Exact SU(2) symmetry and persistent spin helix in a spin-orbit coupled system

Efficient spin accumulation carried by slow relaxons in chiral tellurium

Efficient conversion between charge currents and spin signals is crucial for realizing magnet-free spintronic devices. However, the strong spin-orbit coupling that enhances this conversion also causes rapid spin dissipation, making spin signals difficult to control. Although modern materials science offers novel systems with diverse spin configurations of conduction electrons, understanding their fundamental limitations requires insights into the mechanisms behind the creation and relaxation of spin populations. In this study, we demonstrate that parallel spin-momentum entanglement at the Fermi surface of chiral tellurium crystals gives rise to slow collective relaxation modes, termed relaxons. These relaxons dominate the electrically generated spin and orbital angular momentum accumulation in tellurium, achieving an extraordinary 50% conversion efficiency, and are responsible for a long lifetime of the spin population. We show that the slow relaxons carrying spin density closely resemble the persistent helical spin states observed in GaAs semiconductor quantum wells. This similarity suggests that slow relaxons are a general phenomenon, potentially present in other chiral materials with strong spin-momentum locking, and could be used to generate and transmit spin signals with low heat losses in future electronics.

Gate-Tunable Circular Photogalvanic Effects in Two-dimensional Perovskite Ferroelectric-based Transistor toward Multi-state Memory

Spintronics has long been an exciting branch of condensed matter science, among which the spin splitting of energy bands in an inversion asymmetric material endows the circular photogalvanic effects (CPGE) toward high-performance spin-based optoelectronic devices. Here, we have successfully achieved gate-tunable CPGE in a biaxial perovskite ferroelectric (n-HA)2CsPb2Br7 (1, n-HA is n-heptanamine), involving the broken symmetry from its spontaneous polarization. Strikingly, under left- and right-circularly polarized light, this CPGE acquires a large anisotropy factor for photocurrents up to ~1.04, far beyond most organic semiconductors and chiral counterparts (<0.2). It is the large splitting coefficient along the ky direction (~1.476 eV Å) that contributes to the significant realization of CPGE in 1. Notably, this spin-based CPGE of 1 has been modulated via the gate-voltage manipulation in its transistor-type devices, leading to multi-state memory behaviors. That is, six distinct conductance states are obtained under circularly polarized light, containing the original, high/low-state responses L(-1,0,1) to the left circularly polarized light, as well as three right components R(-1,0,1). This study establishes a pathway for further exploration toward multi-state memory in the field of ferroelectric integrated devices.

Design of Two-Dimensional Hybrid Perovskites with Giant Spin Splitting and Persistent Spin Textures

Semiconductors with large energetic separation ΔE± of energy sub-bands with distinct spin expectation values (spin textures) represent a key target to enable control over spin transport and spin-optoelectronic properties. While the paradigmatic case of symmetry-dictated Rashba spin splitting and associated spin textures remains the most explored pathway toward designing future spin-transport-based quantum information technologies, controlling spin physics beyond the Rashba paradigm by accessing strategically targeted crystalline symmetries holds significant promise. In this paper, we show how breaking the traditional paradigm of octahedron-rotation based structure distortions in 2D organic-inorganic perovskites (2D-OIPs) can facilitate exceptionally large spin splittings (ΔE± > 400 meV) and spin textures with extremely short spin helix lengths (lPSH ∼ 5 nm). A simple bond angle difference captures the distortion-driven global asymmetry and correlates quantitatively with first-principles computed spin-splitting magnitudes. A multiband effective mass model that accounts for interlayer coupling provides a unified understanding of how specific symmetry elements dictate layer- and state-dependent spin polarizations within these multi-quantum-well structures. The general symmetry analysis methodology presented here, together with the potential for rationally creating 2D-OIPs with unique symmetry patterns, opens a pathway to design semiconductors with outstanding spin properties for next generation opto-spintronics.

Spin Dynamics in Hybrid Halide Perovskites - Effect of Dynamical and Permanent Symmetry Breaking

The hybrid organic-inorganic halide perovskite (HOIP), for example, MAPbBr3, exhibits extended spin lifetime and apparent spin lifetime anisotropy in experiments. The underlying mechanisms of these phenomena remain illusive. By utilizing our first-principles density-matrix dynamics approach with quantum scatterings including electron-phonon and electron-electron interactions and self-consistent spin-orbit coupling, we present temperature- and magnetic field-dependent spin lifetimes in hybrid perovskites, in agreement with experimental observations. For centrosymmetric hybrid perovskite MAPbBr3, the experimentally observed spin lifetime anisotropy is mainly attributed to the dynamic Rashba effect arising from the interaction between organic and inorganic components and the rotation of the organic cation. For noncentrosymmetric perovskites, such as MPSnBr3, we found persistent spin helix texture at the conduction band minimum, which significantly enhances the spin lifetime anisotropy. Our study provides theoretical insight into spin dynamics in HOIP and strategies for controlling and optimizing spin transport.

An elemental ferroelectric topological insulator in ψ-bismuthene

A ferroelectric quantum spin Hall insulator (FEQSHI) exhibits coexisting ferroelectricity and time-reversal symmetry protected edge states, holding exciting prospects for inviting both scientific and application advances, particularly in two-dimensional systems. However, FEQSHI candidates that consist of only one constituent element are rarely reported. Here, we show that ψ-bismuthene, an allotrope of bilayer Bi (110), is a concrete example of a two-dimensional elemental FEQSHI. It is demonstrated that ψ-bismuthene possesses measurable ferroelectric polarization and nontrivial band gap with moderate switching barrier, making it highly suitable for the detection and observation of ferroelectric topologically insulating states. Additionally, the auxetic behavior, quantum transport properties and ferroelectric controllable persistent spin helix in ψ-bismuthene are also discussed. These findings make ψ-bismuthene promising for both fundamental physics and technological innovations.

