Presence Of Rashba Spin-orbit Coupling Research Articles

Ultrafast switching in spin field-effect transistors based on borophene nanoribbons.

Borophene, owing to the high mobility and long spin coherent length of its carriers, presents significant opportunities in ultrafast spintronics. In this research, we investigate the spin-dependent conductance of a Datta-Das field-effect transistor (FET) based on an armchair β12-borophene nanoribbon (BNR) using the tight-binding (TB) Hamiltonian in combination with the non-equilibrium Green's function (NEGF) method. The spin FET electrodes are magnetized by ferromagnetic (FM) insulators arranged in both parallel and anti-parallel configurations. This device acts as a controllable spin filter in the presence of Rashba spin-orbit coupling (SOC) for both configurations and its spin current is well modulated by a gate voltage and the strength of the Rashba SOC. For anti-parallel configurations, an energy gap emerges within a certain range of incoming electron energy which can disappear for electrons with flipped spin under the Rashba SOC. Furthermore, our findings indicate that the electron-electron (e-e) interaction helps the spin precession of electrons injected into the spin FET channel, thereby strengthening the Rashba SOC effect. Notably, a gate voltage can adjust the current-voltage (I-V) characteristics of this device. Finally, our calculations demonstrate that under the same conditions, the current magnitude and Ion/Ioff ratio of borophene spin FETs are several times higher than those of graphene and silicene spin FETs.

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.

Topological properties of Xene tuned by perpendicular electric field and exchange field in the presence of Rashba spin–orbit coupling

Xene (X=Si, Ge, Sn) is a typical and promising two-dimensional topological insulator with many novel topological properties. Here, we investigate the topological properties of Xene tuned by a perpendicularly applied electric field, exchange field, and Rashba spin–orbit coupling (RSOC) using the tight-binding (TB) method. We show that in the presence of RSOC, the system can be converted from a quantum spin Hall (QSH) insulator into a conventional band insulator (BI) by a weak perpendicular electric field or into a quantum anomalous Hall (QAH) insulator by a weak exchange field. Additionally, a suitable combination of electric and exchange fields can give rise to a valley-polarized metallic (VPM) state. Furthermore, we explore the competition between the electric field and exchange field in tuning the topological states owing to the Rashba coupling effect. When the electric field is stronger than the exchange field, the system tends to be in a topologically trivial BI state; otherwise, it will be a QAH insulator. More intriguingly, for a fixed exchange field and RSOC, as the perpendicular electric field increase continuously from zero, the system undergoes multiphase (e.g. QSH-VPM-BI) transitions. This paves the way for designing multiphase transition devices through external single-field regulation.

Tunable topological phases in monolayer Pt2HgSe3 with exchange fields

We investigate topological phases of monolayer jacutingaite (${\mathrm{Pt}}_{2}{\mathrm{HgSe}}_{3}$) that arise when considering the competing effects of spin-orbit coupling (SOC), magnetic exchange interactions, and staggered sublattice potential $V$. The interplay between the staggered potential and exchange field offers the possibility of attaining different topological phases. By analyzing the Berry curvatures and computing the Chern numbers and Hall conductivities, we demonstrate that the system is time-reversal-symmetry-broken quantum spin Hall insulator when ${m}_{b}<{\ensuremath{\lambda}}_{\mathrm{so}}$, where ${m}_{b}$ is the exchange field operating on the bottom Hg sublattice and ${\ensuremath{\lambda}}_{\mathrm{so}}$ is the intrinsic SOC. For ${m}_{b}>{\ensuremath{\lambda}}_{\mathrm{so}}$ and in the presence of Rashba SOC, we find that the band gap at valley $K({K}^{\ensuremath{'}})$ is topologically trivial (nontrivial) with Chern number $\mathcal{C}=1$ and valley Chern number ${\mathcal{C}}_{v}=\ensuremath{-}1$, indicating that the system is valley-polarized quantum anomalous Hall insulator. We show that the topology of each valley is swapped (the Chern number becomes $\mathcal{C}=\ensuremath{-}1$) by reversing the sign of the exchange field. The system transitions to a valley-polarized metal and quantum valley Hall phase as $V$ increases. Along the phase boundaries, we observe a single Dirac-cone semimetal states. These findings shed more light on the possibility of realizing and controlling topological phases in spintronics and valleytronics devices.

