Rashba Spin-orbit Coupling Research Articles

Polaron induced local spin texture and anomalous Hall effect in the quadrilateral prism-shaped nanotube with Rashba and Dresselhaus spin–orbit coupling

We theoretically study the spin-texture dynamics and the transverse asymmetric charge deflection induced by the polaron in a quadrilateral prism-shaped nanotube with the Rashba and Dresselhaus spin–orbit coupling (SOC). We reveal the polaron gives rise to the nontrivial local spin textures in the nanotube within the cross section plane. The spins demonstrate oscillations and the oscillating patterns are dependent on the SOC type. For the nanotube containing a segment of the ferromagnetic domain, the sizable asymmetric charge deflections could additionally take place, namely, the anomalous Hall effect. The amount of the deflected charges is determined by the strength and orientations of the ferromagnetic magnetization as well as the SOC type. The work provides a valuable insight of the coherent transport of polaron through a quasi-one-dimensional nanotube with Rashba and Dresselhaus SOC and open avenues for the potential device applications.

Emergence of Sizeable Interfacial Dzyaloshinskii-Moriya Interaction at Cobalt/Fullerene Interface

The interfacial Dzyaloshinskii-Moriya interaction (iDMI) originating from a heavy-metal/ferromagnet (FM) interface plays a crucial role in stabilizing chiral spin textures in magnetic multilayers. Recently, graphene based on the low-spin-orbit-coupling (SOC) element carbon ($\mathrm{C}$) has shown a significant iDMI owing to the Rashba SOC when deposited on top of $\mathrm{Co}$. A similar enhanced SOC has been reported earlier for other $\mathrm{C}$ allotropes, namely fullerene (${\text{C}}_{60}$) and carbon nanotubes, and a sizeable DMI can be expected to emerge from them. In this context, we elucidate the magnetization-reversal mechanism, the domain-wall (DW) dynamics, and the strength of the iDMI in a $\mathrm{Pd}(4.0\phantom{\rule{0.2em}{0ex}}\mathrm{nm})/\mathrm{Co}(0.5\phantom{\rule{0.2em}{0ex}}\mathrm{nm})/{\text{C}}_{60}({t}_{{\mathrm{C}}_{60}})/\text{Pd}(2.0\phantom{\rule{0.2em}{0ex}}\mathrm{nm})$ system with varying ${t}_{{\mathrm{C}}_{60}}$. The field-induced DW velocity measured in the creep region shows a DW velocity 2 orders of magnitude higher for a sample with 1.6 nm of ${\text{C}}_{60}$, due to a lower depinning field and spin-dependent hybridization at the $\text{Co}/{\text{C}}_{60}$ interface. Further, DMI measurements performed by use of the asymmetric DW expansion method exhibit a systematic increase in the iDMI from $\ensuremath{-}0.07$ to $\ensuremath{-}0.46\phantom{\rule{0.2em}{0ex}}\mathrm{mJ}/{\mathrm{m}}^{2}$ with an increase in ${t}_{{\mathrm{C}}_{60}}$. Such an enhanced iDMI turns an achiral Bloch wall into a chiral N\'eel wall. The emergence of a finite DMI (${D}_{\mathrm{Co}/{\mathrm{C}}_{60}}\ensuremath{\sim}\ensuremath{-}0.11\phantom{\rule{0.2em}{0ex}}\mathrm{mJ}/{\mathrm{m}}^{2}$) from the $\text{Co}/{\text{C}}_{60}$ interface is particularly encouraging for the use of $\mathrm{C}$-based materials in chiral-DW-based device applications.

Rashba effect on finite temperature magnetotransport in a dissipative quantum dot transistor with electronic and polaronic interactions

The Rashba spin–orbit coupling induced quantum transport through a quantum dot embedded in a two-arm quantum loop of a quantum dot transistor is studied at finite temperature in the presence of electron–phonon and Hubbard interactions, an external magnetic field and quantum dissipation. The Anderson-Holstein-Caldeira-Leggett-Rashba model is used to describe the system and several unitary transformations are employed to decouple some of the interactions and the transport properties are calculated using the Keldysh technique. It is shown that the Rashba coupling alone separates the spin-up and spin-down currents causing zero-field spin-polarization. The gap between the up and down-spin currents and conductances can be changed by tuning the Rashba strength. In the absence of a field, the spin-up and spin-down currents show an opposite behaviour with respect to spin–orbit interaction phase. The spin-polarization increases with increasing electron–phonon interaction at zero magnetic field. In the presence of a magnetic field, the tunneling conductance and spin-polarization change differently with the polaronic interaction, spin–orbit interaction and dissipation in different temperature regimes. This study predicts that for a given Rashba strength and magnetic field, the maximum spin-polarization in a quantum dot based device occurs at zero temperature.

