Rashba Systems Research Articles

Phase diagram of strongly-coupled Rashba systems

Abstract Motivated by the recent discovery of a possible field-mediated parity switch within the superconducting state of CeRh2As2 [Khim et al., Science 373, 1012 (2021)], we thoroughly investigate the dependence of the superconducting state of a strongly-coupled Rashba mono- and bilayer on internal parameters and an applied magnetic field. The role of interlayer pairing, spin orbit coupling, doping rate and applied magnetic field and their interplay was examined numerically at low temperature within a t-J-like model, uncovering complex phase diagrams and transitions between superconducting states with different symmetry.

Hexagonal warping effects on Bloch oscillations in proximitized Rashba systems

Bloch oscillations (BOs) in Rashba systems, taking into account the effects of hexagonal warping and proximity-induced band gap, are reported. We find that in addition to real-space trajectories, the group and Berry velocities of Bloch electrons exhibit novel BOs which strongly depend on the crystal momentum. This oscillatory motion is affected significantly by variations in the strength of hexagonal warping and the proximity-induced band gap, originating from the substantial changes in the energy spectrum induced by these factors. In addition, it is shown that the Bloch oscillations are modified considerably under the influence of applied uniform in-plane electric and transverse magnetic fields, which allow for a geometric visualization of the Bloch dynamics. Interestingly, when the system is subjected to these fields simultaneously, it undergoes a dynamic phase transition between confined and de-confined states. This phase transition is tuned by the relative strength of the applied fields and is further influenced by variations in the strength of hexagonal warping and proximity-induced band gap. The appearance of such a transition is attributed to the interplay between the external fields and the intrinsic properties of the crystal lattice. Moreover, we find that the direct-current drift velocity shows negative differential conductivity, which is a characteristic feature of the BO regime.

Variety of Mechanically Induced Spin Currents in Rashba Systems

Various types of spin currents, including unconventional types, are generated in Rashba spin-orbit coupled systems by dynamic lattice distortions associated with, for example, surface acoustic waves.

Spin Hall effect modulated by an electric field in asymmetric two-dimensional MoSiAs2Se.

Spin current generation from charge current in nonmagnetic materials promises an energy-efficient scheme for manipulating magnetization in spintronic devices. In some asymmetric two-dimensional (2D) materials, the Rashba and valley effects coexist owing to strong spin-orbit coupling (SOC), which induces the spin Hall effect due to spin-momentum locking of both effects. Herein, we propose a new Janus structure MoSiAs2Se with both valley physics and the Rashba effect and reveal an effective way to modulate the properties of this structure. The results demonstrated that applying an external electric field is an effective means to modulating the electronic properties of MoSiAs2Se, leading to both type I-II phase transitions and semiconductor-metal phase transitions. Furthermore, the coexistence of the Rashba and valley effects in monolayer MoSiAs2Se contributes to the spin Hall effect (SHE). The magnitude and direction of spin Hall conductivity can also be manipulated with an out-of-plane electric field. Our results enrich the physics and materials of the Rashba and valley systems, opening new opportunities for the applications of 2D Janus materials in spintronic devices.

Biaxial strain modulated electronic structures of layered two-dimensional MoSiGeN4 Rashba systems.

The two-dimensional (2D) MA2Z4 family has received extensive attention in manipulating its electronic structure and achieving intriguing physical properties. However, engineering the electronic properties remains a challenge. Herein, based on first-principles calculations, we systematically investigate the effect of biaxial strains on the electronic structure of 2D Rashba MoSiGeN4 (MSGN), and further explore how the interlayer interactions affect the Rashba spin splitting (RSS) in such strained layered MSGN systems. After applying biaxial strains, the band gap decreases monotonically with increasing tensile strains but increases when the compressive strains are applied. An indirect-direct-indirect band gap transition is induced by applying a moderate compressive strain (<5%) in the MSGN systems. Due to the symmetry breaking and moderate spin-orbit coupling (SOC), the monolayer MSGN possesses an isolated RSS near the Fermi level, which could be effectively regulated to the Lifshitz-type spin splitting (LSS) by biaxial strain. For instance, the LSS ← RSS → LSS transformation of the Fermi surface is presented in the monolayer and a more complex and changeable LSS ← RSS → LSS → RSS evolution is observed in bilayer and trilayer MSGN systems as the biaxial strain varies from -8% to 12%, which actually depends on the appearance, variation, and vanish of the Mexican hat band in the absence of SOC under different strains. The contribution of the Mo-dz2 orbital hybridized with the N-pz orbital in the highest valence band plays a dominant role in band evolution under biaxial strains, where the RSS → LSS evolution corresponds to the decreased Mo-dz2 orbital contribution. Our study highlights the biaxial strain controllable RSS, in particular the introduction and even the evolution of LSS near the Fermi surface, which makes the strained MSGN systems promising candidates for future applications in spintronic devices.