Trembling Motion of Exciton Polaritons Close to the Rashba-Dresselhaus Regime

We report the experimental observation of trembling quantum motion, or Zitterbewegung, of exciton polaritons in a perovskite microcavity at room temperature. By introducing liquid-crystal molecules into the microcavity, we achieve spinor states with synthetic Rashba-Dresselhaus spin-orbit coupling and tunable energy splitting. Under a resonant excitation, the polariton fluid exhibits clear trembling motion perpendicular to its flowing direction, accompanied by a unique spin pattern resembling interlocked fingers. Furthermore, leveraging the sizable tunability of energy gaps by external electrical voltages, we observe the continuous transition of polariton Zitterbewegung from relativistic (small gaps) to nonrelativistic (large gaps) regimes. Our findings pave the way for using exciton polaritons in the emulation of relativistic quantum physics.

Enormous and Tunable Bulk Charge/Spin Photovoltaic Effect in Piezoelectric Binary Materials T-IV-VI and T-V-V

Understanding the nonlinear response of light and materials is crucial for fundamental physics and next-generation electronic devices. In this work, we have investigated the second-order nonlinear bulk photovoltaic (BPV) and bulk spin photovoltaic (BSPV) effects in the piezoelectric binary materials T-IV-VI and T-V-V (IV = Ge, Sn; VI = S, Se; and V = P, As, Sb, Bi). The independent nonzero conductivity tensors of charge current are derived for these binaries through the symmetry analysis, along with the mechanism for generating pure spin current. These binaries, with their unique folded structure, exhibit significant charge and spin currents under illumination. Furthermore, we find that strain engineering can effectively modulate charge/spin currents by influencing charge density distribution and built-in electric field due to the piezoelectric effect. Our research suggests that the piezoelectric binary materials possess enormous and tunable charge/spin currents, underscoring their potential for applications in nonlinear flexible optoelectronics and spintronics.

Ferroics in Hybrid Organic-Inorganic Perovskites: Fundamentals, Design Strategies, and Implementation

Hybrid organic-inorganic perovskites (HOIPs) afford highly versatile structure design and lattice dimensionalities; thus, they are actively researched as material platforms for the tailoring of ferroic behaviors. Unlike single-phase organic or inorganic materials, the interlayer coupling between organic and inorganic components in HOIPs allows the modification of strain and symmetry by chirality transfer or lattice distortion, thereby enabling the coexistence of ferroic orders. This review focuses on the principles for engineering one or multiple ferroic orders in HOIPs, and the conditions for achieving multiferroicity and magnetoelectric properties. The prospects of multilevel ferroic modulation, chiral spin textures, and spin orbitronics in HOIPs are also presented.

How to produce spin-splitting in antiferromagnetic materials

Antiferromagnetic (AFM) materials have potential advantages for spintronics due to their robustness, ultrafast dynamics, and magnetotransport effects. However, the missing spontaneous polarization and magnetization hinders the efficient utilization of electronic spin in these AFM materials. Here, we propose a simple way to produce spin-splitting in AFM materials by making the magnetic atoms with opposite spin polarization locating in the different environment (surrounding atomic arrangement), which does not necessarily require the presence of spin-orbital coupling. We confirm our proposal by four different types of two-dimensional AFM materials within the first-principles calculations. Our works provide an intuitional design principle to find or produce spin-splitting in AFM materials.

How spin relaxes and dephases in bulk halide perovskites

Spintronics in halide perovskites has drawn significant attention in recent years, due to their highly tunable spin-orbit fields and intriguing interplay with lattice symmetry. Here, we perform first-principles calculations to determine the spin relaxation time (T1) and ensemble spin dephasing time ([Formula: see text]) in a prototype halide perovskite, CsPbBr3. To accurately capture spin dephasing in external magnetic fields we determine the Landé g-factor from first principles and take it into account in our calculations. These allow us to predict intrinsic spin lifetimes as an upper bound for experiments, identify the dominant spin relaxation pathways, and evaluate the dependence on temperature, external fields, carrier density, and impurities. We find that the Fröhlich interaction that dominates carrier relaxation contributes negligibly to spin relaxation, consistent with the spin-conserving nature of this interaction. Our theoretical approach may lead to new strategies to optimize spin and carrier transport properties.

Exploring Chalcohalide Perovskite-Inspired Materials (Sn2SbX2I3; X = S or Se) for Optoelectronic and Spintronic Applications

Chalcohalide perovskite-inspired materials have attracted attention as promising optoelectronic materials due to their small band gaps, high defect tolerance, nontoxicity, and stability. However, a detailed analysis of their electronic structure and excited-state properties is lacking. Here, using state-of-the-art density functional theory, an effective k·p model analysis, and many-body perturbation theory (within the framework of GW and BSE), we explore the band splitting and excitonic properties of Sn2SbX2I3 (X = S or Se). Our findings reveal that the Cmc21 phase exhibits Rashba and Dresselhaus effects, causing significant band splitting, especially near the conduction and valence band extremes, respectively. Moreover, we find that the exciton binding energy is larger than those of lead halide perovskites but smaller than those of chalcogenide perovskites. We also investigate polaron-facilitated charge carrier mobility, which is found to be similar to that of lead halide perovskites and greater than that of chalcogenide perovskites. These characteristics make these materials promising for applications in spintronics and optoelectronics.