Spin polarization and Fano–Rashba resonance in nonmagnetic graphene

We study the symmetry of spin transport in graphene with the Rashba spin–orbit coupling (SOC) and the staggered potential, which can be produced by depositing the graphene on a transition-metal dichalcogenides substrate. The results show that all three spin polarization components along the x, y and z directions are achieved with a measurable conductance in such a nonmagnetic graphene. The spin transport property near the two valleys is discussed in the light of the symmetry of the system. Both conductance and spin polarization present some certain symmetries with respect to the Rashba SOC (RSOC) and staggered potential. The system could work as a valley-spin polarization transverter which combines valleytronics and spintronics. Furthermore, the asymmetric Fano–Rashba resonance of the conductance and spin polarization could occur in a resonant structure due to interference of spin-polarized discrete and continuum states induced by the RSOC. The Fano–Rashba resonance can be effectively controlled by the gate voltage. The derived symmetry relations and numerical results could provide a guideline for the design of spin-valley-based devices.

Robust Ferrimagnetism in Quasi-Freestanding Graphene

The influence of the size of dislocation loops on sublattice ferrimagnetism in graphene is studied. It is shown that graphene and the underlying gold layer with Au/Co dislocation loops of various sizes are characterized by ferrimagnetic ordering within atomic layers. Additional gold adatoms under graphene enhance the induced Rashba spin–orbit coupling in graphene but do not destroy the ferrimagnetic order in graphene. Since gold clusters can remain during the intercalation of gold on the surface of graphene and under graphene, the number and size of clusters after intercalation can be controlled to enhance the induced Rashba interaction and to obtain a topological phase in graphene.

Current-induced spin polarization in Janus WSSe monolayer

Janus engineering of transition metal dichalcogenide monolayers breaks the vertical mirror symmetry and induces huge built-in polarization and large Rashba spin-orbit coupling. By performing first-principles calculations, we find that the Rashba spin-orbit coupling induces sizable current-induced spin polarization in both the conduction and valence bands in the Janus WSSe monolayer, which is comparable to that in perovskite oxide interfaces. By constructing the low-energy $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ Hamiltonian from the invariant theory, we find a sign change of the current-spin conductivity at chemical potential $\ensuremath{\mu}\ensuremath{\approx}\ensuremath{-}0.73$ eV, which indicates the flip of spin polarization and is attributed to the competition between the intrinsic Rashba spin-orbit coupling and the hexagonal warping of the valence bands. Our numerical and analytic results suggest that the current-induced spin polarization in the Janus WSSe monolayer is insensitive to temperature and impurity concentration but can be effectively tuned by external biaxial or uniaxial strain. The Janus WSSe monolayer could be a promising candidate to realize flexible two-dimensional spintronics devices.

Rashba spin–orbit coupling induced rectified currents in monolayer graphene with exchange field and sublattice potential

We investigate the effect of Rashba spin–orbit coupling (RSOC) on photoconductivities of rectified currents in monolayer graphene with exchange field and sublattice potential. The system shows that the photoconductivities of resonant shift and injection current contributions are nonzero, while the photoconductivities of non-resonant shift current contribution are zero. We find that the RSOC induces a warping term, which leads to the nonzero rectified currents. Moreover, the photoconductivities of resonant injection (shift) current contribution are (not) related to the relaxation rate. The similar behavior can be found in other Dirac materials, and our findings provide a way to tune the nonlinear transport properties of Dirac materials.

