Rashba spin-orbit coupling emerges in materials lacking of structural inversion symmetry, such as heterostructures, quantum wells, surface alloys and polar materials, just to mention few examples. It yields a coupling between the spin and momentum of electrons formally identical to that arising from the weakly-relativistic limit of the Dirac equation. The purpose of the present work is to give an overview of the unconventional dc transport properties of two-dimensional metals with strong Rashba spin-orbit coupling, discussing in addition the effects of thermal broadening.
We discuss the transport properties of a disordered two-dimensional electron gas with strong Rashba spin-orbit coupling. We show that in the high-density regime where the Fermi energy overcomes the energy associated with spin-orbit coupling, dc transport is accurately described by a standard Drude's law, due to a non-trivial compensation between the suppression of back-scattering and the relativistic correction to the quasi-particle velocity. On the contrary, when the system enters the opposite dominant spin-orbit regime, Drude's paradigm breaks down and the dc conductivity becomes strongly se…
We calculate the gate voltage (Vg) dependence of charge conductance in a normal metal (NM)/two dimensional electron gas (2DEG) junction, where Rashba spin-orbit coupling and ferromagnetism exist in the 2DEG. We call this 2DEG as the ferromagnetic Rashba metal (FRM) and the chemical potential of the FRM is controlled by Vg. We clarify the physical origin of the unconventional Vg dependence of charge conductance in the NM/FRM junction found in our previous work [J. Phys. Soc. Jpn. 87, 034710 (2018)], in which the charge conductance increases with Vg, although the number of carries in FRM decreas…
We study the anomalous proximity effect in diffusive normal metal (DN)/unconventional superconductor junctions, where the local density of states (LDOS) in the DN has a zero-energy peak due to the penetration of the odd-frequency spin-triplet $s$-wave pairing. In this study, we consider a two-dimensional unconventional superconductor on the substrate in the presence of a Rashba spin-orbit coupling (RSOC) $λ$, where the Rashba vector is parallel to the $z$-direction. The anomalous proximity effect, originally predicted in spin-triplet $p$-wave superconductor junctions, is sensitive to the RSOC.…
Surface states in Tl/Si(111) and Bi/Si(111) show non-Rashba-type spin splitting. We study spin-transport properties in these surface states. First we construct tight-binding Hamiltonians for Tl/Si and Bi/Si surfaces, which respect crystallographic symmetries. As a result, we find specific terms in the Tl/Si surface Hamiltonian responsible for non-Rashba spin splitting. Using this model we calculate current-induced spin polarization in the Tl/Si Hamiltonian in order to see the effect of non-Rashba spin-orbit interaction. We found that the induced spin polarization is in-plane and perpendicular …
Thermoelectric transport in strongly spin-orbit coupled two-dimensional Rashba system is studied using the exact solution of the linearized Boltzmann equation. Some unusual transport behaviors are revealed. We show that the electrical conductivity takes a Drude form when the Fermi energy $E_{F}$ is above the band crossing point, but a non-Drude form which is a quadratic function of $E_{F}$ when $E_{F}$ lies below the band crossing point. The Mott relation breaks down when $E_{F}$ lies in the vicinity of the band crossing point. It is shown that the thermopower and thermoelectric figure of meri…
The Rashba effect, a spin splitting in electronic band structure, attracts much attention for the potential applications in spintronics with no requirement of external magnetic field. Realizing one-dimensional (1D) Rashba system is a big challenge due to the difficulties of growing high-quality heavy-metal nanowires or introducing strong spin-orbit coupling (SOC) and broken inversion symmetry in flexible materials. Here, based on first-principles calculations, we propose a pathway to realize the Rashba spin-split by adsorbing Gd atom on zigzag graphene nanoribbons (Gd-ZGNR) and further investi…
Rashba spin-orbit coupling appears in 2D systems lacking inversion symmetry, and causes the spin-splitting of otherwise degenerate energy bands into an upper and lower helicity band. In this paper, we explore how impurity scattering affects transport in the ultra-low-density regime where electrons are confined to the lower helicity band. A previous study has investigated the conductivity in this regime using a treatment in the first Born approximation. In this work, we use the full T-matrix to uncover new features of the conductivity. We first compute the conductivity within a semiclassical Bo…
The recent discovery of materials featuring strong Rashba spin-orbit coupling (RSOC) and strong electronic correlation raises questions about the interplay of Mott and Rashba physics. In this work, we employ cluster perturbation theory to investigate the spectral properties of the two-dimensional Hubbard model in the presence of a significant or large RSOC. We show that RSOC strongly favors metallic phases and competes with Mott localization, leading to an unconventional scenario for the Mott transition which is no longer controlled by the ratio between the Hubbard $U$ and an effective bandwid…
We study the "phase diagram" of a Hubbard plaquette with Rashba spin-orbit coupling. We show that the peculiar way in which Rashba coupling breaks the spin-rotational symmetry of the Hubbard model allows a mixing of singlet and triplet components in the ground-state that slows down and it changes the nature of the Mott transition and of the Mott insulating phases.
