Intrinsic Spin Orbit Research Articles

Edge states and quantum phase transition in graphene under in-plane effective exchange fields

We investigated the edge states and quantum phase transition in graphene under an in-plane effective exchange field. The result shows that the combined effects of the in-plane effective exchange field and a staggered sublattice potential can induce zero-energy flat bands of edge states. Such flat-band edge states can evolve into helical-like ones in the presence of intrinsic spin–orbit coupling, with a unique spin texture. We also find that the bulk energy gap induced by the spin–orbit coupling and staggered sublattice potential can be closed and reopened with the in-plane effective exchange field, and the reopened bulk gap can be even larger than that induced by only the spin–orbit coupling and staggered sublattice potential, which is different from the case of an out-of-plane effective exchange field. The calculated spin-dependent Chern numbers suggest that the bulk gap closing and reopening is accompanied by a quantum phase transition from a trivial insulator phase across a metal phase into a spin-dependent quantum Hall phase.

Electric control of spin transport in GaAs (111) quantum wells

We show by spatially and time-resolved photoluminescence that the application of an electric field transverse to the plane of an intrinsic GaAs (111) quantum well (QW) allows the transport of photogenerated electron spins polarized along the direction perpendicular to the QW plane over distances exceeding 10~$\mu$m. We attribute the long spin transport lengths to the compensation of the in-plane effective magnetic field related to the intrinsic spin-orbit (SO) interaction by means of the electrically generated SO-field. Away from SO-compensation, the precession of the spin vector around the SO-field decreases the out-of-plane polarization of the spin ensemble as the electrons move away from the laser generation spot. The results are reproduced by a model for two-dimensional drift-diffusion of spin polarized charge carriers under weak SO-interaction.

Time-reversal breaking and spin transport induced by magnetic impurities in a 2D topological insulator

We employed the formalism of bond currents, expressed in terms of non-equilibrium Green’s function to obtain the local currents and transport features of zigzag silicene ribbon in the presence of magnetic impurity. When only intrinsic and Rashba spin–orbit interactions are present, silicene behaves as a two-dimensional topological insulator with gapless edge states. But in the presence of finite intrinsic spin–orbit interaction, the edge states start to penetrate into the bulk of the sample by increasing Rashba interaction strength. The exchange interaction induced by local impurities breaks the time-reversal symmetry of the gapless edge states and influences the topological properties strongly. Subsequently, the singularity of partial Berry curvature disappears and the silicene nanoribbon becomes a trivial insulator. On the other hand, when the concentration of the magnetic impurities is low, the edge currents are not affected significantly. In this case, when the exchange field lies in the x–y plane, the spin mixing around magnetic impurity is more profound rather than the case in which the exchange field is directed along the z-axis. Nevertheless, when the exchange field of magnetic impurities is placed in the x–y plane, a spin-polarized conductance is observed. The resulting conductance polarization can be tuned by the concentration of the impurities and even completely polarized spin transport is achievable.

Edge magnetism of finite graphene-like nanoribbons in the presence of intrinsic spin–orbit interaction and perpendicular electric field

This paper elucidates the combined effect of intrinsic spin–orbit interaction (ISOI) and perpendicular electric field on edge states in finite graphene-like nanoribbons. It is shown that the ISOI generates magnetic anisotropy which makes the in-plane edge magnetization configuration more energetically stable than the commonly studied out-of-plane one. The anisotropy less severely suppresses the former configuration than the latter. As concerns the Ez effect, the following evolution of electric transport properties is predicted: magnetic insulator, non-magnetic narrow-band semiconductor, and finally non-magnetic band insulator.

Topological features of engineered arrays of adsorbates in honeycomb lattices

Hydrogen adatoms are one of the most the promising proposals for the functionalization of graphene. The adatoms induce narrow resonances near the Dirac energy, which lead to the formation of magnetic moments. Furthermore, they also create local lattice distortions which enhance the spin–orbit coupling. The combination of magnetism and spin–orbit coupling allows for a rich variety of phases, some of which have non-trivial topological features. We analyze the interplay between magnetism and spin–orbit coupling in ordered arrays of adsorbates on honeycomb lattice monolayers, and classify the different phases that may arise. We extend our model to consider arrays of adsorbates in graphene-like crystals with stronger intrinsic spin–orbit couplings. We also consider a regime away from half-filling in which the Fermi level is at the bottom of the conduction band, we find a Berry curvature distribution corresponding to a Valley–Hall effect.