Unidirectional Seebeck effect from Rashba spin-orbit coupling on the subsurface of Ge(111)

A new nonlinear magnetothermal effect, namely unidirectional Seebeck effect(USE), has been recently reported in magnetic/nonmagnetic topological insulator (TI) heterostructure and is ascribed to the asymmetry magnon scattering. Here, we show a new mechanism to generate USE in the Rashba two dimensional electron gas (2DEG), in which the magnetism or magnetic order is completely absent. It's found that the USE has a quantum origin from the spin-momentum locking generated from Rashba spin-orbit coupling. We find that the USE exhibits a sine dependence on the orientation of the magnetic field with respect to the direction of the temperature gradient and is dominant from the states above the Lifshitz point. The USE in the semiconductor Ge(111) subsurface states has been theoretically and systematically investigated.

Theoretical insights into the epitaxial growth of black arsenene enabled on GeS(001)

Black arsenene exhibits many exotic physical properties, such as Rashba spin–orbital coupling, fractional quantum Hall effect (Sheng 2021 Nature 593 56) as well as some advantages in the field of energy storage (Wu et al 2021 J. Mater. Chem. A 9 18793). High-quality and large-area BA monolayer can promote the investigations about BA and its device application. Epitaxial growth mechanism of BA is desirable. Here, based on density functional theory calculation, the epitaxial growth of BA monolayer was simulated. GeS(001) is found to be a suitable substrate for BA monolayer to epitaxially grow on. As a common isomer of arsenene, gray arsenene should be considered during the growth, because it is also energetically and thermodynamically stable in freestanding state. However, black arsenene monolayer is more energetically and thermodynamically stable than gray arsenene monolayer on GeS(001) substrate. During the growth, two arsenene atoms easily form a dimer on GeS(001), which diffuses more quickly and isotropically than arsenene monomer. In addition, the heterojunction consisted of balck arsenene and GeS(001) is an indirect gap semiconductor, but it can transform into a direct gap semiconductor with external tensile strain along zigzag direction. Remarkably, optical adsorption spectra range of BA/GeS(001) can be more abroad than that of BA and GeS(001) bilayers. The theatrical insights shed new light on some ideal substrates that can realize the epitaxial growth of high-quality simple substances of group V.

Symmetry-engineered nodal lines and hourglass fermions in patterned two-dimensional electron gas

In most cases, the formation of topological quantum states requires intrinsic crystalline symmetry to protect either discrete or continuous degeneracies in real materials, which greatly hinders their realization in practice. Patterned two-dimensional electron gas (2DEG), on the other hand, has become a very effective external means to manipulate the symmetry to whatever we want. Here, taking nonsymmorphic symmetries as the focus of attention, based on patterned 2DEG decoration, we reveal rich band-crossing features in two-dimensional systems. It is demonstrated that in the presence of intrinsic spin-orbital coupling (SOC), wallpaper groups $p2mg,p2gg$, and $p4mg$ possess fourfold-degenerate Dirac nodal lines, and if Rashba SOC is further considered, the fourfold-degenerate nodal lines disappear and hourglass Weyl fermions then emerge. Our results not only afford an attractive route for designing robust nodal-line and hourglass Weyl semimetals in reality, but also pave the way for designing ideal macroscale materials through rational extrinsic symmetry engineering.

Rashba spin-orbit coupling enhanced magnetoresistance in junctions with one ferromagnet

We explain how Rashba spin-orbit coupling (SOC) in a two-dimensional electron gas (2DEG), or in a conventional $s$-wave superconductor, can lead to a large magnetoresistance even with one ferromagnet. However, such enhanced magnetoresistance is not generic and can be nonmonotonic and change its sign with Rashba SOC. For an in-plane rotation of magnetization, it is typically negligibly small for a 2DEG and depends on the perfect transmission which emerges from a spin-parity-time symmetry of the scattering states, while this symmetry is generally absent from the Hamiltonian of the system. The key difference from considering the normal-state magnetoresistance is the presence of the spin-dependent Andreev reflection at superconducting interfaces. In the fabricated junctions of quasi-2D van der Waals ferromagnets with conventional $s$-wave superconductors (Fe$_{0.29}$TaS$_2$/NbN) we find another example of enhanced magnetoresistance where the presence of Rashba SOC reduces the effective interfacial strength and is responsible for an equal-spin Andreev reflection. The observed nonmonotonic trend in the out-of-plane magnetoresistance with the interfacial barrier is an evidence for the proximity-induced equal-spin-triplet superconductivity.