Persistent and Quasipersistent Spin Textures in Halide Perovskites Induced by Uniaxial Stress

Persistent spin textures are highly desirable for applications in spintronics, as they allow for long carrier spin lifetimes. However, they are also rare, as they require a delicate balance between spin-momentum coupling parameters. We used density functional theory simulations to predict the possibility of achieving these desirable spin textures through the application of uniaxial stress. Hybrid organic-inorganic perovskite MPSnBr3 (MP = CH3PH3) is a ferroelectric semiconductor which exhibits persistent spin textures near its conduction band minimum and mostly Rashba type spin textures in the vicinity of its valence band maximum. Application of uniaxial stress leads to the gradual evolution of the valence band spin textures from mostly Rashba type to quasipersistent ones under a tensile load and to pure Rashba or quasipersistent ones under a compressive load. The material exhibits flexibility, a rubber-like response, and both positive and negative piezoelectric constants. A combination of such properties may create opportunities for flexible and rubbery spintronic devices.

Dissipationless Circulating Currents and Fringe Magnetic Fields Near a Single Spin Embedded in a Two-Dimensional Electron Gas

Theoretical calculations predict the anisotropic dissipationless circulating current induced by a spin defect in a two-dimensional electron gas. The shape and spatial extent of these dissipationless circulating currents depend dramatically on the relative strengths of spin-orbit fields with differing spatial symmetry, offering the potential to use an electric gate to manipulate nanoscale magnetic fields and couple magnetic defects. The spatial structure of the magnetic field produced by this current is calculated and provides a direct way to measure the spin-orbit fields of the host, as well as the defect spin orientation, e.g., through scanning nanoscale magnetometry.

Topological quantum devices: a review

The introduction of the concept of topology into condensed matter physics has greatly deepened our fundamental understanding of transport properties of electrons as well as all other forms of quasi particles in solid materials. It has also fostered a paradigm shift from conventional electronic/optoelectronic devices to novel quantum devices based on topology-enabled quantum device functionalities that transfer energy and information with unprecedented precision, robustness, and efficiency. In this article, the recent research progress in topological quantum devices is reviewed. We first outline the topological spintronic devices underlined by the spin-momentum locking property of topology. We then highlight the topological electronic devices based on quantized electron and dissipationless spin conductivity protected by topology. Finally, we discuss quantum optoelectronic devices with topology-redefined photoexcitation and emission. The field of topological quantum devices is only in its infancy, we envision many significant advances in the near future.

Controlling Dzyaloshinskii-Moriya interaction in a centrosymmetric nonsymmorphic crystal

Presence of the Dzyaloshinskii-Moriya (DM) interaction in limited noncentrosymmetric materials leads to novel spin textures and exotic chiral physics. The emergence of DM interaction in centrosymmetric crystals could greatly enrich material realization. Here we show that an itinerant centrosymmetric crystal respecting a nonsymmorphic space group is a new platform for the DM interaction. Taking P4/nmm space group as an example, we demonstrate that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction induces the DM interactions, in addition to the Heisenberg exchange and the Kaplan-Shekhtman-Entin-wohlman-Aharony (KSEA) interaction. The direction of DM vector depends on the positions of magnetic atoms in the real space, and the amplitude depends on the location of the Fermi surface in the reciprocal space. The diversity stems from the position-dependent site groups and the momentum-dependent electronic structures guaranteed by the nonsymmorphic symmetries. Our study unveils the role of the nonsymmorphic symmetries in affecting magnetism, and suggests that the nonsymmorphic crystals can be promising platforms to design magnetic interactions.

Imprinting Spatial Helicity Structure of Vector Vortex Beam on Spin Texture in Semiconductors

We present the transfer of the spatially variant polarization of topologically structured light to the spatial spin texture in a semiconductor quantum well. The electron spin texture, which is a circular pattern with repeating spin-up and spin-down states whose repetition rate is determined by the topological charge, is directly excited by a vector vortex beam with a spatial helicity structure. The generated spin texture efficiently evolves into a helical spin wave pattern owing to the spin-orbit effective magnetic fields in the persistent spin helix state by controlling the spatial wave number of the excited spin mode. By tuning the repetition length and azimuthal angle, we simultaneously generate helical spin waves with opposite phases by a single beam.

Circularly Polarized Lasing from a Microcavity Filled with Achiral Single-Crystalline Microribbons

Organic circularly polarized (CP) lasers have received increasing attention due to their future photoelectric applications. Here, we demonstrate a CP laser from a pure organic crystal-filled microcavity without any chiral molecules or chiral structures. Benefited from the giant anisotropy and excellent laser gain of organic crystals, optical Rashba-Dresselhaus spin-orbit coupling effect can be induced and is conductive to the CP laser in such microcavities. The maximum dissymmetry factor of the CP lasing with opposite helicities reachs 1.2. Our strategy may provide a new idea for the design of CP lasers towards future 3D laser displays, information storage and other fields.

Coupled Spin-Valley, Rashba Effect, and Hidden Spin Polarization in WSi2N4 Family

Using first-principles calculations, we report the electronic properties with a special focus on the band splitting in the WSi₂N₄ class of materials. Due to the broken inversion symmetry and strong spin-orbit coupling, we detect coupled spin-valley effects at the corners of the first Brillouin zone (BZ). Additionally, we observe cubically and linearly split bands around the Γ and M points, respectively. The in-plane mirror symmetry (σ_h) and reduced symmetry of the arbitrary k-point, enforce the persistent spin textures (PST) to occur in full BZ. We induce the Rashba splitting by breaking the σ_h through an out-of-plane external electric field (EEF). The inversion asymmetric site point group of the W atom introduces the hidden spin polarization in centrosymmetric layered bulk counterparts. Low energy k.p models demonstrate that the PST along the M-K line is robust to EEF and layer thickness, making them suitable for applications in spintronics and valleytronics.