Effective spin-orbit couplings in an analytical tight-binding model of DNA: Spin filtering and chiral spin transport

We derive a detailed analytical tight-binding (TB) model for a double helix emulating DNA with one type of nucleotide pair and a single oriented $\ensuremath{\pi}$ orbital per base. The TB model incorporates both kinetic and intrinsic spin-orbit (ISO) contributions as well as Rashba-type interactions coupled to an external electric field along the axis of the double helix. The helical structure of the molecule renders the ISO first order in the interaction strength (in the meV range) as in carbon nanotubes. The coupling between the ISO and the chirality of the molecule is manifest in the effective coupling parameters while the Rashba coupling is only weakly dependent on structural chirality. A continuum model at half filling is derived where the dispersion is linear around the Fermi level. Spin transport can be completely solved in the case of ISO and the dominant Rashba type term. Spin selectivity is shown to exist for this minimal model (with features similar to recent experimental findings) when the double helix is biased and thus time reversal symmetry is broken. The model also display robustness toward scattering because of the chiral nature of the eigenstates.

Finite size effects on the helical edge states on the Lieb lattice**Project supported by the National Natural Science Foundation of China (Grant No. 11274102), the Program for New Century Excellent Talents in University of the Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of the Higher Education of China (Grant No.

For a two-dimensional Lieb lattice, that is, a line-centered square lattice, the inclusion of the intrinsic spin–orbit (ISO) coupling opens a topologically nontrivial gap, and gives rise to the quantum spin Hall (QSH) effect characterized by two pairs of gapless helical edge states within the bulk gap. Generally, due to the finite size effect in QSH systems, the edge states on the two sides of a strip of finite width can couple together to open a gap in the spectrum. In this paper, we investigate the finite size effect of helical edge states on the Lieb lattice with ISO coupling under three different kinds of boundary conditions, i.e., the straight, bearded and asymmetry edges. The spectrum and wave function of edge modes are derived analytically for a tight-binding model on the Lieb lattice. For a strip Lieb lattice with two straight edges, the ISO coupling induces the Dirac-like bulk states to localize at the edges to become the helical edge states with the same Dirac-like spectrum. Moreover, it is found that in the case with two straight edges the gapless Dirac-like spectrum remains unchanged with decreasing the width of the strip Lieb lattice, and no gap is opened in the edge band. It is concluded that the finite size effect of QSH states is absent in the case with the straight edges. However, in the other two cases with the bearded and asymmetry edges, the energy gap induced by the finite size effect is still opened with decreasing the width of the strip. It is also proposed that the edge band dispersion can be controlled by applying an on-site potential energy on the outermost atoms.

Electrically tunable spin polarization in silicene: A multi-terminal spin density matrix approach

Recent realized silicene field-effect transistor yields promising electronic applications. Using a multi-terminal spin density matrix approach, this paper presents an analysis of the spin polarizations in a silicene structure of the spin field-effect transistor by considering the intertwined intrinsic and Rashba spin–orbit couplings, gate voltage, Zeeman splitting, as well as disorder. Coexistence of the stagger potential and intrinsic spin–orbit coupling results in spin precession, making any in-plane polarization directions reachable by the gate voltage; specifically, the intrinsic coupling allows one to electrically adjust the in-plane components of the polarizations, while the Rashba coupling to adjust the out-of-plan polarizations. Larger electrically tunable ranges of in-plan polarizations are found in oppositely gated silicene than in the uniformly gated silicene. Polarizations in different phases behave distinguishably in weak disorder regime, while independent of the phases, stronger disorder leads to a saturation value.

Geometrical spin manipulation in Dirac flakes

We investigate numerically the spin properties of electrons in flakes made of materials described by the Dirac equation, in the presence of intrinsic spin–orbit coupling (SOC). We show that electrons flowing along the borders of flakes via edge states become helically spin-polarized for strong SOC, for materials with and without a gap at the Fermi energy, corresponding to the massive and massless Dirac equation respectively. The helically spin-polarized electrons create spin-resolved transport, controlled by the flake’s geometry in a multi-terminal device setup. A simple analytical model containing the basic ingredients of the problem is introduced to get an insight into the helical mechanism, along with our numerical results which are based on an effective tight-binding model.