Majorana-Weyl cones in ferroelectric superconductors

Topological superconductors are predicted to exhibit outstanding phenomena, including non-Abelian anyon excitations, heat-carrying edge states, and topological nodes in the Bogoliubov spectra. Nonetheless, and despite major experimental efforts, we are still lacking unambiguous signatures of such exotic phenomena. In this context, the recent discovery of coexisting superconductivity and ferroelectricity in lightly doped and ultraclean ${\mathrm{SrTiO}}_{3}$ opens new opportunities. Indeed, a promising route to engineer topological superconductivity is the combination of strong spin-orbit coupling and inversion-symmetry breaking. Here we study a three-dimensional parabolic band minimum with Rashba spin-orbit coupling, whose axis is aligned by the direction of a ferroelectric moment. We show that all of the aforementioned phenomena naturally emerge in this model when a magnetic field is applied. Above a critical Zeeman field, Majorana-Weyl cones emerge regardless of the electronic density. These cones manifest themselves as Majorana arc states appearing on surfaces and tetragonal domain walls. Rotating the magnetic field with respect to the direction of the ferroelectric moment tilts the Majorana-Weyl cones, eventually driving them into the type-II state with Bogoliubov Fermi surfaces. We then consider the consequences of the orbital magnetic field. First, the single vortex is found to be surrounded by a topological halo and is characterized by two Majorana zero modes: one localized in the vortex core and the other on the boundary of the topological halo. Based on a semiclassical argument we show that upon increasing the field above a critical value the halos overlap and eventually percolate through the system, causing a bulk topological transition that always precedes the normal state. Finally, we propose concrete experiments to test our predictions.

Fermi-Level-Dependent Charge-to-Spin Conversion of the Two-Dimensional Electron Gas at the γ - Al2O3/KTaO3 Interface

Charge-to-spin conversion is crucial for the application of emerging spintronic devices. A two-dimensional electron gas (2DEG) at a complex oxide interface usually possesses strong Rashba spin-orbit coupling, and spin-momentum locking offers a great possibility for efficient charge-to-spin conversion through the Rashba-Edelstein effect. Here, we report the fabrication of metallic 2DEGs in \ensuremath{\gamma}-${\mathrm{Al}}_{2}{\mathrm{O}}_{3}/{\mathrm{KTaO}}_{3}$ spinel/perovskite heterostructures and investigate the charge-to-spin conversion for Py/\ensuremath{\gamma}-${\mathrm{Al}}_{2}{\mathrm{O}}_{3}/{\mathrm{KTaO}}_{3}$ devices using the technique of spin-torque ferromagnetic resonance. The sizable spin splitting of the band structure results in a large current-induced spin-orbit torque efficiency with values up to around 3.6 at 5 K and about 1.1 at 300 K, which are more than an order of magnitude higher than those of heavy metals (0.07 for $\mathrm{Pt}$ at 300 K). Moreover, both theoretical and experimental results show that the charge-to-spin conversion is strongly dependent on the position of the Fermi level. These results demonstrate that optimizing the band filling of a ${\mathrm{KTaO}}_{3}$-based 2DEG is crucial for maximizing the conversion efficiency.

Strain-tuned spin polarization and optical conductivity in MoS2/EuS heterostructures