Circularly polarized electroluminescence from a single-crystal organic microcavity light-emitting diode based on photonic spin-orbit interactions

Circularly polarized (CP) electroluminescence from organic light-emitting diodes (OLEDs) has aroused considerable attention for their potential in future display and photonic technologies. The development of CP-OLEDs relies largely on chiral-emitters, which not only remain rare owing to difficulties in design and synthesis but also limit the performance of electroluminescence. When the polarization (pseudospin) degrees of freedom of a photon interact with its orbital angular momentum, photonic spin-orbit interaction (SOI) emerges such as Rashba-Dresselhaus (RD) effect. Here, we demonstrate a chiral-emitter-free microcavity CP-OLED with a high dissymmetry factor (g_EL) and high luminance by embedding a thin two-dimensional organic single crystal (2D-OSC) between two silver layers which serve as two metallic mirrors forming a microcavity and meanwhile also as two electrodes in an OLED architecture. In the presence of the RD effect, the SOIs in the birefringent 2D-OSC microcavity result in a controllable spin-splitting with CP dispersions. Thanks to the high emission efficiency and high carrier mobility of the OSC, chiral-emitter-free CP-OLEDs have been demonstrated exhibiting a high g_EL of 1.1 and a maximum luminance of about 60000 cd/m², which places our device among the best performing CP-OLEDs. This strategy opens an avenue for practical applications towards on-chip microcavity CP-OLEDs.

Modulated Rashba-Dresselhaus Spin-Orbit Coupling for Topology Control and Analog Simulations

We show theoretically that Rashba-Dresselhaus spin-orbit coupling (RDSOC) in lattices acts as a synthetic gauge field. This allows us to control both the phase and the magnitude of tunneling coefficients between sites, which is the key ingredient to implement topological Hamitonians and spin lattices useful for simulation perpectives. We use liquid crystal based microcavities in which RDSOC can be switched on and off as a model platform. We propose a realistic scheme for implementation of a Su-Schrieffer-Heeger chain in which the edge states existence can be tuned, and a Harper-Hofstadter model with a tunable contrasted flux for each (pseudo)spin component. We further show that a transverse-field Ising model and classical XY Hamiltonian with tunable parameters can be implemented, opening up prospects for analog physics, simulations, and optimization.

Totally Spin-Polarized Currents in an Interferometer with Spin-Orbit Coupling and the Absence of Magnetic Field Effects

The paper studies the electronic current in a one-dimensional lead under the effect of spin-orbit coupling and its injection into a metallic conductor through two contacts, forming a closed loop. When an external potential is applied, the time reversal symmetry is broken and the wave vector k of the circulating electrons that contribute to the current is spin-dependent. As the wave function phase depends upon the vector k, the closed path in the circuit produces spin-dependent current interference. This creates a physical scenario in which a spin-polarized current emerges, even in the absence of external magnetic fields or magnetic materials. It is possible to find points in the system's parameter space and, depending upon its geometry, the value of the Fermi energy and the spin-orbit intensities, for which the electronic states participating in the current have only one spin, creating a high and totally spin-polarized conductance. For a potential of a few tens of meV, it is possible to obtain a spin-polarized current of the order of μA. The properties of the obtained electronic current qualify the proposed device as a potentially important tool for spintronics applications.

Flying electron spin control gates

The control of "flying" (or moving) spin qubits is an important functionality for the manipulation and exchange of quantum information between remote locations on a chip. Typically, gates based on electric or magnetic fields provide the necessary perturbation for their control either globally or at well-defined locations. Here, we demonstrate the dynamic control of moving electron spins via contactless gates that move together with the spins. The concept is realized using electron spins trapped and transported by moving potential dots defined by a surface acoustic wave (SAW). The SAW strain at the electron trapping site, which is set by the SAW amplitude, acts as a contactless, tunable gate that controls the precession frequency of the flying spins via the spin-orbit interaction. We show that the degree of precession control in moving dots exceeds previously reported results for unconstrained transport by an order of magnitude and is well accounted for by a theoretical model for the strain contribution to the spin-orbit interaction. This flying spin gate permits the realization of an acoustically driven optical polarization modulator based on electron spin transport, a key element for on-chip spin information processing with a photonic interface.

Full-zone persistent spin textures with giant spin splitting in two-dimensional group IV-V compounds

Persistent spin texture (PST), a property of solid-state materials maintaining unidirectional spin polarization in the momentumk-space, offers a route to deliver the necessary long carrier spin lifetimes through the persistent spin helix (PSH) mechanism. However, most of the discovered PST locally occurred in the small part around certain high symmetryk-points or lines in the first Brillouin zone (FBZ), thus limiting the stability of the PSH state. Herein, by symmetry analysis and first-principles calculations, we report the emergence of full-zone PST (FZPST), a phenomenon displaying the PST in the whole FBZ, in the two-dimensional group IV-VA2B2(A= Si, Sn, Ge;B= Bi, Sb) compounds. Due to the existence of the in-plane mirror symmetry operation in the wave vector point group symmetry for the arbitraryk⃗in the whole FBZ, fully out-of-plane spin polarization is observed in thek-space, thus maintaining the FZPST. Importantly, we observed giant spin splitting in which the PST sustains, supporting large spin-orbit coupling parameters and small wavelengths of the PSH states. Ourk⃗⋅p⃗analysis demonstrated that the FZPST is robust for the non-degenerate bands, which can be effectively controlled by the application of an external electric field, thus offering a promising platform for future spintronic applications.