We study the ground-state properties of electrons confined to a quantum wire and subject to a smoothly modulated Rashba spin-orbit coupling. When the period of the modulation becomes commensurate with the band filling, the Rashba coupling drives a quantum phase transition to a nonmagnetic insulating state. Using bosonization and a perturbative renormalization group approach, we find that this state is robust against electron-electron interactions. The gaps to charge- and spin excitations scale with the amplitude of the Rashba modulation with a common interaction-dependent exponent. An estimate…
We proposed that the simultaneous presence of both Rashba and band inversion can lead to a Rashba-like spin-splitting formed by two bands with the same in-plane helical spin texture. Because of this unconventional spin texture, the backscattering is forbidden in edge and bulk conductivity channels. We propose a new non-centrosymmetric honeycomb-lattice quantum spin Hall (QSH) insulator family formed by the IV, V, and VII elements with this property. The system formed by Bi, Pb and I atoms is mechanically stable and has both a large Rashba spin-splitting of 60 meV and a large nontrivial band ga…
It is well known that the critical temperature of multi-gap superconducting 3D heterostructures at atomic limit (HAL) made of a superlattice of atomic layers with an electron spectrum made of several quantum subbands can be amplified by a shape resonance driven by the contact exchange interaction between different gaps. The $T_C$ amplification is achieved tuning the Fermi level near the singular nodal point at a Lifshitz transition for opening a neck. Recently high interest has been addressed to the breaking of inversion symmetry which leads to a linear-in-momentum spin-orbit induced spin spli…
We have studied charge transport in ferromagnetic Rashba metal (FRM), where both Rashba type spin-orbit coupling (RSOC) and exchange coupling coexist. It has nontrivial metallic states, i.e., normal Rashba metal (NRM), anomalous Rashba metal (ARM), and Rashba ring metal (RRM), and they are manipulated by tuning the Fermi level with an applied gate voltage. We theoretically studied tunneling conductance (G) in a normal metal / FRM junction by changing the Fermi level via an applied gate voltage (Vg) on the FRM. We found a wide variation in the Vg dependence of G, which depends on the metallic s…
Theory of Rashba spin-orbit coupling in magnetic metals is worked out from microscopic Hamiltonian describing d-orbitals. When structural inversion symmetry is broken, electron hopping between $d$-orbitals generates chiral ordering of orbital angular momentum, which combines with atomic spin-orbit coupling to result in the Rashba interaction. Rashba parameter characterizing the interaction is band-specific, even reversing its sign from band to band. Large enhancement of the Rashba parameter found in recent experiments is attributed to the orbital mixing of 3d magnetic atoms with non-magnetic h…
We study the spatial distribution of spin torque induced by a strong Rashba spin-orbit coupling (RSOC) in a ferromagnetic (FM) metal layer, using the Keldysh non-equilibrium Green's function method. In the presence of the s-d interaction between the non-equilibrium conduction electrons and the local magnetic moments, the RSOC effect induces a torque on the moments, which we term as the Rashba spin torque. A correlation between the Rashba spin torque and the spatial spin current is presented in this work, clearly mapping the spatial distribution of Rashba Spin torque in a nano-sized ferromagnet…
We theoretically studied the in-plane tunneling spectroscopy of the hybrid structure composed of a metal and a semiconductor with Rashba spin-orbit coupling. We found that the energy spacing between two distinct features in the conductance spectrum can be used to measure the Rashba energy of the semiconductor. We also considered the effect that varying the probability of spin-conserving and spin-flip scattering at the interface has on the overall conductance. Surprisingly, an increase in interface scattering probability can actually result in increased conductance under certain conditions. Par…
