Rashba Spin-orbit Coupling Research Articles

Twist-angle dependent proximity induced spin-orbit coupling in graphene/topological insulator heterostructures

The proximity-induced spin-orbit coupling (SOC) in heterostructures of twisted graphene and topological insulators (TIs) Bi$_2$Se$_3$ and Bi$_2$Te$_3$ is investigated from first principles. To build commensurate supercells, we strain graphene and correct thus resulting band offsets by applying a transverse electric field. We then fit the low-energy electronic spectrum to an effective Hamiltonian that comprises orbital and spin-orbit terms. For twist angles 0$^\circ\leq\Theta \lessapprox 20^\circ$, we find the dominant spin-orbit couplings to be of the valley-Zeeman and Rashba types, both a few meV strong. We also observe a sign change in the induced valley-Zeeman SOC at $\Theta\approx 10^\circ$. Additionally, the in-plane spin structure resulting from the Rashba SOC acquires a non-zero radial component, except at $0^\circ$ or $30^\circ$. At $30^\circ$ the graphene Dirac cone interacts directly with the TI surface state. We therefore explore this twist angle in more detail, studying the effects of gating, TI thicknesses, and lateral shifts on the SOC parameters. We find, in agreement with previous results, the emergence of the proximitized Kane-Mele SOC, with a change in sign possible by electrically tuning the Dirac cone within the TI bulk band gap.

Large Rashba spin-orbit coupling and high-temperature quantum anomalous Hall effect in Re-intercalated graphene/CrI3 heterostructure

In 2010, the quantum anomalous Hall effect (QAHE) in graphene was proposed in the presence of Rashba spin-orbit coupling and a ferromagnetic exchange field. After a decade of experimental exploration, the anomalous Hall conductance can only reach about 0.25 in units of $2{e}^{2}/h$, which was attributed to the tiny Rashba spin-orbit coupling. Here, we show theoretically that Re-intercalation in a $\text{graphene}/{\mathrm{CrI}}_{3}$ heterostructure can not only induce sizable Rashba spin-orbit coupling ($>40$ meV), but also open up large band gaps at valleys $K$ (22.2 meV) and ${K}^{\ensuremath{'}}$ (30.3 meV), and a global band gap over 5.5 meV (19.5 meV with random Re distribution) hosting QAHE. A low-energy continuum model is constructed to explain the underlying physical mechanism. We find that Rashba spin-orbit coupling is robust against external stress whereas a tensile strain can increase the global bulk gap. Furthermore, we comprehensively explore the electronic properties of $3d, 4d, 5d$ transition-metal intercalation in graphene/${\mathrm{CrI}}_{3}$ systems.

Explicit derivation of the chiral and generic helical edge states for the Kane-Mele model: Closed expressions for the wave function, dispersion relation, and spin rotation

Although one of the most important and intriguing features of the topological insulators is the presence of edge states, the closed-form expressions for the edge states of some famous topological models are still lacking. Here, we focus on the Kane-Mele model with and without Rashba spin-orbit coupling as a well-known model to describe a two-dimensional version of the ${\mathbb{Z}}_{2}$ topological insulator to study the properties of its edge states analytically. By considering the tight-binding model on a honeycomb lattice with zigzag boundaries and introducing a perturbative approach, we derive explicit expressions for the wave functions, energy dispersion relations, and the spin rotations of the (generic) helical edge states. To this end, we first map the edge states of the ribbon geometry into an effective two-leg ladder model with momentum-dependent energy parameters. Then, we split the Hamiltonian of the system into an unperturbed part and a perturbation. The unperturbed part has a flat-band energy spectrum and can be solved exactly, which allows us to consider the remaining part of the Hamiltonian perturbatively. The resulting energy dispersion relation within the first-order perturbation, surprisingly, is in excellent agreement with the numerical spectra over a very wide range of wave numbers. Our perturbative framework also allows deriving an explicit form for the rotation of the spins of the momentum edge states in the absence of axial spin symmetry due to the Rashba spin-orbit interaction.

Thermal entanglement and quantum coherence of a single electron in a double quantum dot with Rashba interaction

In this work, we study the thermal quantum coherence and fidelity in a semiconductor double quantum dot. The device consists of a single electron in a double quantum dot with Rashba spin-orbit coupling in the presence of an external magnetic field. In our scenario, the thermal entanglement of the single electron is driven by the charge and spin qubits, the latter controlled by Rashba coupling. Analytical expressions are obtained for thermal concurrence and correlated coherence using the density matrix formalism. The main goal of this work is to provide a good understanding of the effects of temperature and several parameters in quantum coherence. In addition, our findings show that we can use the Rashba coupling to tune in the thermal entanglement, quantum coherence, as well as, the thermal fidelity behavior of the system. Moreover, we focus on the role played by thermal entanglement and correlated coherence responsible for quantum correlations. We observe that the correlated coherence is more robust than the thermal entanglement in all cases, so quantum algorithms based only on correlated coherence may be stronger than those based on entanglement.