Magnetoelectric effects in Josephson junctions

The review is devoted to the fundamental aspects and characteristic features of the magnetoelectric effects, reported in the literature on Josephson junctions (JJs). The main focus of the review is on the manifestations of the direct and inverse magnetoelectric effects in various types of Josephson systems. They provide a coupling of the magnetization in superconductor/ferromagnet/superconductor JJs to the Josephson current. The direct magnetoelectric effect is a driving force of spin torques acting on the ferromagnet inside the JJ. Therefore it is of key importance for the electrical control of the magnetization. The inverse magnetoelectric effect accounts for the back action of the magnetization dynamics on the Josephson subsystem, in particular, making the JJ to be in the resistive state in the presence of the magnetization dynamics of any origin. The perspectives of the coupling of the magnetization in JJs with ferromagnetic interlayers to the Josephson current via the magnetoelectric effects are discussed.

Realizing Optical Persistent Spin Helix and Stern-Gerlach Deflection in an Anisotropic Liquid Crystal Microcavity

Spin-orbit interactions which couple the spin of a particle with its momentum degrees of freedom lie at the center of spintronic applications. Of special interest in semiconductor physics are Rashba and Dresselhaus spin-orbit coupling. When equal in strength, the Rashba and Dresselhaus fields result in SU(2) spin rotation symmetry and emergence of the persistent spin helix only investigated for charge carriers in semiconductor quantum wells. Recently, a synthetic Rashba-Dresselhaus Hamiltonian was shown to describe cavity photons confined in a microcavity filled with optically anisotropic liquid crystal. In this Letter, we present a purely optical realization of two types of spin patterns corresponding to the persistent spin helix and the Stern-Gerlach experiment in such a cavity. We show how the symmetry of the Hamiltonian results in spatial oscillations of the spin orientation of photons traveling in the plane of the cavity.

Impacts of Crystal Quality on Carrier Recombination and Spin Dynamics in (110)-Oriented GaAs/AlGaAs Multiple Quantum Wells at Room Temperature

We have systematically investigated the structural properties, carrier lifetimes, namely, photoluminescence (PL) lifetimes (τ_PL), and electron spin relaxation times (τ_s) in (110) GaAs/AlGaAs multiple quantum wells (MQWs) by using time-resolved PL measurements. The MQWs were grown by molecular beam epitaxy within a wide range of the growth temperature T_g (430–600 °C) and a high V/III flux ratio using As₂. At 530 °C < T_g < 580 °C, we found that the quality of the heterointerfaces is significantly improved, resulting in τ_PL~40 ns at RT, one order of magnitude longer than those reported so far. Long τ_s (~6 ns) is also observed at RT.

Highly persistent spin textures with giant tunable spin splitting in the two-dimensional germanium monochalcogenides

The ability to control the spin textures in semiconductors is a fundamental step toward novel spintronic devices, while seeking desirable materials exhibiting persistent spin texture (PST) remains a key challenge. The PST is the property of materials preserving a unidirectional spin orientation in the momentum space, which has been predicted to support an extraordinarily long spin lifetime of carriers. Herein, by using first-principles density functional theory calculations, we report the emergence of the PST in the two-dimensional (2D) germanium monochalcogenides (GeMC). By considering two stable formation of the 2D GeMC, namely the pure GeX and Janus Ge2XY monolayers (X, Y = S, Se, and Te), we observed the PST around the valence band maximum where the spin orientation is enforced by the lower point group symmetry of the crystal. In the case of the pure GeX monolayers, we found that the PST is characterized by fully out-of-plane spin orientation protected by C2v point group, while the canted PST in the y - z plane is observed in the case of the Janus Ge2XY monolayers due to the lowering symmetry into Cs point group. More importantly, we find large spin-orbit coupling (SOC) parameter in which the PST sustains, which could be effectively tuned by in-plane strain. The large SOC parameter observed in the present systems leads to the small wavelength of the spatially periodic mode of the spin polarization, which is promising for realization of the short spin channel in the spin Hall transistor devices.

Canted Persistent Spin Texture and Quantum Spin Hall Effect in WTe_{2}

We report an unconventional quantum spin Hall phase in the monolayer WTe_{2}, which exhibits hitherto unknown features in other topological materials. The low symmetry of the structure induces a canted spin texture in the yz plane, which dictates the spin polarization of topologically protected boundary states. Additionally, the spin Hall conductivity gets quantized (2e^{2}/h) with a spin quantization axis parallel to the canting direction. These findings are based on large-scale quantum simulations of the spin Hall conductivity tensor and nonlocal resistances in multiprobe geometries using a realistic tight-binding model elaborated from first-principle methods. The observation of this canted quantum spin Hall effect, related to the formation of topological edge states with nontrivial spin polarization, demands for specific experimental design and suggests interesting alternatives for manipulating spin information in topological materials.