We investigate strain-tuned spin transport and optical conductivity in a monolayer (ML) $n$-type ${\mathrm{MoS}}_{2}/\mathrm{EuS}$ heterostructure under linearly polarized terahertz radiation using a low-energy effective Hamiltonian, which takes displacement of the Dirac point induced by strain into account. Through modifying the strain modulus, we find an adjustable relationship between the band edge energy and the strain. Thus the threshold and range of allowed angles are strongly dependent on the strength of strain $\ensuremath{\epsilon}$, whereas the angle $\ensuremath{\theta}$ along which the strain is applied only acts on the former. Due to spin-flipped scattering generated by Rashba spin-orbit coupling, the in-plane spin polarizations (i.e., ${P}_{X}$ and ${P}_{Y}$) can be achieved, and their intensity can be enhanced by increasing $\ensuremath{\epsilon}$. Interestingly, we find that the out-of-plane spin polarization (i.e., ${P}_{Z}$) is related to the synergy of $\ensuremath{\epsilon}$ and the Rashba parameter ${\ensuremath{\lambda}}_{R}$. Especially, ${P}_{Z}$ can approach $100%$ when $\ensuremath{\epsilon}=9%$ and ${\ensuremath{\lambda}}_{R}=2$ meV. Furthermore, the optical transition between the spin-splitting subbands of the conduction band under the strain is studied. It is shown that by varying $\ensuremath{\epsilon}$ we can control the magnitude of both absorption peaks and absorption valleys in optical conductivity. Moreover, the presence of ${\ensuremath{\lambda}}_{R}$ can be used to further enhance the absorption peaks and valleys because ${\ensuremath{\lambda}}_{R}$ can tune the energy difference between the spin-splitting subbands within a specific valley and thus affect the optical transition channels. Our findings demonstrate that the strain can influence the tunneling behavior and valley Hall conductivity in a ML $n$-type ${\mathrm{MoS}}_{2}/\mathrm{EuS}$ heterostructure, and these features are applicable to other two-dimensional ML transition metal dichalcogenides, which is promising for terahertz and valleytronic devices.

Conductance modulation and spin/valley polarized transmission in silicene coupled with ferroelectric layer

We investigate the interplay of the Rashba spin orbit coupling (SOC) and the Klein tunneling effect on the valley and spin polarized transport in a heterostructure consisting of silicene coupled with a ferroelectric layer in a n-p-n configuration. We found that the combination of SOC and electric field, which opens up an energy gap, can significantly modulate the carrier transmission properties in ferroelectrically coupled silicene, in marked contrast with those of gapless two-dimensional (2D) systems. The combined effects of the SOC, electric field, and the coupling to the ferroelectric layer suppress the transmission probability at normal incidence compared to the conventional Klein effect. We also show that when the electric field, Fermi energy and barrier height are appropriately tuned, the transmitted current is composed of primarily one spin (valley) contribution for a fixed valley (spin) selection, resulting in almost pure spin/ valley polarized current. Our results have ramifications for prospective device applications of silicene heterostructures and next-generation spintronics and valleytronics.

Single-point spin Chern number in a supercell framework

We present an approach for the calculation of the topological invariant in non-crystalline two-dimensional quantum spin Hall insulators. While topological invariants were originally mathematically introduced for crystalline periodic systems, and crucially hinge on tracking the evolution of occupied states through the Brillouin zone, the introduction of disorder or dynamical effects can break the translational symmetry and imply the use of larger simulation cells, where the k-point sampling is typically reduced to the single Γ-point. Here, we introduce a single-point formula for the spin Chern number that enables to adopt the supercell framework, where a single Hamiltonian diagonalisation is performed. Inspired by the work of Prodan (2009 Phys. Rev. B 80 125327), our single-point approach allows to calculate the spin Chern number even when the spin operator does not commute with the Hamiltonian, as in the presence of Rashba spin–orbit coupling. We validate our method on the Kane–Mele model, both pristine and in the presence of Anderson disorder. Finally, we investigate the disorder-driven transition from the trivial phase to the topological state known as topological Anderson insulator. Beyond disordered systems, our approach is particularly useful to investigate the role of defects, to study topological alloys and in the context of ab-initio molecular dynamics simulations at finite temperature.

Rashba spin-orbit coupling induced modulation of magnetic anisotropy in canted antiferromagnetic heterostructures

The combined effect of charge transfer, broken symmetries, and spin-orbit coupling (SOC) yields interfacial magnetism and transport in spatially asymmetric quantum oxide heterostructures. The polar nature of such interfaces activates the Rashba effect which provides a platform to modify the electronic band structure, whereas the presence of competing magnetic anisotropies is essential for deriving the topologically nontrivial spin textures. Entanglement of these two effects wherein the Rashba physics can be utilized to manipulate magnetic anisotropy (MA) is contemplated as a pathway to alternative electronic states. Here, using the $\mathrm{CaMn}{\mathrm{O}}_{3}/\mathrm{CaIr}{\mathrm{O}}_{3}$ heterostructure as a template, we demonstrate that Rashba SOC modulates the MA and controls the sign and magnitude of anomalous Hall conductivity consequent to the modification in the electronic band structure via the reconstruction of Berry curvature. This approach to tune and control the multipronged magnetotransport phenomena via Rashba SOC (without external bias voltage) is potentially relevant for spin-orbitronics functionalities.

