the Rashba effect for tuning thermoelectric properties. Fundamentally, we discover that the Rashba effect originates from the specific atomic site displacement. Experimentally, Sn-doped GeTe has a strong Rashba effect and yields an ultra-high power factor, meanwhile additional Sb alloying effectively tunes the carrier concentration. Moreover, microstructure characterizations reveal that the co-existence of grain boundaries, nanoprecipitates, and stacking faults significantly reinforces phonon scatterings and leads to an ultra-low lattice thermal conductivity. Finally, a high figure of merit is achieved in Ge1−x−ySnxSbyTe. The demonstrated benchmark figure of merit originated from the Rashba effect can provide a promising arena for enhancing thermoelectric performance in wide materials.

The influence of a magnetic field on the Rashba spin–orbit interaction in an anisotropic quantum dot is theoretically studied, and the expression of the ground state energy of a magnetopolaron is obtained with the Pekar variational method. The ground state energy of the magnetopolaron splits into two branches due to the Rashba effect, and the splitting appears saturated phenomenon with increasing the transverse and longitudinal effective confinement lengths. Because the contribution of the magnetic field cyclotron resonance frequency to the Rashba spin–orbit splitting is a positive value, the energy spacing becomes larger as the magnetic field cyclotron resonance frequency increases. Due to the spin–orbit coupling interaction, the energy splits at zero magnetic field. The total energy is reduced due to the presence of phonons. Therefore, the polaron state is more stable than the bare electron state, and the polaron energy splitting is more stable.

The spin effect of bound magnetopolaron in an asymmetry quantum well is studied by Pekar variational method. The expression of the ground state energy of bound magnetopolaron is obtained through theoretical derivation. The relationship between the ground state energy of the polaron and the wave vector, the well width, the magnetic field cyclotron resonance frequency, and the Coulomb bound potential are discussed, respectively. Due to the crystal structural inversion asymmetry and the time inversion asymmetry, the polaron energy occurs Rashba spin–orbit splitting and Zeeman splitting. Under the strong and weak magnetic fields, we discussed the dominant position of Rashba effect and Zeeman effect, respectively. Due to the presence of impurities, the polaron is more stable than the bare electron state, and the energy splitting of polaron is more stable.

In this work I review of the theoretical and experimental issue related to the Rashba Spin-Orbit interaction in semiconductor nanostructures. The Rashba spin-orbit interaction has been a promising candidate for controlling the spin of electrons in the field of semiconductor spintronics. In this work, I focus study of the electrons spin and holes in isolated semiconductor quantum dots and rings in the presence of magnetic fields. Spin-dependent thermodynamic properties with strong spin-orbit coupling inside their band structure in systems are investigated in this work. Additionally, specific heat and magnetization in two dimensional, one-dimensional quantum ring and dot nanostructures with Spin Orbit Interaction are discussed.

The properties of the first excited state of a magnetopolaron in a patabolic quantum dot (PQD) are studied with the Lee-Low-Pines unitary transformation (LLPUT) and variational method of Pekar-type (VMPT). We find that the external magnetic field and the motion of the electron can trigger the Rashba effect in the first excited state and they play a virtual role in determining properties of the magnetopolaron in the parabolic PQD system. Furthermore, our results indicate the Rashba spin-orbit coupling(RSOC), confined potential, electron-phonon coupling, magnetic field and phonon wave vector promote a variation of the first excited state energy (FESE). In addition, the rule that the first excited state energy changes with one of four factors is not affected by the RSOC.