Kondo effect under the influence of spin-orbit coupling in a quantum wire

The analysis of the impact of spin-orbit coupling (SOC) on the Kondo state has generated considerable controversy, mainly regarding the dependence of the Kondo temperatureTKon SOC strength. Here, we study the one-dimensional (1D) single impurity Anderson model (SIAM) subjected to Rashba (α) and Dresselhaus (β) SOC. It is shown that, due to time-reversal symmetry, the hybridization function between impurity and quantum wire is diagonal and spin independent (as it is the case for the zero-SOC SIAM), thus the finite-SOC SIAM has a Kondo ground state similar to that for the zero-SOC SIAM. This similarity allows the use of the Haldane expression forTK, with parameters renormalized by SOC, which are calculated through a physically motivated change of basis. Analytic results for the parameters of the SOC-renormalized Haldane expression are obtained, facilitating the analysis of the SOC effect overTK. It is found that SOC acting in the quantum wire exponentially decreasesTKwhile SOC at the impurity exponentially increases it. These analytical results are fully supported by calculations using the numerical renormalization group (NRG), applied to the wide-band regime, and the projector operator approach, applied to the infinite-Uregime. Literature results, using quantum Monte Carlo, for a system with Fermi energy near the bottom of the band, are qualitatively reproduced, using NRG. In addition, it is shown that the 1D SOC SIAM for arbitraryαandβdisplays a persistent spin helix SU(2) symmetry similar to the one for a 2D Fermi sea with the restrictionα=β.

Persistent Spin-texture and Ferroelectric Polarization in 2D Hybrid Perovskite Benzylammonium Lead-halide

Density functional theory calculations were performed for the electronic and the ferroelectric properties of the bulk and the monolayer benzylammonium lead-halide (BA₂PbCl₄). Our calculations indicate that both the bulk and monolayer systems display a band gap of ∼3.3 eV (HSE06+SOC) and a spontaneous polarization of ∼5.4 μC/cm². The similar physical properties of bulk and monolayer systems suggest a strong decoupling among the layers in this hybrid organic-inorganic perovskite. Both the ferroelectricity, through associated structure distortion, and the spin-orbit coupling, through splitting induced in the electronic bands, significantly influence the band gaps. Most importantly, we found for the first time in a two-dimensional hybrid organic-inorganic class of material, a peculiar spin texture topology such as a unidirectional spin-orbit field, which may lead to a protection against spin decoherence.

Effective Manipulation of Spin Dynamics by Polarization Electric Field in InGaN/GaN Quantum Wells at Room Temperature

III-nitride wide bandgap semiconductors are favorable materials for developing room temperature spintronic devices. The effective manipulation of spin dynamics is a critical request to realize spin field-effect transistor (FET). In this work, the dependence of the spin relaxation time on external strain-induced polarization electric field is investigated in InGaN/GaN multiple quantum wells (MQWs) by time-resolved Kerr rotation spectroscopy. Owing to the almost canceled two different spin-orbit coupling (SOC), the spin relaxation time as long as 311 ps in the MQWs is obtained at room temperature, being much longer than that in bulk GaN. Furthermore, upon applying an external uniaxial strain, the spin relaxation time decreases sensitively, which originates from the breaking of the SU(2) symmetry. The extracted ratio of the SOC coefficients shows a linear dependence on the external strain, confirming the essential role of the polarization electric field. This effective manipulation of the spin relaxation time sheds light on GaN-based nonballistic spin FET working at room temperature.

Symmetry indicators of band topology

Topological materials are quantum materials with nontrivial ground-state entanglement that are irremovable so long as certain rules, like invariance under symmetries and the existence of an energy gap, are respected. They showcase unconventional properties like robust anomalous surface states and quantized physical responses. The intense research efforts in understanding topological materials result in a modernized perspective on the decades-old theory of symmetry representations in electronic band structures, and inspire the development of general theories that enable the efficient diagnosis of topological materials using only symmetry data. One example is the theory of symmetry indicators of band topology, which is the focus of this topical review. We will aim at providing a pedagogical introduction to the key concepts and constructions in the theory, alongside with a brief summary of the latest development.

Resistive State of Superconductor-Ferromagnet-Superconductor Josephson Junctions in the Presence of Moving Domain Walls

We describe resistive states of the system combining two types of orderings-a superconducting and a ferromagnetic one. It is shown that in the presence of magnetization dynamics such systems become inherently dissipative and in principle cannot sustain any amount of the superconducting current because of the voltage generated by the magnetization dynamics. We calculate generic current-voltage characteristics of a superconductor-ferromagnet-superconductor Josephson junction with an unpinned domain wall and find the low-current resistance associated with the domain wall motion. We suggest the finite slope of Shapiro steps as the characteristic feature of the regime with domain wall oscillations driven by the ac external current flowing through the junction.

Engineering spin-orbit synthetic Hamiltonians in liquid-crystal optical cavities

Spin-orbit interactions lead to distinctive functionalities in photonic systems. They exploit the analogy between the quantum mechanical description of a complex electronic spin-orbit system and synthetic Hamiltonians derived for the propagation of electromagnetic waves in dedicated spatial structures. We realize an artificial Rashba-Dresselhaus spin-orbit interaction in a liquid crystal–filled optical cavity. Three-dimensional tomography in energy-momentum space enabled us to directly evidence the spin-split photon mode in the presence of an artificial spin-orbit coupling. The effect is observed when two orthogonal linear polarized modes of opposite parity are brought near resonance. Engineering of spin-orbit synthetic Hamiltonians in optical cavities opens the door to photonic emulators of quantum Hamiltonians with internal degrees of freedom.

Dynamical Spin-Orbit Coupling of a Quantum Gas

We realize the dynamical 1D spin-orbit coupling (SOC) of a Bose-Einstein condensate confined within an optical cavity. The SOC emerges through spin-correlated momentum impulses delivered to the atoms via Raman transitions. These are effected by classical pump fields acting in concert with the quantum dynamical cavity field. Above a critical pump power, the Raman coupling emerges as the atoms superradiantly populate the cavity mode with photons. Concomitantly, these photons cause a backaction onto the atoms, forcing them to order their spin-spatial state. This SOC-inducing superradiant Dicke phase transition results in a spinor-helix polariton condensate. We observe emergent SOC through spin-resolved atomic momentum imaging and temporal heterodyne measurement of the cavity-field emission. Dynamical SOC in quantum gas cavity QED, and the extension to dynamical gauge fields, may enable the creation of Meissner-like effects, topological superfluids, and exotic quantum Hall states in coupled light-matter systems.