Graphene bilayer and trilayer moiré lattice with Rashba spin-orbit coupling

We study the behavior of equilibrium spin currents near the magic angles of twisted bilayer and trilayer graphene in the presence of Rashba spin-orbit coupling. There is a substantial difference in the properties of local observables in twisted graphene layers, as compared with those in single and/or untwisted graphene layers. Remarkably, when plotted as a function of the twist angle $\ensuremath{\theta}$, the electronic charge density and the equilibrium spin currents are nonanalytic at angles that are close to within 1% of the magic angles. In addition to the occurrence of rich spin texture patterns, these findings enable the determination of magic angles within an accuracy of less than $0.{01}^{\ensuremath{\circ}}$ in terms of a scanning tunneling microscopy measurement of the local density and spin-resolved measuring devices for measuring equilibrium spin currents.

Symmetry-enforced nodal lines in the band structures of vacancy-engineered graphene

We elaborate that single-layer graphene with periodic vacancies can have a band structure containing nodal lines or nodal loops, opening the possibility of graphene-based electronic or spintronic devices with novel functionalities. The principle is that by removing carbon atoms such that the lattice becomes nonsymmorphic, every two sublattices in the unit cell will map to each other under glide plane operation. This mapping yields degenerate eigenvalues for the glide plane operation, which guarantees that the energy bands must stick together pairwise at a boundary of the Brillouin zone. Moving away from the Brillouin zone boundary causes the symmetry-enforced nodal lines to split, resulting in accidental nodal lines caused by the crossings of the split bands. Moreover, the density of states at the Fermi level may be dramatically enhanced if the nodal lines crosses the Fermi level. The nodal lines occur a variety of vacancy configurations even in the presence of Rashba spin-orbit coupling. Finally, our theory also explains the nodal loops surrounding the entire Brillouin zone of a chevron-type nanoporous graphene fabricated in a recent experiment.

Localization, PT symmetry breaking, and topological transitions in non-Hermitian quasicrystals

The topological phase transition in a Hermitian system is associated with a change in the topological invariant that characterizes the band structure of the two distinct phases. Recently, the delocalization-localization transition in a quasicrystal described by the non-Hermitian $\mathcal{PT}$-symmetric extension of the Aubry-Andr\'e-Harper (AAH) Hamiltonian has been related to a topological phase transition. Interestingly, the $\mathcal{PT}$ symmetry also breaks down at the same point. In this article, we have shown that the delocalization-localization transition and the breaking of $\mathcal{PT}$ symmetry are not connected to a topological phase transition. We have studied the non-Hermitian $\mathcal{PT}$-symmetric AAH Hamiltonian in the presence of Rashba spin-orbit coupling. It has been demonstrated that except in some particular cases, the delocalization-localization and the topological transition points are not identical. In fact, it precedes the topological transition point whenever they do not coincide. However, the breaking of $\mathcal{PT}$ symmetry occurs simultaneously with the delocalization-localization transition. Moreover, we have discovered that the Lyapunov exponent, which is often used as a primary signature to characterize the delocalization-localization transition, does not always determine it correctly. The Lyapunov exponent rather identifies the topological transition point in quasicrystals.

Self-duality of one-dimensional quasicrystals with spin-orbit interaction

Noninteracting spinless electrons in one-dimensional quasicrystals, described by the Aubry-Andr\'e-Harper (AAH) Hamiltonian with nearest-neighbor hopping, undergo a metal-to-insulator transition at a critical strength of the quasiperiodic potential. The AAH Hamiltonian is also known to be self-dual. Interestingly, the critical point and the self-dual point are identical in this case. In this work, we have studied the one-dimensional quasiperiodic AAH Hamiltonian in the presence of spin-orbit coupling of Rashba-type, which introduces an additional spin-conserving complex hopping and a spin-flip hopping. We have found that the AAH Hamiltonian remains self-dual in the presence of Rashba spin-orbit coupling, and the self-dual point follows a simple rescaled relationship among the parameters of the Hamiltonian. This system also undergoes a metal-to-insulator transition, and the nature of this transition has been found to be identical with the original AAH Hamiltonian. However, the critical points do not follow the same relationship as the self-dual points in general. In fact, the metal-to-insulator transition happens earlier than the self-dual point, except in some special cases in which they are observed to coincide.