We report the observation of magnetoresistance originating from Rashba spin-orbit coupling (SOC) in a metallic heterostructure: the Rashba-Edelstein (RE) magnetoresistance. We show that the simultaneous action of the direct and inverse RE effects in a Bi/Ag/CoFeB trilayer couples current-induced spin accumulation to the electric resistance. The electric resistance changes with the magnetic-field angle, reminiscent of the spin Hall magnetoresistance, despite the fact that bulk SOC is not responsible for the magnetoresistance. We further found that, even when the magnetization is saturated, the …
We report an unconventional behavior of electron transport in the limit of zero magnetic flux in a one-dimensional disordered ring, be it completely random or any correlated one, subjected to Rashba spin-orbit (SO) coupling. It exhibits much higher circulating current compared to a fully perfect ring for a wide range of SO coupling yielding larger electrical conductivity which is clearly verified from our Drude weight analysis.
We report an intrinsic form of the inverse spin Hall effect (ISHE) in ferromagnetic (FM) metal with Rashba spin orbit coupling (RSOC), which is driven by a normal charge current. Unlike the conventional form, the ISHE can be induced without the need for spin current injection from an external source. Our theoretical results show that Hall voltage is generated when the FM moment is perpendicular to the ferromagnetic layer. The polarity of the Hall voltage is reversed upon switching the FM moment to the opposite direction, thus promising a useful readback mechanism for memory or logic applicatio…
We calculate the current-voltage characteristic of a one-dimensional band insulator with magnetic field and Rashba spin-orbit coupling which is connected to nonmagnetic leads. Without spin-orbit coupling we find a complete spin-filtering effect, meaning that the electric transport occurs in one spin channel only. For a large magnetic field which closes the band gap, we show that spin-orbit coupling leads to a transition from metallic to insulating behavior. The oscillations of the different spin-components of the current with the length of the transport channel are studied as well.
We study how the Rashba spin-orbit interaction influences unconventional superconductivity in a two dimensional electron gas partially spin-polarized by a magnetic field. Somewhat surprisingly, we find that for all field orientations, only the larger Fermi surface is superconducting. When the magnetic field is oriented out-of-plane the system realizes a topological $p+ip$ pairing state. When the field is rotated in-plane the order parameter develops nodes along the field direction and finite center-of-mass-momentum pairing is realized. We demonstrate that the pairing symmetry of the system can…
By using the momentum-space Lanczos recursive method which considers rigorously all multiple-scattering events, we unveil that the non-perturbative disorder effect has dramatic impact on the charge transport of a two-dimensional electron system with Rashba spin-orbit coupling in the low-density region. Our simulations find a power-law dependence of the dc longitudinal conductivity on the carrier density, with the exponent linearly dependent on the Rashba spin-orbit strength but independent of the disorder strength. Therefore, the classical charge transport influenced by complicated multiple-sc…
We show theoretically that conversion between spin and charge by spin-orbit interaction in metals occurs even in a non-local setup where magnetization and spin-orbit interaction are spatially separated if electron diffusion is taken into account. Calculation is carried out for the Rashba spin-orbit interaction treating the coupling with a ferromagnet perturbatively. The results indicate the validity of the concept of effective spin gauge field (spin motive force) in the non-local configuration. The inverse Rashba-Edelstein effect observed for a trilayer of a ferromagnet, a normal metal and a h…
The magnetoresistance of a three-dimensional Rashba material placed on top of a ferromagnetic insulator is theoretically investigated. In addition to the intrinsic Rashba spin-orbit interaction, we also consider extrinsic spin-orbit coupling via side-jump and skew scattering, and the Elliott-Yafet spin relaxation mechanism. The latter is anisotropic due to the mass anisotropy which reflects the noncentrosymmetric crystal structure of three-dimensional Rashba metals. A quasiclassical approach is employed to derive a set of coupled spin-diffusion equations, which are supplemented by boundary con…