Light-induced giant Rashba spin-orbit coupling at superconducting KTaO3 (110) heterointerfaces.

The two-dimensional electron system (2DES) at KTaO3 surface or heterointerface with 5d orbitals hosts extraordinary physical properties including the stronger Rashba spin-orbit coupling (RSOC), higher superconducting transition temperature, and potential of topological superconductivity. Herein, we report a huge enhancement of RSOC under light illumination achieved at a superconducting amorphous-Hf0.5 Zr0.5 O2 /KTaO3 (110) heterointerfaces. The superconducting transition is observed with Tc = 0.62 K and temperature dependent upper critical field reveals the interaction between spin-orbit scattering and superconductivity. A strong RSOC with Bso =1.9 T is revealed by weak antilocalization in normal state, which undergoes sevenfold enhancement under light illumination. Furthermore, RSOC strength develops a dome-shaped dependence of carrier density with the maximum of Bso =12.6 T achieved near the Lifshitz transition point nc ∼ 4.1×1013 cm-2 . The highly tunable giant RSOC at KTaO3 (110)-based superconducting interfaces show great potential for spintronics. This article is protected by copyright. All rights reserved.

Magnetic‐Field Regulation of Nodal Topological Superconducting States in Monolayer Ising Superconductor NbSe2

The nodal topological superconducting (NTSC) state with Majorana flat bands (MFBs) is an exotic matter of state hosting Majorana fermions that obey non‐Abelian statistics. Recently, monolayer Ising superconductor NbSe2 is shown to be an ideal platform for realizing an NTSC state. Through tight‐binding calculations based on the Bogoliubov–de–Gennes Hamiltonian, it is demonstrated that the in‐plane magnetic field B combined with superconducting pairing Δs, Rashba spin–orbit coupling (SOC) Vr, and chemical potential μ can regulate the topological properties of the NTSC state. First, B larger than Δs effectively induces an NTSC state with nodal points (NPs) located on the high‐symmetry line of the Brillouin zone. The length of the resulting MFBs in the ribbon increases with B. Second, Rashba SOC greatly affects the number and locations of NPs by tilting bands near Fermi level (EF), leading to unidirectional Majorana edge states. Finally, when B > Δs, μ affects the bulk band structure at EF, resulting in an NTSC state with 6, 12, 18, 24 NPs and 0, 2, 3, 4 MFBs. These results are important to clarifying the behavior of the NTSC state under a B and designing a quantum computing platform based on exotic Majorana fermions.

Effects of spin-orbit coupling on proximity-induced superconductivity

We investigate the effect of spin orbit coupling on proximity induced superconductivity in a normal metal attached to a superconductor. Specifically, we consider a heterostructure where the presence of interfaces gives rise to a Rashba spin orbit coupling. The properties of the induced superconductivity in these systems are addressed within the tunneling Hamiltonian formalism. We find that the spin orbit coupling induces a mixture of singlet and triplet pairing and, under specific circumstances, an odd frequency, even parity, spin triplet pairs can arise. We also address the effect of impurity scattering on the induced pairs, and discuss our results in context of heterostructures consisting of materials with spin-momentum locking.

Reduction of carrier density and enhancement of the bulk Rashba spin-orbit coupling strength in Bi2Te3/GeTe superlattices

Featured with the large Rashba constant (αR ∼ 4.2 eVÅ) coupled with the ferroelectricity, GeTe has attracted much interest, proposing novel energy-efficient spintronic devices. However, those approaches are hampered by the high hole density of GeTe around 1020-1021 cm−3, which deteriorates both the ferroelectricity and the bulk Rashba effect of GeTe. To solve this problem, we have investigated the superlattices composed of Bi2Te3 and GeTe ([BT|GT] SL), the former of which is known as a topological insulator (TI) with typically n-type conduction and strong spin-orbit coupling. We have investigated the magnetotransport properties of 25 [BTx|GTy]z SLs with varying thicknesses (x, y: the thickness in the multiples of the unit cell of the respective layer) of each layer and the repetition number (z) systematically. We have observed a minimum carrier density of 5.7 × 1019 cm−3 in [BT6|GeTe6]6 superlattice sample smaller than that (∼4.4 ×1020 cm−3) of GeTe single film by an order. In addition, we have found that some [BT|GT] SLs with reduced carrier density have a larger Rashba constant compared to that of a single GeTe film. This is explained by the change of the spin polarization which can be modulated by the Fermi level in the Rashba band. These results provide a viable way to realize robust ferroelectricity and strong SOC in GeTe-related material systems simultaneously.