Two-dimensional (2D) Janus transition-metal dichalcogenides (TMDs) (MXY, M = Mo, W; X, Y = S, Se, Te; X ≠ Y) have desirable energy gaps and high stability in ambient conditions, similar to traditional 2D TMDs with potential applications in electronics. But different from traditional 2D TMDs, 2D Janus TMDs possess intrinsic Rashba spin splitting due to out-of-plane mirror symmetry breaking, with promising applications in spintronics. Here we demonstrate a new and effective way to manipulate the Rashba effect in 2D Janus TMDs, that is, charge doping, by using first-principles density functional theory (DFT) calculations. We find that electron doping can effectively strengthen the Rashba spin splitting at the valence band maximum (VBM) and conduction band minimum (CBM) in 2D Janus TMDs without constant energy consumption, superior to traditional techniques (electric fields and strain engineering), but hole doping would weaken the Rashba effect in 2D Janus TMDs. By combining the DFT calculations with the electric-triple-layer model, we also reveal the intrinsic mechanism of tuning the Rashba effect in 2D Janus TMDs by charge doping, and find that the charge transfer plays an important role in tuning the Rashba spin splitting in 2D polar semiconductors. In particular, the Rashba constants are linearly dependent on the charge transfer between X (or Y) and M atoms in 2D Janus TMDs. These results enrich the fundamental understanding of the Rashba effect in 2D semiconductors, which can be promising candidates for spin field-effect transistors (FETs) in experiments.

Based on the extensive investigation on graphene and graphene derivatives asymmetrically functionalized with a variety of molecular groups and the concept of Janus materials with asymmetric facial properties, Janus two-dimensional (2D) materials as derivatives of the 2D material family, including Janus graphene, Janus transition metal chalcogenides, etc., have attracted much attention in recent years. Janus 2D materials have been demonstrated experimentally and theoretically to possess unique properties such as an out-of-plane piezoelectric polarization and strong Rashba effect due to their out-of-plane asymmetry. Here, the recent progress of emerging Janus 2D materials, including Janus graphene, prediction and fabrication of various different Janus 2D materials and Janus 2D van der Waals heterostructures, is presented. The investigations on the unique properties and potential device applications of Janus 2D materials are summarized. Finally, the conclusion and prospects for the future explorations on Janus 2D materials are also provided.

Recently, trigonal layered GeTe was exfoliated from the rhombohedral germanium telluride using a sonication-assisted liquid-phase method in experiments. We identify the blue phosphorene-like MTe (M = Ge, Sn, and Pb) monolayers and bilayers as two-dimensional semiconductors with a large Rashba-type spin–orbit coupling effect that can be modulated by the external electric field. It is found that Rashba-type spin splitting occurs around the Γ point for both monolayer and bilayer MTe. For the bilayer MTe, we predict that the Rashba effect induced spin and momentum mismatch will give rise to a low recombination rate and long carrier lifetimes. We also obtain Rashba parameters and band gap values that are tunable with the perpendicular external electric field. In general, the low-dimensional MTe materials exhibit excellent functional characteristics, thus being promising for designing spin field-effect transistors and optoelectronic applications.

Named after the two-faced Roman god of transitions, transition metal dichalcogenide (TMDs) Janus monolayers have two different chalcogen surfaces, inherently breaking the out of plane mirror symmetry.[ 4] The broken mirror symmetry and the resulting potential gradient lead to the emergence of quantum properties[ 7] such as the Rashba effect[ 8] and the formation of dipolar excitons.[ 11] Experimental access to these quantum properties, however, hinges on the ability to produce high-quality 2D Janus monolayers. Here, our results introduce a holistic 2D Janus synthesis technique that allows real-time monitoring of the growth process. Our prototype chamber integrates in-situ spectroscopy, offering fundamental insights into the structural evolution and growth kinetics, that allow us to evaluate and optimize the quality of Janus monolayers. We demonstrate the versatility of this method by synthesizing and monitoring the conversion of SWSe, SNbSe, and SMoSe Janus monolayers. Deterministic conversion and real-time data collection further aid us to convert exfoliated TMDs to Janus monolayers for the first time and reach unparalleled exciton linewidth values compared to the current best standard. The results offer an insight into the process kinetics and aid in the development of new Janus monolayers with high optical quality, which is much needed to access their exotic properties. This article is protected by copyright. All rights reserved.

We investigate the behavior of both pure spin and spin-polarized currents measured with four-probe non-local and two probe local configurations up to room temperature and under an external gate voltage in a lateral graphene transistor, produced using a standard large-scale microfabrication process. The high spin diffusion length of pristine graphene in the channel, measured both directly and by the Hanle effect, and the tuning of the relationship between the electrode resistance areas present in the device architecture allowed us to observe local tunnel magnetoresistance at room temperature, a new finding for this type of device. The results also indicate that while pure spin currents are less sensitive to temperature variations, spin-polarized current switching by an external voltage is more efficient, due to a combination of the Rashba effect and a change in carrier mobility by a Fermi level shift.