The anomalous Hall effect (AHE) is a quantum coherent transport phenomenon that conventionally vanishes at elevated temperatures because of thermal dephasing. Therefore, it is puzzling that the AHE can survive in heavy metal (HM)/antiferromagnetic (AFM) insulator (AFMI) heterostructures at high temperatures yet disappears at low temperatures. In this paper, we report that an unconventional high-temperature AHE in HM/AFMI is observed only around the Néel temperature of AFM, with large anomalous Hall resistivity up to 40 n$Ω$ cm. This mechanism is attributed to the emergence of a noncollinear AF…
We propose that the hybridization between two sets of Rashba bands can lead to an unconventional topology where the two Fermi circles from different bands own in-plane helical spin textures with the same chiralities, and possess group velocities with the same directions. Under the weak spin injection, the two Fermi circles both give the positive contributions to the spin-to-charge conversion and thus induce the giant inverse Rashba-Edelstein Effect with large conversion efficiency, which is very different from the conventional Rashba-Edelstein Effect. More importantly, through the first-princi…
This paper considers a model consisting of a kinetic term, Rashba spin-orbit coupling and short-range Coulomb interaction at zero-temperature. The Coulomb interaction is decoupled by a mean-field approximation in the spin channel using field theory methods. The results feature a first-order phase transition for any finite value of the chemical potential and quantum criticality for vanishing chemical potential. The Hall conductivity is also computed using Kubo formula in a mean-field effective Hamiltonian. In the limit of infinite mass the kinetic term vanishes and all the phase transitions are…
Microscopic origin of Rashba coupling from first principles: Layer-resolved orbital asymmetry in transition metal dichalcogenides
University of Hamburg（汉堡大学）；Max Planck Institute for the Structure and Dynamics of Matter（马克斯·普朗克物质结构与动力学研究所）；The Hamburg Centre for Ultrafast Imaging（汉堡超快成像中心）
The spin-galvanic (inverse Edelstein) and inverse spin-Hall effects are calculated for a hybrid system that combines thin superconductor and Rashba-metal layers. These effects are produced by a nonequilibrium spin polarization which is injected into the normal metal layer. This polarization gives rise to an electric potential that relaxes within some characteristic length, which is determined by Andreev reflection. Within this length the dissipative electric current of quasiparticles in the normal layer converts into the supercurrent. This process involves only subgap states and at low tempera…
The ability of spin-orbit interactions to convert charge current into spin current, most often in the bulk of heavy metal thin films, has been the hallmark of spintronics in the last decade. In this study, we demonstrate how the insertion of light metal element interface profoundly affects both the nature of spin-orbit torque and its efficiency in terms of damping-like ($H_{\text{DL}}$) and field-like ($H_{\text{FL}}$) effective fields in ultrathin Co ferromagnet. Indeed, we measure unexpectedly large $H_{\text{FL}}$/$H_{\text{DL}}$ ratio ($\sim$2.5) upon inserting a 1.4 nm thin Al layer in Pt…
Odd-angular momentum exciton states are dark to light in monolayers of transition-metal dichalcogenides and can be addressed only by two-photon probes. Besides, $2p$ excitons states are expected to show a fine splitting that arises from the peculiar electronic band structure of the material, characterized by a finite Berry curvature around each valley. In this work we study in detail the coupling of photons to $p$ exciton states and we find that the Rashba spin-orbit interaction or a Skyrmion in the transition-metal dichalcogenide substrate can be exploited to engineer finite optical selection…
In metallic noncentrosymmetric crystals and at surfaces the response of spin currents and charge currents to applied electric fields contains contributions that are second order in the electric field, which are forbidden by symmetry in centrosymmetric systems. Thereby, photocurrents and spin photocurrents can be generated in inversion asymmetric metals by the application of femtosecond laser pulses. We study the laser-induced charge current in the ferromagnetic Rashba model with in-plane magnetization and find that this \textit{magnetic photogalvanic effect} can be tuned to be comparable in si…