Compacton existence and spin-orbit density dependence in Bose-Einstein condensates.

We demonstrate the existence of compactons matter waves in binary mixtures of Bose-Einstein condensates (BEC) trapped in deep optical lattices (OL) subjected to equal contributions of intraspecies Rashba and Dresselhaus spin-orbit coupling (SOC) under periodic time modulations of the intraspecies scattering length. We show that these modulations lead to a rescaling of the SOC parameters that involves the density imbalance of the two components. This gives rise to density dependent SOC parameters that strongly influence the existence and the stability of compacton matter waves. The stability of SOC-compactons is investigated both by linear stability analysis and by time integrations of the coupled Gross-Pitaevskii equations. We find that SOC restricts the parameter ranges for stable stationary SOC-compacton existence but, on the other side, it gives a more stringent signature of their occurrence. In particular, SOC-compactons should appear when the intraspecies interactions and the number of atoms in the two components are perfectly balanced (or close to being balanced for the metastable case). The possibility to use SOC-compactons as a tool for indirect measurements of the number of atoms and/or the intraspecies interactions is also suggested.

Tunable correlation effects of magnetic impurities by cubic Rashba spin-orbit coupling

We theoretically study the influence of the $k$-cubic Rashba spin-orbit coupling (SOC) on the correlation effects of magnetic impurities by combining the variational method and the Hirsch-Fye quantum Monte Carlo (HFQMC) simulations. Markedly different from the normal $k$-linear Rashba SOC, even a small cubic Rashba term can greatly alter the band structure and induce a Van Hove singularity in a wide range of energy; thus, the single impurity local moment becomes largely tunable. The cubic Rashba SOC adopted in this paper breaks the rotational symmetry, but the host material is still invariant under the operations ${\mathcal{R}}^{z}(\ensuremath{\pi}), {\mathcal{IR}}^{z}(\ensuremath{\pi}/2), {\mathcal{M}}_{xz}, {\mathcal{M}}_{yz}$, where ${\mathcal{R}}^{z}(\ensuremath{\theta})$ is the rotation of angle $\ensuremath{\theta}$ about the $z$ axis, $\mathcal{I}$ is the inversion operator, and ${\mathcal{M}}_{xz}$ (${\mathcal{M}}_{yz}$) is the mirror reflection about the $x\text{\ensuremath{-}}z$ ($y\text{\ensuremath{-}}z$) principal plane. Saliently, various components of spin-spin correlation between the single magnetic impurity and the conduction electrons show three- or sixfold rotational symmetry. This unique feature is due to the triple winding of the spins with a $2\ensuremath{\pi}$ rotation of $\mathbf{k}$, which is a hallmark of the cubic Rashba effect, and can possibly be an identifier to distinguish the cubic Rashba SOC from the normal $k$-linear Rashba term in experiments. Although the cubic Rashba term drastically alters the electronic properties of the host, we find that the spatial decay rate of the spin-spin correlation function remains essentially unchanged. Moreover, the carrier-mediated Ruderman-Kittel-Kasuya-Yosida interactions between two magnetic impurities show twisted features, the ferromagnetic diagonal terms dominate when two magnetic impurities are very close, but the off-diagonal terms become important at long distances.

Unlocking hidden spins in centrosymmetric 1T transition metal dichalcogenides by vacancy-controlled spin-orbit scattering

Spin current generation and manipulation remain the key challenge of spintronics, in which relativistic spin-orbit coupling (SOC) plays a ubiquitous role. In this paper, we demonstrate that hidden Rashba spins in the nonmagnetic, centrosymmetric lattice of multilayer ${\mathrm{SnSe}}_{2}$ can be efficiently activated by spin-orbit scattering introduced by Se vacancies. Via vacancy scattering, conduction electrons with hidden spin-momentum locked polarizations acquire out-of-plane magnetization components, which effectively break the chiral symmetry between the two Se sublattices of an ${\mathrm{SnSe}}_{2}$ monolayer when electron spins start precession in the strong built-in Rashba SOC field. The resulting spin separations are manifested in quantum transport as vacancy concentration- and temperature-dependent crossovers from weak antilocalization to weak localization, with the distinctive spin relaxation mechanism of the D'yakonov-Perel' type. In a nonlocal geometry, the generated spins exhibit a long diffusion length exceeding 5 $\textmu{}\mathrm{m}$, when fast momentum scattering protects the effective spin polarizations by driving the random-walk evolution of spin precessions subject to rapidly changing Rashba SOC field. Our study shows the great potential of two-dimensional systems with hidden-spin textures for spintronics.