Microscopic Analysis of Lattice Distortion Effects in Rashba Systems

Microscopic Analysis of Lattice Distortion Effects in Rashba Systems

Nonlinear Hall effect in Rashba systems with hexagonal warping

Rashba spin-orbit coupled systems are an important class of materials noted for diverse fundamental and applied phenomena. Recently, the emergence of non-linear Hall effect under conditions of time-reversal symmetry has been discovered in materials with broken inversion symmetry. In this work, we study the second- and third-order Hall response in Rashba systems with hexagonal warping. Starting with a low-energy model, we obtain the analytic expressions and discover the unique dipole profile in Rashba systems with hexagonal warping. Furthermore, we extend the analysis using a realistic tight-binding model. Next, we predict the existence of a third-order Hall effect in these systems, and calculate the Berry connection polarizability tensor analytically. We also show how the model parameters affect the third-order conductivity. Our predictions can help in the experimental realization of Berry curvature multipole physics in Rashba materials with hexagonal warping, and provide a new platform for engineering the non-linear Hall effects.

A toy model for dichroism in angle resolved photoemission

Angle-resolved photoemission spectroscopy (ARPES) measures the interference of dipole allowed Coulomb wavelets from the individual orbital emitters that contribute to an electronic band. If Coulomb scattering of the outgoing electron is neglected, this Huygens view of ARPES simplifies to a Fraunhofer diffraction experiment, and the relevant cross-sections to orbital Fourier transforms. This plane wave approximation (PWA) is surprisingly descriptive of photoelectron distributions, but fails to reproduce kinetic energy dependent final state effects like dichroism. Yet, Huygens principle of ARPES can be parsimoniously adapted to allow for distortion and phase shift of the outgoing Coulomb wave. This retains the strong physical intuition and low computational cost of the PWA, but naturally captures momentum dependent interference phenomena that so far required relativistic one-step modeling, such as linear dichroism in Rashba systems BiAg2 and AgTe.

Direct visualization of Rashba-split bands and spin/orbital-charge interconversion at KTaO3 interfaces

Rashba interfaces have emerged as promising platforms for spin-charge interconversion through the direct and inverse Edelstein effects. Notably, oxide-based two-dimensional electron gases display a large and gate-tunable conversion efficiency, as determined by transport measurements. However, a direct visualization of the Rashba-split bands in oxide two-dimensional electron gases is lacking, which hampers an advanced understanding of their rich spin-orbit physics. Here, we investigate KTaO3 two-dimensional electron gases and evidence their Rashba-split bands using angle resolved photoemission spectroscopy. Fitting the bands with a tight-binding Hamiltonian, we extract the effective Rashba coefficient and bring insight into the complex multiorbital nature of the band structure. Our calculations reveal unconventional spin and orbital textures, showing compensation effects from quasi-degenerate band pairs which strongly depend on in-plane anisotropy. We compute the band-resolved spin and orbital Edelstein effects, and predict interconversion efficiencies exceeding those of other oxide two-dimensional electron gases. Finally, we suggest design rules for Rashba systems to optimize spin-charge interconversion performance.

The Giant Spin-to-Charge Conversion of the Layered Rashba Material BiTeI.

Rashba spin-orbit coupling (SOC) could facilitate an efficient interconversion between spin and charge currents. Among various systems, BiTeI holds one of the largest Rashba-type spin splittings. Unlike other Rashba systems (e.g., Bi/Ag and Bi2Se3), an experimental investigation of the spin-to-charge interconversion in BiTeI remains to be explored. Through performing an angle-resolved photoemission spectroscopy (ARPES) measurement, such a large Rashba-type spin splitting with a Rashba parameter αR = 3.68 eV Å is directly identified. By studying the spin pumping effect in the BiTeI/NiFe bilayer, we reveal a very large inverse Rashba-Edelstein length λIREE ≈ 1.92 nm of BiTeI at room temperature. Furthermore, the λIREE monotonously increases to 5.00 nm at 60 K, indicating an enhanced Rashba SOC at low temperature. These results suggest that BiTeI films with the giant Rashba SOC are promising for achieving efficient spin-to-charge interconversion, which could be implemented for building low-power-consumption spin-orbitronic devices.