Probing Rashba spin-orbit coupling by subcycle lightwave control of valley polarization

We perform nonperturbative calculations of light-field driven valley-polarization process in monolayer ${\mathrm{MoS}}_{2}$ which has additional Rashba spin-orbit couplings (SOCs). The ultrafast electron dynamics is simulated within the independent particle picture by solving density-matrix equations in the basis of linear combination of atomic orbitals, where tight-binding (TB) models including both intrinsic atomic and Rashba SOCs are used to calculate relevant matrix elements. We demonstrate that the Rashba-type SOCs can be manifested by suboptical-cycle control of valley selectivity excitations, in particular necessary via using few-cycle linearly polarized pulse with controlled carrier-envelope phase (CEP). This procedure will lead to a CEP-dependent valley Hall conductivity (VHC), which exhibits an important phase shift among different Rashba coupling strengths. The additional analysis shows that this phase shift is mainly determined by the ${d}_{z}^{2}$-orbital TB Rashba parameter from Mo atom and originates from contribution of conduction bands to VHC, where the Berry curvature modified by Rashba SOC plays a crucial role. Moreover, we also provide a qualitative interpretation on the Rashba-dependent VHC in terms of suboptical-cycle Landau-Zener-St\"uckelberg interference. Our results suggest a feasible approach for probing Rashba SOCs in hexagonal two-dimensional materials, and might pave the way of achieving more controls in the future valleytronics application.

Increased localization of Majorana modes in antiferromagnetic chains on superconductors

Magnet-superconductor hybrid (MSH) systems are a key platform for custom-designed topological superconductors. Ideally, the ends of a one-dimensional MSH structure will host Majorana zero-modes (MZMs), the fundamental unit of topological quantum computing. However, some of the experiments with ferromagnetic chains show a more complicated picture. Due to tiny gap sizes and hence long coherence lengths MZMs might hybridize and lose their topological protection. Recent experiments on a niobium surface have shown that both ferromagnetic and antiferromagnetic chains may be engineered, with the magnetic order depending on the crystallographic direction of the chain. While ferromagnetic chains are well understood, antiferromagnetic chains are less so. Here we study two models inspired by the niobium surface: a minimal model to elucidate the general topological properties of antiferromagnetic chains, and an extended model to more closely simulate a real system by mimicking the proximity effect. We find that in general for antiferromagnetic chains the topological gap is larger than for ferromagnetic ones and thus coherence lengths are shorter for antiferromagnetic chains, yielding more pronounced localization of MZMs in these chains. While topological phases for both ferromagnetic and antiferromagnetic chains both depend on the magnetic moment of the adatoms and the chemical potential, we find that antiferromagnetic chains also have a strong dependence on the magnitude of Rashba spin-orbit coupling at the surface.

Steady-state dc transport through an Anderson impurity coupled to leads with spin-orbit coupling

We study the steady-state dc transport characteristics of a system comprised of an interacting quantum dot, modelled as an Anderson impurity, coupled to two metallic non-interacting leads with Rashba SOC, using an interpolative perturbative approach (IPA). The single-particle spectra, current and differential conductance are obtained in weak and strong coupling regimes over a wide range of SOC and bias values. Extensive benchmarking of the IPA validates the method in the linear as well as non-linear response regime. The universal, zero bias ($V_{sd}=0$) peak with a width proportional to the Kondo scale ($T_K$) and two non-universal finite bias peaks around $V_{sd}=\pm U$ in the zero temperature differential conductance show a clear separation with increasing $U$ or increasing SOC. In the strong coupling regime, increasing temperature induces melting of the zero bias peak leading to a crossover from a three-peak conductance to a two-peak conductance. Recent experiments find the emergence of a two-peak structure by increasing SOC at a fixed temperature. Our results appear to provide a qualitative explanation of these observations as a SOC tuned crossover from weak/intermediate to strong coupling, and a simultaneous crossover from low $T/T_K$ to high $T/T_K$ ratio. We also reproduce the experimentally observed temperature dependence of the zero bias conductance.