Au(111) or similar noble metal surfaces feature Tamm-Shockley surface states that are known to possess considerable spin-orbit splitting of the Rashba type of order $Δ=0.1$ eV. When interacting with an electromagnetic field such states are expected to have resonances when the frequency of the field is near the energy of the spin-orbit splitting $Δ$. These resonances originate in the intersubband transitions between spin-split subbands. Such resonances can be observed in the frequency dependence of the surface impedance. Plasmons in thin metal films are gapless and can be strongly affected by t…
We investigate the Rashba-type spin splitting in the Shockley surface states on Au(111) and Ag(111) surfaces, based on first-principles calculations. By turning on and off spin-orbit interaction (SOI) partly, we show that although the surface states are mainly of p-orbital character with only small d-orbital one, d-channel SOI determines the splitting and the spin direction while p-channel SOI has minor and negative effects. The small d-orbital character of the surface states, present even without SOI, varies linearly with the crystal momentum k, resulting in the linear k dependence of the spl…
The weak interlayer Van Der Waals material \{beta}-Bi2Pd has recently been established as a strong topological superconductor candidate with unconventional spin-triplet pairing and Majorana zero modes at vortices. In this letter, we study the topological characters and the superconducting pairing, which are still obscure in monolayer \{beta}-Bi2Pd, in light of our effective theoretical model. We find that the non-Rashba spin-orbital coupling plays a critical role in realizing and tuning various novel topological natures. In particular, the spin-triplet p-wave superconducting pairing with Major…
Two-dimensional (2D) Rashba systems have been intensively studied in the last decade due to their unconventional physics, tunability capabilities, and potential for spin-charge interconversion when compared to conventional heavy metals. With the advent of a new generation of spin-based logic and memory devices, the search for Rashba systems with more robust and larger conversion efficiencies is expanding. Conventionally, demanding techniques such as angle- and spin-resolved photoemission spectroscopy are required to determine the Rashba parameter $α_{R}$ that characterizes these systems. Here,…
Despite its extremely weak intrinsic spin-orbit coupling (SOC), graphene has been shown to acquire considerable SOC by proximity coupling with exfoliated transition metal dichalcogenides (TMDs). Here we demonstrate strong induced Rashba SOC in graphene that is proximity coupled to a monolayer TMD film, MoS2 or WSe2, grown by chemical vapor deposition with drastically different Fermi level positions. Graphene/TMD heterostructures are fabricated with a pickup-transfer technique utilizing hexagonal boron nitride, which serves as a flat template to promote intimate contact and therefore a strong i…
Strong spin-orbit coupling in noncentrosymmetric materials and interfaces results in remarkable physical phenomena, such as nontrivial spin textures, which may exhibit Rashba, Dresselhaus, and other intricated configurations. This provides a promising basis for nonvolatile spintronic devices and further implications. Here, we simulate from first principles a two-dimensional electron gas in ultrathin platinum and palladium layers grown on ferroelectric PbTiO$_3$(001). The latter allows, in principle, to switch and control the spin-to-charge conversion by the polarization reversal. We show how t…
We explore transport properties of a normal metal-superconductor-normal metal (NSN) junction, where the superconducting region supports mixed singlet and chiral triplet pairings. We show that in the subgapped regime when the chiral triplet pairing amplitude dominates over that of the singlet, a resonance phenomena emerges out where all the quantum mechanical scattering probabilities acquire a value of 0.25. At the resonance, crossed Andreev reflection mediating through such junction, acquires a zero energy peak. This reflects as a zero energy peak in the conductance as well in the topological …