Prediction of intrinsic topological superconductivity in Mn-doped GeTe monolayer from first-principles

The recent discovery of topological superconductors (TSCs) has sparked enormous interest. The realization of TSC requires a delicate tuning of multiple microscopic parameters, which remains a great challenge. Here, we develop a first-principles approach to quantify realistic conditions of TSC by solving self-consistently Bogoliubov-de Gennes equation based on a Wannier function construction of band structure, in presence of Rashba spin-orbit coupling, Zeeman splitting and electron-phonon coupling. We further demonstrate the power of this method by predicting the Mn-doped GeTe (Ge1-xMnxTe) monolayer—a well-known dilute magnetic semiconductor showing superconductivity under hole doping—to be a Class D TSC with Chern number of −1 and chiral Majorana edge modes. By constructing a first-principles phase diagram in the parameter space of temperature and Mn concentration, we propose the TSC phase can be induced at a lower-limit transition temperature of ~40 mK and the Mn concentration of x~0.015%. Our approach can be generally applied to TSCs with a phonon-mediated pairing, providing useful guidance for future experiments.

Topological properties of Josephson current between two s- and p-wave superconducting nanowires with Majorana fermions

Josephson current between two one-dimensional nanowires with proximity induced either s-wave or p-wave pairing and separated by a narrow dielectric barrier is calculated in the presence of Rashba spin-orbit interaction, in-plane and normal Zeeman magnetic fields. We show that Andreev retro-tunneling is realized by means of two channels. The main contribution to the Josephson current in junction of s- or p-wave superconductors is shown to give Andreev scattering in a conventional particle-hole channel, when an electron-like quasiparticle reflects to a hole-like quasiparticle with opposite spin yielding a current which depends only on the order parameters’ phase differences φ and oscillates with fractional 4π period. Nevertheless Andreev bound state energy in second anomalous particle-hole channel, corresponding to the reflection of an incident electron-like quasiparticle to a hole-like quasiparticle with the same spin orientation, survives only in the presence of the in-plane magnetic field, and oscillates with 4π period not only with φ but also with orientational angle of the in-plane magnetic field θ resulting in a magneto-Josephson effect. In the presence of Rashba spin-orbit coupling (SOC) and normal-to-plane magnetic field h, a forbidden gap is shown to open in the dependence of Andreev bound state energies on the phases φ and θ at several values of SOC strength and magnetic field, where Josephson current seems to vanish. The magnetic fields destroy also the particle-hole symmetry of the mid-gap states around Fermi level.

Josephson current between two p-wave superconducting nanowires in the presence of Rashba spin-orbit interaction and Zeeman magnetic fields

Josephson current between two one-dimensional nanowires with proximity induced p-wave superconducting pairing is calculated in the presence of Rashba spin-orbit interaction, in-plane and normal magnetic fields. We show that Andreev retro-reflection is realized by means of two different channels. The main contribution to the Josephson current gives a scattering in a conventional particle-hole channel, when an electron-like quasiparticle reflects to a hole-like quasiparticle with opposite spin yielding a current which depends only on the order parameters’ phase differences φ and oscillates with 4π period. Second anomalous particle-hole channel, corresponding to the Andreev reflection of an incident electron-like quasiparticle to an hole-like quasiparticle with the same spin orientation, survives only in the presence of the in-plane magnetic field. The contribution of this channel to the Josephson current oscillates with 4π period not only with φ but also with orientational angle of the in-plane magnetic field θ resulting in a magneto-Josephson effect. In the presence of Rashba spin-orbit coupling (SOC) and normal-to-plane magnetic field h, a forbidden gap is shown to open in the dependence of Andreev bound state energies on the phases φ and θ at several values of SOC strength and magnetic field, where Josephson current seems to vanish. We present a detailed theoretical analysis of both DC and AC Josephson effects in such a system showing contributions from these channels and discuss experiments which can test our theory.

Flat bands and ferrimagnetic order in electronically correlated dice-lattice ribbons

We study ribbons of the dice two-dimensional lattice (that we call ``dice ladders'') known to have nontrivial topological properties, such as Chern numbers 2 [Wang and Y. Ran, Phys. Rev. B {\bf 84}, 241103 (2011)]. Our main results are two folded: (1) Analyzing the tight-binding model in the presence of Rashba spin-orbit coupling and an external magnetic field, we observed that dice ladders qualitatively display properties similar to their two-dimensional counterpart all the way to the limit of only two legs in the short direction. This includes flat bands near the Fermi level, edge currents and edge charge localization near zero energy when open boundary conditions are used, two chiral edge modes, and a nonzero Hall conductance. (2) We studied the effect of Hubbard correlation $U$ in the two-leg dice ladder using Lanczos and density matrix renormalization group techniques. We show that increasing $U$ the flat bands split without the need of introducing external fields. Moreover, robust ferrimagnetic order develops. Overall, our work establishes dice ladders as a promising playground to study the combined effect of topology and correlation effects, one of the frontiers in Quantum Materials.