Tuning spin-orbit coupling and realizing inverse persistent spin helix by an extra above-barrier radiation in a GaAs/Al0.3Ga0.7As heterostructure.

A persistent spin helix with equal strength of the Rashba and Dresselhaus spin-orbit coupling (SOC) is expected for future spintronic devices due to the suppression of spin relaxation. In this work we investigate the optical tuning of the Rashba and Dresselhaus SOC by monitoring the spin-galvanic effect (SGE) in a GaAs/Al0.3Ga0.7As two dimensional electron gas. An extra control light above the bandgap of the barrier is introduced to tune the SGE excited by a circularly polarized light below the bandgap of GaAs. We observe different tunability of the Rashba- and Dresselhaus-related SGE currents and extract the ratio of the Rashba and Dresselhaus coefficients. It decreases monotonously with the power of the control light and reaches a particular value of ∼-1, implying the formation of the inverse persistent spin helix state. By analyzing the optical tuning process phenomenologically and microscopically, we reveal greater optical tunability of the Rashba SOC than that of the Dresselhaus SOC.

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.

Anomalous Josephson effect between d-wave superconductors through a two-dimensional electron gas with both Rashba spin–orbit coupling and Zeeman splitting

Based on the Bogoliubov–de Gennes equation and the extended McMillan’s Green’s function formalism, we study theoretically the Josephson effect between two d-wave superconductors bridged by a ballistic two-dimensional electron gas with both Rashba spin–orbit coupling and Zeeman splitting. We show that due to the interplay of Rashba spin–orbit coupling and Zeeman splitting and d-wave pairing, the current–phase relation in such a heterostructure may exhibit a series of novel features and can change significantly as some relevant parameters are tuned. In particular, anomalous Josephson current may occur at zero phase bias under various different situations if both time reversal symmetry and inversion symmetry of the system are simultaneously broken, which can be realized by tuning some relevant parameters of the system, including the relative orientations and the strengths of the Zeeman field and the spin–orbit field in the bridge region, the relative orientations of the a axes in two superconductor leads, or the relative orientations between the Zeeman field in the bridge region and the a axes in the superconductor leads. We show that both the magnitude and the direction of the anomalous Josephson current may depend sensitively on these relevant parameters.

Magnetic excitations in the helical Rashba superconductor

We investigate the magnetic excitation spectrum in the helical state of a noncentrosymmetric superconductor with inversion symmetry breaking and strong Rashba spin–orbit coupling. For this purpose we derive the general expressions of the dynamical spin response functions under the presence of strong Rashba splitting of conduction bands, superconducting gap and external field which lead to stabilization of Cooper pairs with finite overall momentum in a helical state. The latter is characterized by momentum space regions of paired and unpaired states with different quasiparticle dispersions. The magnetic response is determined by i) excitations within and between both paired and unpaired regions ii) anomalous coherence factors and iii) additional spin matrix elements due to helical Rashba spin texture of bands. We show that as a consequence typical correlated real space and spin space anisotropies appear in the dynamical susceptibility which would be observable as a characteristic fingerprint for a helical superconducting state in inelastic neutron scattering investigations.

Exceptional degeneracies in non-Hermitian Rashba semiconductors

Exceptional points (EPs) are spectral degeneracies of non-Hermitian (NH) systems where eigenvalues and eigenvectors coalesce, inducing unique topological phases that have no counterpart in the Hermitian realm. Here we consider an NH system by coupling a two-dimensional semiconductor with Rashba spin–orbit coupling (SOC) to a ferromagnet lead and show the emergence of highly tunable EPs along rings in momentum space. Interestingly, these exceptional degeneracies are the endpoints of lines formed by the eigenvalue coalescence at finite real energy, resembling the bulk Fermi arcs commonly defined at zero real energy. We then show that an in-plane Zeeman field provides a way to control these exceptional degeneracies although higher values of non-Hermiticity are required in contrast to the zero Zeeman field regime. Furthermore, we find that the spin projections also coalescence at the exceptional degeneracies and can acquire larger values than in the Hermitian regime. Finally, we demonstrate that the exceptional degeneracies induce large spectral weights, which can be used as a signature for their detection. Our results thus reveal the potential of systems with Rashba SOC for realizing NH bulk phenomena.

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.