Evidence of the nontrivial Berry phase at γ -Al2O3/SrTiO3 heterointerfaces

The nontrivial Berry phase in correlated oxide heterostructures has been highly attractive due to the Rashba spin–orbit interactions originating from the inversion symmetry breaking at the heterointerfaces. Despite the theoretically predicated nontrivial π Berry phase in Rashba systems, its experimental detection among all Rashba oxide interfaces remains elusive. Here, we report a nontrivial Berry phase at the interface between γ-Al2O3 and SrTiO3 as evidenced by the quantum oscillations. Analysis of transport properties under the high magnetic field up to 32 T reveals the weak anti-localization (WAL) effect and Shubnikov–de Haas (SdH) oscillations. Both the WAL effect and the nontrivial π Berry phase extracted from the SdH oscillations manifest the significance of the Rashba spin–orbit coupling in γ-Al2O3/SrTiO3. Physical quantities concerning the Fermi surface, such as effective mass, scattering time, etc., are experimentally accessed as well. Our work provides insights into the nontrivial Berry phase in correlated oxide interfaces.

Geometric origin of intrinsic spin hall effect in an inhomogeneous electric field

In recent years, the spin Hall effect has received great attention because of its potential application in spintronics and quantum information processing and storage. However, this effect is usually studied under the external homogeneous electric field. Understanding how the inhomogeneous electric field affects the spin Hall effect is still lacking. Here, we investigate a two-dimensional two-band time-reversal symmetric system and give an expression for the intrinsic spin Hall conductivity in the presence of the inhomogeneous electric field, which is shown to be expressed through the geometric quantities: quantum metric and interband Berry connection. We show that for Rashba and Dresselhaus systems, the inhomogeneous intrinsic spin Hall conductivity can be tuned with the Fermi energy. On the other hand, when people get physical intuition on transport phenomena from the wave packet, one issue appears. It is shown that the conductivity obtained from the conventional wave packet approach cannot be fully consistent with the one predicted by the Kubo-Greenwood formula. Here, we attempt to solve this problem.

Magnus spin Hall and spin Nernst effects in gapped two-dimensional Rashba systems

We study the Magnus transport in a gapped two-dimensional electron gas with Rashba spin-orbit coupling using semiclassical Boltzmann transport formalism. Apart from its signature in the charge transport coefficients, the inclusion of Magnus velocity in the spin current operator enables us to study Magnus spin transport in the system. In particular, we study the roles of mass gap and Fermi surface topology on the behavior of Magnus Hall and Nernst conductivities and their spin counterparts. We find that the Magnus spin Hall conductivity vanishes in the limit of zero gap, unlike the universal spin Hall conductivity ${\ensuremath{\sigma}}_{s}=e/(8\ensuremath{\pi})$. The Magnus spin currents with spin polarization perpendicular to the applied bias (electrical/thermal) are finite while with polarization along the bias vanishes. Each Magnus conductivity displays a plateau as Fermi energy sweeps through the gap and has peaks (whose magnitudes decrease with the gap) when the Fermi energy is at the gap edges.

Designing Rashba systems for high thermoelectric performance based on the van der Waals heterostructure

The electronic structures of semiconductors and their related transport properties can be tuned via the Rashba effect, which improves thermoelectric performance. The Rashba effect is caused by spin–orbit coupling and breaking of inversion symmetry. Here, we engineer the Rashba effect by constructing two-dimensional (2D) van der Waals heterostructures (vdWHs) Sb/As and Bi/Sb. These break the z-inversion symmetry by removing the reflection along the z-direction, affording Rashba splitting at the top of the valence band. The resulting complex energy bands exhibit enhanced electronic density of states near the band edge and maintain the electrical conductivity. The Sb/As heterostructure has Seebeck coefficients 1.5 times larger than those of the corresponding monolayers, and the Bi/Sb system has an enhanced Seebeck coefficient at high carrier concentrations. Our work demonstrates that 2D vdWHs can be used to induce Rashba splitting with band structure changes that yield favorable thermoelectric properties. This offers a new strategy for designing novel 2D functional materials.

Fluctuating spin-orbital texture of Rashba-split surface states in real and reciprocal space

Spin-orbit interaction (SOI) in low-dimensional systems, namely Rashba systems and the edge states of topological materials, is extensively studied in this decade as a promising source to realize various fascinating spintronic phenomena, such as the source of the spin current and spin-mediated energy conversion. Here, we show the odd fluctuation in the spin-orbital texture in a surface Rashba system on Bi/InAs(110)-(2$\times$1) by spin- and angle-resolved photoelectron spectroscopy and a numerical simulation based on a density-functional theory (DFT) calculation. The surface state shows a paired parabolic dispersion with the spin degeneracy lifted by the Rashba effect. Although its spin polarization should be fixed in a particular direction based on the Rashba model, the observed spin polarization varies greatly and even reverses its sign depending on the wavenumber. DFT calculations also reveal that the spin directions of two inequivalent Bi chains on the surface change from nearly parallel (canted-parallel) to anti-parallel in real space in the corresponding wavevector region. These results point out an oversimplification of the nature of spin in Rashba and Dirac systems and provide more freedom than expected for spin manipulation of photoelectrons.