Oxygen Vacancy‐Induced Topological Hall Effect in a Nonmagnetic Band Insulator

AbstractThe discovery of skyrmions has recently sparked tremendous interest in topologically nontrivial spin textures. The signature of the noncoplanar nature of magnetic moments can be observed as topological Hall effect (THE) in electrical measurement. Realization of such nontrivial spin textures in new materials and through new routes is an ongoing endeavor due to their huge potential for future ultra‐dense, low‐power memory applications. In this work, oxygen vacancy (OV)‐induced THE and anomalous Hall effect (AHE) in a 5d0 system KTaO3 are reported. The observation of weak antilocalization behavior and THE in the same temperature range strongly implies the crucial role of spin–orbit coupling (SOC) behind the origin of THE. Ab initio calculations reveal the formation of the magnetic moment on Ta atoms around the OV and Rashba‐type spin texturing of conduction electrons. In the presence of Rashba SOC, the local moments around vacancy can form bound magnetic polarons (BMPs) with noncollinear spin texture, resulting in THE. Scaling analysis between transverse and longitudinal resistance establishes skew scattering‐driven AHE in the present case. This study opens a route to realize topological phenomena through defect engineering.

Classical phase diagram of the Rashba-Hubbard model in the strongly correlated limit on square lattice

In this work, we investigate the interacting electrons on a square lattice in the presence of Rashba spin-orbit coupling. We first obtain the effective spin model from the Rashba-Hubbard model in the strongly correlated limit using the second perturbation theory. The effective spin model includes isotropic Heisenberg terms, nearest- and next-nearest-neighbor interactions, as well as the anisotropic ones as Kane-Mele and Dzyaloshinski-Moriya interactions. We proceed to study the influence of Rashba spin-orbit coupling on the stability of the magnetic phases of isotropic Heisenberg using Luttinger-Tisza and variational minimization classical methods. Our classical calculations show that the anisotropic terms leads to the instability of the Neel, classical degenerate and collinear phases of the isotropic Heisenberg model on the square lattice into an incommensurate planar phase. The spiral magnetic order in the two-dimensional frustrated magnets can be disordered by considering the quantum fluctuations. In a heterostructure including a noncollinear magnet and a singlet superconductor, singlet Cooper pairs can be converted to triplet pairings due to the broken spin rotational symmetry. Therefore, we can engineer a topological superconductor using noncollinear magnet in a heterostructure system.

Anisotropy of the spin-polarized edge current in monolayer transition metal dichalcogenide zigzag nanoribbons

We report anisotropic spin polarization of edge currents in ${\mathrm{MoS}}_{2}$ and ${\mathrm{WS}}_{2}$ monolayer zigzag nanoribbons (ZNRs) deposited on either nonmagnetic or ferromagnetic insulator substrates. We employ an 11-band tight-binding model to calculate the electronic band structures of transition metal dichalcogenide (TMDC) monolayers and their corresponding nanoribbons in the presence of Rashba spin-orbit coupling (RSOC) and magnetic proximity effect produced by ferromagnetic substrate. We adopt the nonequilibrium Green's function method together with Landauer-B\uttiker formalism to study the quantum transport behavior stemming from the edge states of ZNRs. We demonstrate that the spin-polarized edge current can be generated in both ${\mathrm{MoS}}_{2}$ and ${\mathrm{WS}}_{2}$ ZNRs with RSOC. We find that the spin polarization spreads out in all three directions. This is in stark contrast to what occurs in zigzag graphene nanoribbons, for which the polarization only exists in the transverse direction (across the width of ribbons). In addition, the spin polarization direction strongly depends on the strength of the intrinsic SOC component. The interplay of Rashba and intrinsic SOC is crucial for the spin polarization of the currents in any spatial direction. For TMDCs with stronger intrinsic SOC such as in ${\mathrm{WS}}_{2}$ monolayer ZNRs, we observe that the spin polarization along the perpendicular direction to the plane of the ZNR can be as large as $90%$. Moreover, the unusual anisotropy of the spin polarization can be further enhanced by the magnetic proximity effect. These results open up possibilities for the generation of tunable high-spin polarization currents in ZNRs without application of an external magnetic field.