We report on a general theory for analyzing quantum transport through devices in the Metal-QD-Metal configuration where QD is a quantum dot or the device scattering region which contains Rashba spin-orbital and electron-electron interactions. The metal leads may or may not be ferromagnetic, they are assumed to weakly couple to the QD region. Our theory is formulated by second quantizing the Rashba spin-orbital interaction in spectral space (instead of real space), and quantum transport is then analyzed within the Keldysh nonequilibrium Green's function formalism. The Rashba interaction causes …
Magnetic electric effects in ferromagnetic metals are discussed from the viewpoint of effective spin electromagnetic field that couples to conduction electron spin. The effective field in the adiabatic limit is the spin Berry's phase in space and time, and it leads to spin motive force (voltage generated by magnetization dynamics) and topological Hall effect due to spin chirality. Its gauge coupling to spin current describes the spin transfer effect, where magnetization structure is driven by an applied spin current. The idea of effective gauge field can be extended to include spin relaxation …
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 (2DEGs) display a large and gate-tunable conversion efficiency, as determined by transport measurements. However, a direct visualization of the Rashba-split bands in oxide 2DEGs is lacking, which hampers an advanced understanding of their rich spin-orbit physics. Here, we investigate KTaO$_3$-2DEGs and evidence their Rashba-split bands using angle resolved photoemission spectroscopy. Fitting the bands with a …
Recent experiments in semiconductor nanowires with a spin-orbit coupling and proximity-induced superconductivity exhibit signatures of Majorana bound states predicted to exist in the topological phase. In this work we predict that these nanowire systems exhibit unconventional magnetoelectric effects showing a sharp crossover behavior at the topological phase transition. We find that magnetic fields with a component parallel to the spin-orbit field can give rise to currents in equilibrium. Surprisingly, also fields perpendicular to the spin-orbit field may induce currents and can be employed in…
We have studied spin-orbit (SO) field in Ni$_{80}$Fe$_{20}$(Py)/W/Pt trilayer by means of spin-torque ferromagnetic resonance, and demonstrated that the W/Pt interface generates an extra SO field acting on the Py layer. This unprecedented field originates from the following three processes, 1) spin accumulation at W/Pt interface via the Rashba-Edelstein effect, 2) diffusive spin transport in the W layer, and 3) spin absorption into the Py layer through accumulation at the Py/W interface. Our result means that we can create extra SO field away from the ferromagnet/ metal interface and control i…
We show that a chain of nonmagnetic impurities deposited on a fully gapped two- or three-dimensional superconductor can become a topological one-dimensional superconductor with protected Majorana bound states at its end. A prerequisite is that the pairing potential of the underlying superconductor breaks the spin-rotation symmetry, as it is generically the case in systems with strong spin-orbit coupling. We illustrate this mechanism for a spinless triplet-superconductor p+ip and a time-reversal symmetric Rashba superconductor with a mixture of singlet and triplet pairing. For the latter, we sh…
Thanks to its unique symmetry, the unidirectional spin Hall and Rashba-Edelstein magnetoresistance (USRMR) is of great fundamental and practical interest, particularly in the context of reading magnetization states in two-terminal spin-orbit torque switching memory and logic devices. Recent studies show that topological insulators could improve USRMR amplitude. However, the topological insulator device configurations studied so far in this context, namely ferromagnetic metal/topological insulator bilayers and magnetically doped topological insulators, suffer from current shunting by the metall…
We theoretically investigate the magnetization inside a normal metal containing the Rashba spin-orbit interaction (RSOI) induced by the proximity effect in an s-wave superconductor/normal metal/ferromagnetic metal/s-wave superconductor (S/N/F/S) Josephson junction. By solving the linearized Usadel equation taking account of the RSOI,we find that the direction of the magnetization induced by the proximity effect in N can be reversed by tuning the RSOI.Moreover, we also find that the direction of the magnetization inside N can be reversed by changing the superconducting phase difference, i.e., J…