Competition between spin–orbit interaction and exchange coupling within a honeycomb lattice ribbon

Spin density patterns of a pinned magnetic impurity that is embedded in a honeycomb lattice with zigzag edges are investigated by employing a mean-field assisted Landauer–Keldysh formalism. Both the intrinsic spin–orbit coupling and the extrinsic localized magnetic moments are considered, and the effects of the pinning directions and the species of the sublattice on the electron spins are analyzed. A local time-reversal symmetry breaking cannot destroy the equilibrium edge-state spin accumulation that is induced by intrinsic spin–orbit coupling when the pinning field lies in the plane of the ribbon and the embedding position is the A-site at the edge. The induced local spin can be either parallel or antiparallel to the localized impurity moment, depending on the location of the pinned impurity, because itinerant electrons are found only at the B-site of the edge, but not at the A-site.

Tetragonal bismuth bilayer: a stable and robust quantum spin hall insulator

Topological insulators (TIs) exhibit novel physics with great promise for new devices, but considerable challenges remain to identify TIs with high structural stability and large nontrivial band gap suitable for practical applications. Here we predict by first-principles calculations a two-dimensional (2D) TI, also known as a quantum spin Hall (QSH) insulator, in a tetragonal bismuth bilayer (TB-Bi) structure that is dynamically and thermally stable based on phonon calculations and finite-temperature molecular dynamics simulations. Density functional theory and tight-binding calculations reveal a band inversion among the Bi-p orbits driven by the strong intrinsic spin–orbit coupling, producing a large nontrivial band gap, which can be effectively tuned by moderate strains. The helical gapless edge states exhibit a linear dispersion with a high Fermi velocity comparable to that of graphene, and the QSH phase remains robust on a NaCl substrate. These remarkable properties place TB-Bi among the most promising 2D TIs for high-speed spintronic devices, and the present results provide insights into the intriguing QSH phenomenon in this new Bi structure and offer guidance for its implementation in potential applications.

Evidence for two-dimensional Ising superconductivity in gated MoS₂.

The Zeeman effect, which is usually detrimental to superconductivity, can be strongly protective when an effective Zeeman field from intrinsic spin-orbit coupling locks the spins of Cooper pairs in a direction orthogonal to an external magnetic field. We performed magnetotransport experiments with ionic-gated molybdenum disulfide transistors, in which gating prepared individual superconducting states with different carrier dopings, and measured an in-plane critical field B(c2) far beyond the Pauli paramagnetic limit, consistent with Zeeman-protected superconductivity. The gating-enhanced B(c2) is more than an order of magnitude larger than it is in the bulk superconducting phases, where the effective Zeeman field is weakened by interlayer coupling. Our study provides experimental evidence of an Ising superconductor, in which spins of the pairing electrons are strongly pinned by an effective Zeeman field.

Enhanced spin–orbit coupling in dilute fluorinated graphene

The preservation and manipulation of a spin state mainly depends on the strength of the spin–orbit interaction. For pristine graphene, the intrinsic spin–orbit coupling (SOC) is only in the order of few μeV, which makes it almost impossible to be used as an active element in future electric field controlled spintronics devices. This stimulates the development of a systematic method for extrinsically enhancing the SOC of graphene. In this letter, we study the strength of SOC in weakly fluorinated graphene devices. We observe high non-local signals even without applying any external magnetic field. The magnitude of the signal increases with increasing fluorine adatom coverage. From the length dependence of the non-local transport measurements, we obtain SOC values of ∼5.1 meV and ∼9.1 meV for the devices with ∼0.005% and ∼0.06% fluorination, respectively. Such a large enhancement, together with the high charge mobility of fluorinated samples (μ ∼ 4300 cm2 V−1 s−1–2700 cm2 V−1 s−1), enables the detection of the spin Hall effect even at room temperature.

Fidelity susceptibility in multiband one-dimensional topological superconducting system

We use the fidelity susceptibility to study the topological properties of multi-layer nanowire system, with intrinsic spin–orbit coupling and proximity induced superconductivity. We introduce a Hamiltonian of three layer lattice chain to model the system, and consider the effects of applied Zeeman field. In pure system, we find a peak in fidelity susceptibility, which signals the topological quantum phase transition (TQPT) in the system. We then study the disorder effects in our model and find more peaks in fidelity susceptibility. We reveal that these peaks provide information on the zero energy Majorana states of the system, which appear after the TQPT.