Most studies of the Rashba effect have focused on interfacial Rashba spin–orbit coupling. Recently, bulk Rashba materials have attracted considerable interest owing to their potential to enhance the Rashba spin–orbit torque. By employing a bulk Rashba material, GeTe, as a spin–orbit channel in GeTe/NiFe bilayers, a large field-like spin–orbit torque up to 15.8 mT/(107 A cm−2) is measured. This value is one of the largest reported field-like torques and is attributed to the interfacial spin–orbit coupling being enhanced by the bulk Rashba effect in the GeTe channel. Furthermore, the large field-like torque is maintained even for a 20-nm-thick NiFe layer. This unconventional dependence on the thickness of both the GeTe and NiFe layers cannot be described by conventional theory, but it is believed to stem from the additional bulk Rashba effect-induced term. The large field-like torque over a wide range of ferromagnet thicknesses results in scalable in-plane spin–orbit torque devices. This result calls for a further theoretical study on spin transport in heterostructures, including bulk Rashba materials. We find a very large field-like spin-orbit torque in a bulk Rashba channel/ferromagnet structure and this large value of spin-orbit torque is attributed to the interfacial spin-orbit coupling enhanced by the well-grown bulk Rashba material.

We study the effects of Rashba splitting on two-leg ladders with weakly screened Coulomb interactions. Past research has shown that in this class of systems the two backscattering channels with the largest amplitude favor ordering of canonically conjugated collective fields which effectively renders the system gapless. Here we show that the band-dependent Rashba spin-orbit interaction breaks this symmetry of scattering channels, leading to a new fixed point with yet unexplored instabilities. Exotic properties can be found, for instance, the mixing of the magnetism with the charge-density wave. We then investigate the physical consequences of this partial spectral gap opening. We find a striking difference in signatures of order observed in single-particle (spectral-function) and two-body (susceptibilities) experimental probes. We conclude this paper by comparing theoretical and experimental results obtained on the Au-Si(553) platform. In STM measurements, we identify the lowest-lying soliton excitation as a hallmark of the gapped sine-Gordon model in an apparently metallic system. This implies the presence of partial spectral gaps opening. Furthermore, by ARPES measurements we confirm the expected temperature dependence of the outer bands backfolding. These two findings constitute the experimental evidence of the many-body physics proposed here.

With an ever intensifying hunt for quantum materials with integrated functionalities, transition metal oxides provide a simple yet rich option to explore. In this article, we bring out the potential of a perovskite oxide KTaO3 (KTO) as a candidate for future generation quantum technologies as well as a hunting ground to understand the topological effects in oxides. We show that the heterostructures of insulating KTO with other insulating oxides LaVO3 (LVO) and EuO are not only conducting, but have strong spin-orbit coupling leading to momentum-dependent spin-splitting—the Rashba effect. In LVO–KTO, the Rashba spin-split bands are shown to give rise to anisotropic magnetoresistance and planar Hall effect, while in EuO–KTO, a non-trivial Berry’s phase analysed from the quantum Shubnikov-de Haas oscillations is observed.

The energy problem has recently become increasingly more serious, therefore the rational use of heat energy and conversion into electrical energy is particularly important. The thermoelectric (TE) field is closely related to human life, as heat from automobiles, heat dissipation from high-power electrical appliances, or other electrical products that produce a lot of heat, can all be transformed with TE materials. The search for TE materials with an excellent performance and effective TE optimization strategies (STs) has attracted significant attention owing to the fact that thermal energy can be directly converted into electric energy. In contrast to the common TE-optimized STs, such as constructing point defects or reducing dimensionality, spin-related optimization STs have emerged from previous published research, such as the spin Seebeck effect or the Rashba effect, in which the Rashba effect shows an effective method to break through the bottleneck of ZT optimization. In this review, typical high ZT materials, common traditional optimized STs, Rashba-type TE materials and their corresponding ZT values are comprehensively discussed. The TE performance of Rashba-type materials is analysed, such as BiTeX (X = I, Br), GeTe, BiSbSeTe2, and the BiSb monolayer. Moreover, the TE optimization mechanisms (band engineering, phonon engineering, and Rashba spin-split engineering) are summarised. Finally, the development and challenges of Rashba spin-split combined with TE in breaking the bottleneck in ZT optimization are highlighted.