Levitons in helical liquids with Rashba spin-orbit coupling probed by a superconducting contact

We consider transport properties of a single edge of a two-dimensional topological insulators, in presence of Rashba spin-orbit coupling, driven by two external time-dependent voltages and connected to a thin superconductor. We focus on the case of a train of Lorentzian-shaped pulses, which are known to generate coherent single-electron excitations in two-dimensional electron gas, and prove that they are minimal excitations for charge transport also in helical edge states, even in the presence of spin-orbit interaction. Importantly, these properties of Lorentzian-shaped pulses can be tested computing charge noise generated by the scattering of particles at the thin superconductor. This represents a novel setup where electron quantum optics experiments with helical states can be implemented, with the superconducting contact as an effective beamsplitter. By elaborating on this configuration, we also evaluate charge noise in a collisional Hong-Ou-Mandel configuration, showing that, due to the peculiar effects induced by Rashba interaction, a non-vanishing dip at zero delay appears.

Switchable crossed spin conductance in a graphene-based junction: The role of spin-orbit coupling

We theoretically investigate the crossed spin conductance (CSC) of a graphene-based heterostructure consists of ferromagnet, Rashba spin-orbit and superconductor regions. Using Dirac Bogoliubov-de Gennes formalism in the ballistic regime, we show that in the presence of Rashba spin-orbit coupling there are an anomalous crossed Andreev reection and spin-ipped co-tunneling in the process of quantum transport. We demonstrate that the CSC can be reversed with respect to charge conductance by tuning the Rashba spin-orbit coupling which experimentally can be adjusted by the applied perpendicular electric field on the graphene sheet. This feature in addition to a long spin relaxation time of Dirac fermions in graphene proposes designing a device with a non-local spin switch which is crucial for spintronics circuits.

Rashba Cavity QED: A Route Towards the Superradiant Quantum Phase Transition.

We develop a theory of cavity quantum electrodynamics for a 2D electron gas in the presence of Rashba spin-orbit coupling and perpendicular static magnetic field, coupled to spatially nonuniform multimode quantum cavity photon field. We demonstrate that the lowest polaritonic frequency of the full Hamiltonian can vanish for realistic parameters, achieving the Dicke superradiant quantum phase transition. This singular behavior originates from soft spin-flip transitions possessing a nonvanishing dipole moment at nonzero wave vectors and can be viewed as a static paramagnetic instability.

One-dimensional topological superconductivity at the edges of twisted bilayer graphene nanoribbons

Twisted bilayer graphene is one of the simplest van der Waals structures, and its inhomogeneous interlayer coupling can induce rich electronic properties. In twisted bilayer graphene nanoribbons (tBLGNRs), the interlayer coupling strengths are different for two ribbon edges due to the inhomogeneous bonding, which splits the edge states into two individuals in energy. The lower-energy state, localizing at the ribbon edge with the stronger interlayer coupling, is a good candidate to generate one-dimensional (1D) topological superconductivity in the presence of Rashba spin-orbit coupling, Zeeman field, and $s$-wave superconductivity. Majorana zero modes (MZMs) are found to be localized at both ends of this edge. The topological invariants of the system are explored by evaluating the Berry phase for infinite-length ribbons and Majorana polarization for quasi-1D ribbons, giving the same topological phase diagram. More importantly, by adjusting interlayer dislocation and uniaxial strain of tBLGNRs across the critical values, the lower-energy edge changes and 1D topological superconductivity can ``jump'' from one ribbon edge to the other one. Finally, by applying a gate voltage bias between bilayers or changing the interlayer distance, a MZM can transfer along the ribbon edge. The tBLGNRs provide an alternative platform to study 1D topological superconductivity and MZMs.

Connection between zero-energy Yu-Shiba-Rusinov states and0−πtransitions in magnetic Josephson junctions

We study the bound state spectrum and 0-$\pi$ transitions in ballistic quasi-1D superconductor/ferromagnetic insulator/superconductor (S/FI/S) Josephson junctions. In addition to the Andreev bound states, stemming from the phase coherence, the magnetic barrier gives rise to qualitatively different Yu-Shiba-Rusinov (YSR) bound states with genuine spectral features and spin characteristics. We show that zero-energy YSR states are much more robust against scalar tunneling than their Andreev counterparts and also fingerprint a quantum phase transition from the junctions' 0 into the $\pi$ phase, connected to a measurable reversal of the Josephson current flow; this coincidence persists also in the presence of Rashba spin-orbit coupling.