Unidirectional Spin-Orbit Interaction Induced by the Line Defect in Monolayer Transition Metal Dichalcogenides for High-Performance Devices

Spin-orbit (SO) interaction is an indispensable element in the field of spintronics for effectively manipulating the spin of carriers. However, in crystalline solids, the momentum-dependent SO effective magnetic field generally results in spin randomization by a process known as the Dyakonov-Perel spin relaxation, leading to the loss of spin information. To overcome this obstacle, the persistent spin helix (PSH) state with a unidirectional SO field was proposed but difficult to achieve in real materials. Here, on the basis of first-principles calculations and tight-binding model analysis, we report for the first time a unidirectional SO field in monolayer transition metal dichalcogenides (TMDs, MX₂, M = Mo, W; and X = S, Se) induced by two parallel chalcogen vacancy lines. By changing the relative positions of the two vacancy lines, the direction of the SO field can be tuned from x to y. Moreover, using k·p perturbation theory and group theory analysis, we demonstrate that the emerging unidirectional SO field is subject to both the structural symmetry and 1D nature of such defects engineered in 2D TMDs. In particular, through transport calculations, we confirm that the predicted SO states carry highly coherent spin current. Our findings shed new light on creating PSH states for high-performance spintronic devices.

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

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

Modified exchange interaction between magnetic impurities in spin-orbit coupled quantum wires

Indirect exchange interaction between magnetic impurities in one dimensional systems is a matter of long discussions since Kittel has established that in the asymptotic limit it decays as the inverse of distance x between the impurities. In this work we investigate this problem in a quantum wire with Rashba spin-orbit coupling (SOC). By employing a second order perturbation theory we find that one additional oscillatory term appears in each of the Ruderman-Kittel-Kasuya-Yosida (RKKY), the Dzaloshinkii-Moryia and the Ising couplings. Remarkably, these extra terms resulting from the spin precession of the conduction electrons induced by the SOC do not decay as in the usual RKKY interaction. We show that these extra oscillations arise from the finite momenta band splitting induced by the spin-orbit coupling that modifies the spin-flip scatterings occurring at the Fermi energy. Our findings open up a new perspective in the long-distance magnetic interactions in solid state systems.

Unique Spin Vortices and Topological Charges in Quantum Dots with Spin-orbit Couplings

Spin textures of one or two electrons in a quantum dot with Rashba or Dresselhaus spin-orbit couplings reveal several intriguing properties. We show here that even at the single-electron level stable spin vortices with tunable topological charges exist. These topological textures appear in the ground state of the dots. The textures are stabilized by time-reversal symmetry breaking and are robust against the eccentricity of the dot. The topological charge is directly related to the sign of the z component of the spin in a large dot, allowing a direct probe of its topological properties. This would clearly pave the way to possible future topological spintronics. The phenomenon of spin vortices persists for the interacting two-electron dot in the presence of a magnetic field.

Quantum Spin Dynamics in a Normal Bose Gas with Spin-Orbit Coupling

In this Letter, we investigate spin dynamics of a two-component Bose gas with spin-orbit coupling realized in cold atom experiments. We derive coupled hydrodynamic equations for number and spin densities as well as their associated currents. Specializing to the quasi-one-dimensional situation, we obtain analytic solutions of the spin helix structure and its dynamics in both adiabatic and diabatic regimes. In the adiabatic regime, the transverse spin decays parabolically in the short-time limit and exponentially in the long-time limit, depending on initial polarization. In contrast, in the diabatic regime, transverse spin density and current oscillate in a way similar to the charge-current oscillation in an undamped LC circuit. The effects of Rabi coupling on the short-time spin dynamics is also discussed. Finally, using realistic experimental parameters for ^{87}Rb, we show that the timescales for spin dynamics is of the order of milliseconds to a few seconds and can be observed experimentally.

Persistent spin texture enforced by symmetry

Persistent spin texture (PST) is the property of some materials to maintain a uniform spin configuration in the momentum space. This property has been predicted to support an extraordinarily long spin lifetime of carriers promising for spintronics applications. Here, we predict that there exists a class of noncentrosymmetric bulk materials, where the PST is enforced by the nonsymmorphic space group symmetry of the crystal. Around certain high symmetry points in the Brillouin zone, the sublattice degrees of freedom impose a constraint on the effective spin-orbit field, which orientation remains independent of the momentum and thus maintains the PST. We illustrate this behavior using density-functional theory calculations for a handful of promising candidates accessible experimentally. Among them is the ferroelectric oxide BiInO3-a wide band gap semiconductor which sustains a PST around the conduction band minimum. Our results broaden the range of materials that can be employed in spintronics.