Helicity current generation by distorted Rashba coupling

We theoretically study spin transport in two-or three-dimensional Rashba systems dynamically distorted by surface acoustic waves. The spin currents in the linear response to lattice distortion dynamics are calculated on the basis of a microscopic theory combined with local coordinate transformations. As a result, we find a mechanism of direct spin-current generation from lattice distortion not associated with a charge current or spin accumulation. Moreover, the in-plane helicity currents are generated by shear surface acoustic waves via the present mechanism. The generated helicity currents are not parallel to the vorticity of the lattice, and cannot be created with the conventional methods. Thus, our findings offer an alternative functionality of the conventional Rashba systems in the field of spintronics.

Acoustic Rashba–Edelstein effect

We theoretically study the mechanical induction of the spin density via the Rashba spin–orbit interaction (SOI). The spin density in the linear response to lattice distortion dynamics is calculated based on the microscopic theory. We reveal that there are two mechanisms of spin induction: one is the acoustic Edelstein effect (AEE) from the acceleration of the lattice dynamics and the other is caused by the Rashba spin–vorticity coupling (RSVC). We find that the AEE induces a more efficient spin-to-charge conversion in comparison with the conventional electric Edelstein effect. The induced spin density due to the RSVC can be attributed to the spatial symmetry breaking due to the Rashba SOI. Our work demonstrates high-efficiency spin generation in Rashba systems.

Giant Rashba-like spin–orbit splitting with distinct spin texture in two-dimensional heterostructures* *Project supported by the Science Fund from the Ministry of Science and Technology of China (Grant Nos. 2017YFA0204904 and 2019YFA0210004), the National Natural Science Foundation of China (Grant Nos. 11674299 and 11634011), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB30000000), the Fund of

Based on first-principles density functional theory calculation, we discover a novel form of spin-orbit (SO) splitting in two-dimensional (2D) heterostructures composed of a single Bi(111) bilayer stacking with a 2D semiconducting In2Se2 or a 2D ferroelectric α-In2Se3 layer. Such SO splitting has a Rashba-like but distinct spin texture in the valence band around the maximum, where the chirality of the spin texture reverses within the upper spin-split branch, in contrast to the conventional Rashba systems where the upper branch and lower branch have opposite chirality solely in the region below the band crossing point. The ferroelectric nature of α-In2Se3 further enables the tuning of the spin texture upon the reversal of the electric polarization with the application of an external electric field. Detailed analysis based on a tight-binding model reveals that such SO splitting texture results from the interplay of complex orbital characters and substrate interaction. This finding enriches the diversity of SO splitting systems and is also expected to promise for spintronic applications.

Generation of Current Vortex by Spin Current in Rashba Systems

Employing unbiased large-scale time-dependent density-matrix renormalization-group simulations, we demonstrate the generation of a charge-current vortex via spin injection in the Rashba system. The spin current is polarized perpendicular to the system plane and injected from an attached antiferromagnetic spin chain. We discuss the conversion between spin and orbital angular momentum in the current vortex that occurs because of the conservation of the total angular momentum and the spin-orbit interaction. This is in contrast to the spin Hall effect, in which the angular-momentum conservation is violated. Finally, we predict the electromagnetic field that accompanies the vortex with regard to possible future experiments.

Role of Berry curvature in the generation of spin currents in Rashba systems

We study the background (equilibrium), linear and nonlinear spin currents in 2D Rashba spin-orbit coupled systems with Zeeman splitting and in 3D noncentrosymmetric metals using modified spin current operator by inclusion of the anomalous velocity. The linear spin Hall current arises due to the anomalous velocity of charge carriers induced by the Berry curvature. The nonlinear spin current occurs due to the band velocity and/or the anomalous velocity. For 2D Rashba systems, the background spin current saturates at high Fermi energy (independent of the Zeeman coupling), linear spin current exhibits a plateau at the Zeeman gap and nonlinear spin currents are peaked at the gap edges. The magnitude of the nonlinear spin current peaks enhances with the strength of Zeeman interaction. The linear spin current is polarized out of plane, while the nonlinear ones are polarized in-plane. We witness pure anomalous nonlinear spin current with spin polarization along the direction of propagation. In 3D noncentrosymmetric metals, background and linear spin currents are monotonically increasing functions of Fermi energy, while nonlinear spin currents vary non-monotonically as a function of Fermi energy and are independent of the Berry curvature. These findings may provide useful information to manipulate spin currents in Rashba spin-orbit coupled systems.