Spin-orbit torques (SOTs) allow controlling the magnetization of diverse classes of magnetic multilayers and devices. The mechanism utilizes spin-orbit interactions such as spin Hall effect in heavy metals and/or Rashba effect at ferromagnetic/heavy-metal interface with broken inversion symmetry. The SOTs have damping-like (HDL) and field-like (HFL) effective field components. In this talk, we will present the mechanism of spin-transport in ultrathin magnetic multilayer whose thicknesses span across the characteristic spin-dephasing length, and how it results in HDL and HFL nearby the crossing point of this specific length. To this aim, we have quantified SOTs in a series of samples Pt 8|Co x|Al 1.4|Pt 3 with x = 0.55, 0.7, 0.9, 1.2, 1.4 nm. Our experiments demonstrate the presence of very large field-like torque arising from Co|Al interface for Co thickness smaller than spin-dephasing length. The results suggest the contribution of additional mechanisms of spin-current generation.

In the work by Tarnopolsky et al. [Phys. Rev. Lett. 122, 106405 (2019)] they obtained the magic angles for superconductivity in twisted bilayer graphene (TBG) with a fundamental continuum model for TBG which captures the physics of the flat band. In this Letter we study the continuum model in detail and demonstrate that the system of TBG described by the continuum model is equivalent to a dynamical system that is composed of three parts of effective interactions: the coupling between two effective non-Abelian gauge fields originating from the periodic hopping potential and two effective massless fermion fields which have 1/2 lattice pseudospin and a twist-angle-dependent effective charge, the coupling between a pseudomagnetic field created by gauge fields and a layer pseudospin, and an effective pseudo-Rashba effect in an equivalent unrotated single layer with twist-angle-dependent Rashba coupling strength. The effective Rashba effect is shown to be also the sum of the pseudo-Rashba effects in two effective twisted single layers with a relative twist angle $\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta}$. The longitudinal component ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\tau}}}^{z}$ of the layer pseudospin vector is revealed to have the physical meaning of an interlayer electric field. Due to the relative twist between the two layers it geometrically leads to the nonvanishing curvature on a vector bundle in a two-dimensional effective hexagonal lattice. The geometric curvature on the vector bundle creates a pseudomagnetic field physically and interacts with the layer pseudospin.

Recent studies have shown that the non-relativistic antiferromagnetic ordering could generate momentum-dependent spin splitting analogous to the Rashba effect, but free from the requirement of relativistic spin-orbit coupling. Whereas the classification of such compounds can be illustrated by different spin-splitting prototypes (SSTs) from symmetry analysis and density functional theory calculations, the significant variation in bonding and structure of these diverse compounds representing different SSTs clouds the issue of how much of the variation in spin splitting can be traced back to the symmetry-defined characteristics, rather to the underlining chemical and structural diversity. The alternative model Hamiltonian approaches do not confront the issues of chemical and structural complexity, but often consider only the magnetic sublattice, dealing with the all-important effects of the non-magnetic ligands via renormalizing the interactions between the magnetic sites. To this end we constructed a 'DFT model Hamiltonian' that allows us to study SSTs at approximate 'constant chemistry', while retaining the realistic atomic scale structure including ligands. This is accomplished by using a single, universal magnetic skeletal lattice (Ni2+ ions in Rocksalt NiO) and designing small displacements of the non-magnetic (oxygen) sublattice which produce, by design, the different SSTs magnetic symmetries. We show that (i) even similar crystal structures having very similar band structures can lead to contrasting behavior of spin splitting vs. momentum, and (ii) even subtle deformations of the non-magnetic ligand sublattice could cause a giant spin splitting in AFM-induced SST. This is a paradigm shift relative to the convention of modeling magnets without considering the non-magnetic ligand that mediate indirect magnetic interaction (e.g., super exchange)., Comment: 23 pages, 5. figures