Quantum anomalous Hall effect and topological phase transition in two-dimensional antiferromagnetic Chern insulator NiOsCl6

By doing calculations based on density functional theory, we predict that the two-dimensional anti-ferromagnetic (AFM) NiOsCl₆ as a Chern insulator can realize the quantum anomalous Hall (QAH) effect. We investigate the magnetocrystalline anisotropy energies in different magnetic configurations and the Néel AFM configuration is proved to be ground state. When considering spin-orbit coupling (SOC), this layered material with spins perpendicular to the plane shows properties as a Chern insulator characterized by an inversion band structure and a nonzero Chern number. The nontrivial band gap is 37 meV and the Chern number C  =  -1, which are induced by a strong SOC and AFM order. With strong SOC, the NiOsCl₆ system performs a continuous topological phase transition from the Chern insulator to the trivial insulator upon the increasing Coulomb repulsion U. The critical U _c is indicated as 0.23 eV, at which the system is in a metallic phase with [Formula: see text]. Upon increasing U, the E _g reduces linearly with C  =  -1 for 0  <  U  <  U _c and increases linearly with C  =  0 for U  >  U _c . At last we analysis the QAH properties and this continuous topological phase transition theoretically in a two-band [Formula: see text] model. This AFM Chern insulator NiOsCl₆ proposes not only a promising way to realize the QAH effect, but also a new material to study the continuous topological phase transition.

Spin-helix Larmor mode

A two-dimensional electron gas (2DEG) with equal-strength Rashba and Dresselhaus spin-orbit coupling sustains persistent helical spin-wave states, which have remarkably long lifetimes. In the presence of an in-plane magnetic field, there exist single-particle excitations that have the character of propagating helical spin waves. For magnon-like collective excitations, the spin-helix texture reemerges as a robust feature, giving rise to a decoupling of spin-orbit and electronic many-body effects. We prove that the resulting spin-flip wave dispersion is the same as in a magnetized 2DEG without spin-orbit coupling, apart from a shift by the spin-helix wave vector. The precessional mode about the persistent spin-helix state is shown to have an energy given by the bare Zeeman splitting, in analogy with Larmor’s theorem. We also discuss ways to observe the spin-helix Larmor mode experimentally.

Drift-Induced Enhancement of Cubic Dresselhaus Spin-Orbit Interaction in a Two-Dimensional Electron Gas

We investigated the effect of an in-plane electric field on drifting spins in a GaAs quantum well. Kerr rotation images of the drifting spins revealed that the spin precession wavelength increases with increasing drift velocity regardless of the transport direction. A model developed for drifting spins with a heated electron distribution suggests that the in-plane electric field enhances the effective magnetic field component originating from the cubic Dresselhaus spin-orbit interaction.

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

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

Anisotropy and Suppression of Spin-Orbit Interaction in a GaAs Double Quantum Dot

The spin-flip tunneling rates are measured in GaAs-based double quantum dots by time-resolved charge detection. Such processes occur in the Pauli spin blockade regime with two electrons occupying the double quantum dot. Ways are presented for tuning the spin-flip tunneling rate, which on the one hand gives access to measuring the Rashba and Dresselhaus spin-orbit coefficients. On the other hand, they make it possible to turn on and off the effect of spin-orbit interaction with a high on/off ratio. The tuning is accomplished by choosing the alignment of the tunneling direction with respect to the crystallographic axes, as well as by choosing the orientation of the external magnetic field with respect to the spin-orbit magnetic field. Spin lifetimes of 10 s are achieved at a tunneling rate close to 1 kHz.

Solution of the Lindblad equation for spin helix states

Using Lindblad dynamics we study quantum spin systems with dissipative boundary dynamics that generate a stationary nonequilibrium state with a nonvanishing spin current that is locally conserved except at the boundaries. We demonstrate that with suitably chosen boundary target states one can solve the many-body Lindblad equation exactly in any dimension. As solution we obtain pure states at any finite value of the dissipation strength and any system size. They are characterized by a helical stationary magnetization profile and a ballistic spin current which is independent of system size, even when the quantum spin system is not integrable. These results are derived in explicit form for the one-dimensional spin-1/2 Heisenberg chain and its higher-spin generalizations, which include the integrable spin-1 Zamolodchikov-Fateev model and the biquadratic Heisenberg chain.

Anderson Transition of Cold Atoms with Synthetic Spin-Orbit Coupling in Two-Dimensional Speckle Potentials

We investigate the metal-insulator transition occurring in two-dimensional (2D) systems of noninteracting atoms in the presence of artificial spin-orbit interactions and a spatially correlated disorder generated by laser speckles. Based on a high order discretization scheme, we calculate the precise position of the mobility edge and verify that the transition belongs to the symplectic universality class. We show that the mobility edge depends strongly on the mixing angle between Rashba and Dresselhaus spin-orbit couplings. For equal couplings a non-power-law divergence is found, signaling the crossing to the orthogonal class, where such a 2D transition is forbidden.

Universal modeling of weak antilocalization corrections in quasi-two-dimensional electron systems using predetermined return orbitals

We have developed a method to calculate the weak localization and antilocalization corrections based on the real-space simulation, where we provide 147 885 predetermined return orbitals of quasi-two-dimensional electrons with up to 5000 scattering events that are repeatedly used. Our model subsumes that of Golub [L. E. Golub, Phys. Rev. B 71, 235310 (2005)PRBMDO1098-012110.1103/PhysRevB.71.235310] when the Rashba spin-orbit interaction (SOI) is assumed. Our computation is very simple, fast, and versatile, where the numerical results, obtained all at once, cover wide ranges of the magnetic field under various one-electron interactions H^{'} exactly. Thus, it has straightforward extensibility to incorporate interactions other than the Rashba SOI, such as the linear and cubic Dresselhaus SOIs, Zeeman effect, and even interactions relevant to the valley and pseudo spin degrees of freedom, which should provide a unique tool to study new classes of materials like emerging 2D materials. Using our computation, we also demonstrate the robustness of a persistent spin helix state against the cubic Dresselhaus SOI.