Spin–orbit interaction in bent carbon nanotubes: resonant spin transitions

We develop an effective tight-binding Hamiltonian for spin–orbit (SO) interaction in bent carbon nanotubes (CNT) for the electrons forming the π bonds between the nearest neighbor atoms. We account for the bend of the CNT and the intrinsic spin–orbit interaction which introduce mixing of π and σ bonds between the pz orbitals along the CNT. The effect contributes to the main origin of the SO coupling—the folding of the graphene plane into the nanotube. We discuss the bend-related contribution of the SO coupling for resonant single-electron spin and charge transitions in a double quantum dot. We report that although the effect of the bend-related SO coupling is weak for the energy spectra, it produces a pronounced increase of the spin transition rates driven by an external electric field. We find that spin-flipping transitions driven by alternate electric fields have usually larger rates when accompanied by charge shift from one dot to the other. Spin-flipping transition rates are non-monotonic functions of the driving amplitude since they are masked by stronger spin-conserving charge transitions. We demonstrate that the fractional resonances—counterparts of multiphoton transitions for atoms in strong laser fields—occurring in electrically controlled nanodevices already at moderate ac amplitudes—can be used to maintain the spin-flip transitions.

Magnetotransport properties of corrugated stanene in the presence of electric modulation and tilted magnetic field

We investigated the effects of external electric and magnetic fields on the electronic and transport properties of corrugated stanene. We match density functional calculations with the effective Dirac model and applied external fields in the Dirac model. We calculate both the Fermi velocity and the strength of spin–orbit interaction in stanene within the framework of density functional theory. In the presence of intrinsic spin–orbit interaction accompanying with external electric field splits spin‐up and down states. We also study the spin‐dependent Landau levels and transport for stanene in the presence of periodically modulated electric and tilted magnetic fields with corrugation. Additionally, the Weiss and spin‐polarization oscillations with inverse of magnetic field in stanene are reported.

ChemInform Abstract: The Electronic Structure Calculations of Two‐Dimensional Transition‐Metal Dichalcogenides in the Presence of External Electric and Magnetic Fields

AbstractReview: 50 refs.

Long-range spin-triplet correlations and edge spin currents in diffusive spin–orbit coupled SNS hybrids with a single spin-active interface

Utilizing a SU(2) gauge symmetry technique in the quasiclassical diffusive regime, we theoretically study finite-sized two-dimensional intrinsic spin–orbit coupled superconductor/normal-metal/superconductor (S/N/S) hybrid structures with a single spin-active interface. We consider intrinsic spin–orbit interactions (ISOIs) that are confined within the N wire and absent in the s-wave superconducting electrodes (S). Using experimentally feasible parameters, we demonstrate that the coupling of the ISOIs and spin moment of the spin-active interface results in maximum singlet-triplet conversion and accumulation of spin current density at the corners of the N wire nearest the spin-active interface. By solely modulating the superconducting phase difference, we show how the opposing parities of the charge and spin currents provide an effective venue to experimentally examine pure edge spin currents not accompanied by charge currents. These effects occur in the absence of externally imposed fields and moreover are insensitive to the arbitrary orientations of the interface spin moment. The experimental implementation of these robust edge phenomena are also discussed.

Spontaneous edge accumulation of spin currents in finite-size two-dimensional diffusive spin–orbit coupled SFS heterostructures

We theoretically study spin and charge currents through finite-size two-dimensional s-wave superconductor/uniform ferromagnet/s-wave superconductor (S/F/S) junctions with intrinsic spin–orbit interactions (ISOIs) using a quasiclassical approach. Considering experimentally realistic parameters, we demonstrate that the combination of spontaneously broken time-reversal symmetry and lack of inversion symmetry can result in spontaneously accumulated spin currents at the edges of finite-size two-dimensional magnetic S/F/S hybrids. Due to the spontaneous edge spin accumulation, the corners of the F wire host the maximum spin current density. We further reveal that this type edge phenomena is robust and independent of either the actual type of ISOIs or exchange field orientation. Moreover, we study the spin current-phase relations in these diffusive spin–orbit coupled S/F/S junctions. Our results unveil net spin currents, not accompanied by charge supercurrents, that spontaneously accumulate at the sample edges through a modulating superconducting phase difference. Finally, we discuss possible experimental implementations to observe these edge phenomena.

Effect of external strain on electronic structure of stanene

In this article we study the effect of applied strain on the electronic and mechanical properties of stanene, the Tin counterpart of graphene. Due to the relatively large intrinsic spin–orbit coupling we used the fully-relativistic pseudo-potentials to consider the effect of spin–orbit in the density functional calculations. The spin–orbit interaction opens a 70meV energy gap in the K point but by applying strain the energy gap in the band structure is closed. The density functional theory and simple molecular mechanic models are used to estimate the Young’s modulus of stanene. According to our calculations we estimate the in-plane stiffness of stanene Ys=40N/m. By matching DFT and molecular mechanic results of stanene, we investigate the size and chirality effects on the in-plane stiffness of stanene nano ribbons.