The long charge-transfer excited state (CTES) lifetime of organometal complexes make them very promising in the applications of photovoltaic, photocatalysis and photosensor. Employing the spin–orbit coupling (SOC) of noble metals for achieving long-lived CTES are often essential to guarantee high performance. There is much interest in replacing these noble metals with non-noble metals due to low cost and environmental friendliness. However, despite the exploration of advanced molecular designs, it is failing to access a long-lived CTES of earth-abundant metal-containing complexes by the SOC effect. Because weak ligand field splitting of non-noble metals causes rapid deactivation of CTES. Here, the SOC of orderly aligned non-noble metals on a layered double hydroxide (LDH) nanosheet is enhanced through the Rashba effect caused by breaking of the inversion symmetry. Taking porphyrins-Pd (Pd-TCPP) as a model chromophore, a series of (LDHs/Pd-TCPP)n films are fabricated, and a high polar distortion (alinged P...

Up to now, two-dimensional (2D) materials with both valley polarization and the Rashba effect are still rare. In this work, a new kind of Janus monolayers TiXY (X ≠ Y, X/Y = Cl, Br, I) is demonstrated to have physical properties of benefit for spintronics and valleytronics. In particular, Janus TiBrI shows Zeeman-type spin splitting of 70 meV, large Berry curvature of 106.22 bohr

It is shown, based on the density functional theory (DFT) calculations, that weak van der Waals interaction between monolayers of Pb and MoTe2 introduce a symmetry breaking that gives rise to spin polarized interface states. This is a departure from a conventional picture of band spin splitting in the adsorption systems as it is usually associated with the strong surface interactions e.g. covalent bonds, which results in electronic charge asymmetry in the vicinity of the adatom's nuclei. The analysis based on the effective Hamiltonian within the orbital-angular-momentum approach to the Rashba effect indicates that the observed spin splitting originates directly from the atomic spin-orbit coupling, with the orbital angular momentum unquenched due to broken inversion symmetry.

Hybrid organic-inorganic perovskites (HOIPs) are a new generation of high-performance materials for solar cells and light emitting diodes. Beyond these applications, ferroelectricity and spin-related properties of HOIPs are increasingly attracting interests. The presence of strong spin-orbit coupling, allied with symmetry breaking ensured by remanent polarization, should give rise to Rashba-type splitting of electronic bands in HOIP. However, the report of both ferroelectricity and Rashba effect in HOIP is rare. Here we report the observation of robust ferroelectricity and Rashba effect in two-dimensional Dion-Jacobson perovskites. NRF (Natl Research Foundation, S’pore) ASTAR (Agency for Sci., Tech. and Research, S’pore) MOE (Min. of Education, S’pore) Accepted version

The success of halide perovskites in a host of optoelectronic applications is often attributed to their long photoexcited carrier lifetimes, which has led to charge-carrier recombination processes being described as unique compared to other semiconductors. Here, we integrate recent literature findings to provide a critical assessment of the factors we believe are most likely controlling recombination in the most widely studied halide perovskite systems. We focus on four mechanisms that have been proposed to affect measured charge carrier recombination lifetimes, namely: (1) recombination via trap states, (2) polaron formation, (3) the indirect nature of the bandgap (e.g., Rashba effect), and (4) photon recycling. We scrutinize the evidence for each case and the implications of each process on carrier recombination dynamics. Although they have attracted considerable speculation, we conclude that multiple trapping or hopping in shallow trap states, and the possible indirect nature of the bandgap (e.g., Rashba effect), seem to be less likely given the combined evidence, at least in high-quality samples most relevant to solar cells and light-emitting diodes. On the other hand, photon recycling appears to play a clear role in increasing apparent lifetime for samples with high photoluminescence quantum yields. We conclude that polaron dynamics are intriguing and deserving of further study. We highlight potential interdependencies of these processes and suggest future experiments to better decouple their relative contributions. A more complete understanding of the recombination processes could allow us to rationally tailor the properties of these fascinating semiconductors and will aid the discovery of other materials exhibiting similarly exceptional optoelectronic properties.

While spintronics has traditionally relied on ferromagnetic metals as spin generators and detectors, spin–orbitronics exploits the efficient spin–charge interconversion enabled by spin–orbit coupling in non-magnetic systems. Although the Rashba picture of split parabolic bands is often used to interpret such experiments, it fails to explain the largest conversion effects and their relationship with the electronic structure. Here, we demonstrate a very large spin-to-charge conversion effect in an interface-engineered, high-carrier-density SrTiO3 two-dimensional electron gas and map its gate dependence on the band structure. We show that the conversion process is amplified by enhanced Rashba-like splitting due to orbital mixing and in the vicinity of avoided band crossings with topologically non-trivial order. Our results indicate that oxide two-dimensional electron gases are strong candidates for spin-based information readout in new memory and transistor designs. Our results also emphasize the promise of topology as a new ingredient to expand the scope of complex oxides for spintronics. A very large spin-to-charge conversion arising from a combination of the Rashba effect and topologically non-trivial states is realized at the interface of strontium titanate and aluminium, with implications for the role of topology in memory and transistor designs.

Organic-inorganic hybrid perovskites simultaneously possess strong spin-orbit coupling (SOC) and structure inversion asymmetry, establishing a Rashba effect to influence light emission and photovoltaics. Here, we use mechanical bending as a convenient approach to investigate the Rashba effect through SOC in perovskite (MAPbI3-xClx) films by elastically deforming grains. It is observed that applying a concave bending can broaden the line shape of the magnetophotocurrent, increasing the internal magnetic parameter B0 from 121 to 205 mT, which indicates an enhancement on SOC. Interestingly, the PL lifetime is found to be enlarged from 9.9 to 14.8 ns under this bending, which suggests that introducing compressive strain can essentially increase the Rashba effect through SOC, leading to an increase upon indirect band transition. Furthermore, the PL peak associated with the Rashba effect is shifted from 776 to 780 nm under this mechanical bending. Therefore, mechanical bending provides a convenient experimental method to approach the Rashba effect in hybrid perovskites.

Using Pekar variational method, we studied the influence of Rashba effect on the bound magnetopolaron in an anisotropic quantum dot. The expression of the ground state energy of the bound magnetopolaron is obtained by theoretical derivation. Due to the influence of the Rashba effect, the ground state energy of the bound magnetopolaron splits into two branches. This phenomenon fully demonstrates that the influence of orbit and spin interaction in different directions on the energy of the polaron is not negligible. Because the contribution of the magnetic field cyclotron resonance frequency to the Rashba spin-orbit splitting is a positive value, the energy spacing becomes larger as the magnetic field cyclotron resonance frequency increases. Due to the presence of phonons and impurities, the polaron is more stable than the bare electron state, and the energy splitting is more stable.

The spin effect of bound magnetopolaron in a triangular quantum well is investigated within Pekar variational method. The expression of the bound magnetopolaron ground-state energy is obtained through theoretical calculation. The relationship between the ground-state energy of the polaron and the wave vector, the electron areal density, the magnetic field cyclotron resonance frequency and the Coulomb bound potential is discussed, respectively. Due to the crystal structural inversion asymmetry and the time inversion asymmetry, the polaron energy experiences Rashba spin–orbit splitting and Zeeman splitting. We discussed the dominant position of Rashba effect and Zeeman effect in strong and weak magnetic fields, respectively. Due to the presence of impurities, the polaron is more stable than the bare electron state, and the energy splitting of polaron is more stable.

By using the Lee-Low-Pines unitary transformation and the Pekar type variational method, we studied Rashba effects on the first excited state of the bound polarons in a quantum pseudodot. In the paper, we have derived the energy of the first excited state of the polaron, which is a function of the electron-LO phonon coupling strength, the wave vector, the constraint size, the chemical potential and the Coulomb bound potential. According to the theoretical analysis, we get the following conclusions: The first excited state energy increases with the wave vector and the chemical potential increasing, and decreases with the increase of the electron-LO phonon coupling strength and the constraint size rising. And when the condition is different, the law of change of the first excited state energy of the polaron with the Coulomb bound potential is different. Under the influence of the Rashba spin-orbit interaction , the first excited state energy splits into different branches. Relatively, the Rashba effect is obviously affected by the constraint size.

In this study we investigate the role of coupling between surface orbitals in a giant spin splitting (GSS) observed in the Pb/Ge(111)-1 × 1 adsorption system along Γ − M − Γ ′ . We report, based on the density functional theory that, the magnitude of the GSS depends on the bonding structure of the Pb/Ge interface, varying from 242 to 667 meV for the metallic surface bands. The splitting is shown to be SOC enhanced, with ∼ 93% of the effect being of SOC origin. The split-energy difference observed in the system is a result of a different coupling strength between px/py(Pb) and pz(Pb) orbitals, which produces corresponding values of unquenched orbital angular momentum. The described spin-split pattern corresponds to those observed in Tl/Si(111)-1 × 1, Bi/Si(111)-( 3 × 3 ) R 30 ∘ , and 4/3ML Pb/Ge(111)-( 3 × 3 ) R 30 ∘ , which suggests that, their GSS may also be SOC enhanced.

The bright emission observed in cesium lead halide perovskite nanocrystals (NCs) has recently been explained in terms of a bright exciton ground state [Becker et al. Nature 2018, 553, 189−193], a claim that would make these materials the first known examples in which the exciton ground state is not an optically forbidden dark exciton. This unprecedented claim has been the subject of intense experimental investigation that has so far failed to detect the dark ground-state exciton. Here, we review the effective-mass/electron–hole exchange theory for the exciton fine structure in cubic and tetragonal CsPbBr_3 NCs. In our calculations, the crystal field and the short-range electron–hole exchange constant were calculated using density functional theory together with hybrid functionals and spin–orbit coupling. Corrections associated with long-range exchange and surface image charges were calculated using measured bulk effective mass and dielectric parameters. As expected, within the context of the exchange model, we find an optically inactive ground exciton level. However, in this model, the level order for the optically active excitons in tetragonal CsPbBr_3 NCs is opposite to what has been observed experimentally. An alternate explanation for the observed bright exciton level order in CsPbBr_3 NCs is offered in terms of the Rashba effect, which supports the existence of a bright ground-state exciton in these NCs. The size dependence of the exciton fine structure calculated for perovskite NCs shows that the bright–dark level inversion caused by the Rashba effect is suppressed by the enhanced electron–hole exchange interaction in small NCs.

The presented work provides a new prospective of quantum computer hardware development through ballistic nanowires with Rashba effect. We address Rashba effect as a possible mechanism to realize novel qubit gates in nanowires. We apply our results to the design of a new quantum circuit for Fourier algorithm, which shows an improved quantum cost in terms of the number of gates. The current system can be successfully implemented to increase the production of quantum computer experimentally thanks to the absence of impurities. The introduced circuit will enhance the scope of experimental and theoretical research for the realization of other quantum algorithms, such as phase estimation and Shor's algorithms.

Rashba effect is much related to next-generation spintronic devices. It is highly desirable to search for Rashba materials with large Rashba spin splitting, which is considered as the key factor for the application of spin field-effect transistor. Here, we design a two-dimensional monolayer of fluorated-InTe (InTeF) with large Rashba spin splitting and direct bandgap on the basis of first-principles calculations. InTeF monolayer is energetically and dynamically stable based on the calculations of cohesive energy and phonon dispersion. Remarkably, the Rashba parameter αR is about 1.08 eV·A, comparable to that of the BiTeI monolayer (1.86 eV·A). The direct bandgap is estimated to be 2.48 eV by HSE06 hybrid functional, which shows good prospects in light-emitting devices and photodetectors. To further explore the effect of substrates on the electronic structure of InTeF monolayer, we build two heterostructures, and the results show that the strength of Rashba effect and the direct bandgap nature in InTeF monolayer can be well preserved under the influence of substrates. Based on the above findings in our work, InTeF monolayer is considered to be one of the promising 2D materials for the application of spintronics as well as optoelectronics.