Rashba-like Spin-orbit Coupling Research Articles

Nanoscale studies of electric field effects on monolayer 1T\u2032-WTe2

Monolayer 1 T′-WTe2 is a quantum spin Hall insulator with a gapped 2D-bulk and gapless helical edge states persisting to temperatures ~100 K. Despite the far-ranging interest, the magnitude of the bulk gap, the effect of gating on the 2D-band structure, as well the role interactions are not established. In this work we use STM spectroscopy to measure the intrinsic bulk gap of monolayer 1 T′-WTe2 and show that gate induced electric fields cause large changes of the gap magnitude. Our first-principles DFT-derived tight-binding model reveal that a combination of spatial localization of the conduction and valance bands and Rashba-like spin-orbit coupling leads to a gating induced spin-splitting of the 2D-bulk bands in the tens of meV, thereby reducing the band gap. Our work explains the large sensitivity of the band structure to electric fields and suggests a new avenue for realizing proximity induced non-trivial superconductivity in monolayer 1 T′-WTe2.

Majorana braiding racetracks from charge Chern insulator–superconductor hybrids

Recent experiments have provided evidence for chiral charge order in Kagome superconductors (SCs). This intriguing possibility motivates us to unveil the first pathway to engineer topological superconductivity by harnessing the interplay of charge Chern insulators (CIs) and conventional SCs. We here identify under which conditions a pyramidal SC/CI/SC heterostructure induces an effective 1D spinless p-wave SC that allows pinning Majorana zero modes (MZMs) at termination edges and domain walls. As we reveal, such a MZM track is controlled by the phase difference of the two SCs involved and additional magnetic fields which are required for generating Rashba-like spin-orbit coupling. Further, we show that a SC/CI/SC/CI/SC double-pyramidal hybrid defines a double MZM track, in which braiding occurs by varying the two superconducting phase differences in space and adiabatically in time. Given the geometry of the MZM racetrack, we propose to employ the time-averaged quadrupolar differential conductance to confirm the here-termed MZM track exchange process which is pivotal for braiding. In addition, we identify experimental knobs which enable the fusion of MZM pairs, and the detection of the underlying non-Abelian topological order and twofold many-body ground state degeneracy by encoding it in a topological invariant.

Janus monolayers of magnetic transition metal dichalcogenides as an all-in-one platform for spin-orbit torque

We theoretically predict that vanadium-based Janus dichalcogenide monolayers constitute an ideal platform for spin-orbit-torque memories. Using first principles calculations, we demonstrate that magnetic exchange and magnetic anisotropy energies are higher for heavier chalcogen atoms, while the broken inversion symmetry in the Janus form leads to the emergence of Rashba-like spin-orbit coupling. The spin-orbit torque efficiency is evaluated using optimized quantum transport methodology and found to be comparable to heavy nonmagnetic metals. The coexistence of magnetism and spin-orbit coupling in such materials with tunable Fermi-level opens new possibilities for monitoring magnetization dynamics in the perspective of non-volatile magnetic random access memories.

Gate-tunable imbalanced Kane-Mele model in encapsulated bilayer jacutingaite

We study free, capped and encapsulated bilayer jacutingaite Pt$_2$HgSe$_3$ from first principles. While the free standing bilayer is a large gap trivial insulator, we find that the encapsulated structure has a small trivial gap due to the competition between sublattice symmetry breaking and sublattice-dependent next-nearest-neighbor hopping. Upon the application of a small perpendicular electric field, the encapsulated bilayer undergoes a topological transition towards a quantum spin Hall insulator. We find that this topological transition can be qualitatively understood by modeling the two layers as uncoupled and described by an imbalanced Kane-Mele model that takes into account the sublattice imbalance and the corresponding inversion-symmetry breaking in each layer. Within this picture, bilayer jacutingaite undergoes a transition from a 0+0 state, where each layer is trivial, to a 0+1 state, where an unusual topological state relying on Rashba-like spin orbit coupling emerges in only one of the layers.

Controlling the Superconducting Transition by Rotation of an Inversion Symmetry-Breaking Axis

We consider a hybrid structure where a material with Rashba-like spin-orbit coupling is proximity coupled to a conventional superconductor. We find that the superconducting critical temperature T_{c} can be tuned by rotating the vector n characterizing the axis of broken inversion symmetry. This is explained by a leakage of s-wave singlet Cooper pairs out of the superconducting region, and by conversion of s-wave singlets into other types of correlations, among these s-wave odd-frequency pairs robust to impurity scattering. These results demonstrate a conceptually different way of tuning T_{c} compared to the previously studied variation of T_{c} in magnetic hybrids.

Spin-Polarized Electron Transmission in DNA-Like Systems.

The helical distribution of the electronic density in chiral molecules, such as DNA and bacteriorhodopsin, has been suggested to induce a spin–orbit coupling interaction that may lead to the so-called chirality-induced spin selectivity (CISS) effect. Key ingredients for the theoretical modelling are, in this context, the helically shaped potential of the molecule and, concomitantly, a Rashba-like spin–orbit coupling due to the appearance of a magnetic field in the electron reference frame. Symmetries of these models clearly play a crucial role in explaining the observed effect, but a thorough analysis has been largely ignored in the literature. In this work, we present a study of these symmetries and how they can be exploited to enhance chiral-induced spin selectivity in helical molecular systems.

Spin-orbit torque in a three-dimensional topological insulator–ferromagnet heterostructure: Crossover between bulk and surface transport

Current-driven spin-orbit torques are investigated in a heterostructure composed of a ferromagnet deposited on top of a three dimensional topological insulator using the linear response formalism. We develop a tight-binding model of the heterostructure adopting a minimal interfacial hybridization scheme that promotes induced magnetic exchange on the topological surface states, as well as induced Rashba-like spin-orbit coupling in the ferromagnet. Therefore, our model accounts for spin Hall effect from bulk states together with inverse spin galvanic and magnetoelectric effects at the interface on equal footing. By varying the transport energy across the band structure, we uncover a crossover from surface-dominated to bulk-dominated transport regimes. We show that the spin density profile and the nature of the spin-orbit torques differ substantially in both regimes. Our results, which compare favorably with experimental observations, demonstrate that the large damping torque reported recently is more likely attributed to interfacial magnetoelectric effect, while spin Hall torque remains small even in the bulk-dominated regime.

Formation of Majorana fermions in finite-size graphene strips

We investigate the formation of Majorana fermions in finite-size graphene strips with open boundary conditions in both directions, in the presence of an in-plane magnetic field and in the proximity of a superconducting substrate. We show that for long enough strips the Majorana states can form in the presence of a Rashba-like spin-orbit coupling, as well as in the presence of an inhomogeneous magnetic field. We find that, unlike infinite graphene ribbons in which Majorana states arise solely close to the bottom of the band and the Van Hove singularities, for finite-size systems this can happen also at much smaller doping values, close to the Dirac points, and depends strongly on the type of the short edges of the systems (e.g. armchair vs. zigzag), as well as on the width of the ribbons.

Tight-binding approach to strain and curvature in monolayer transition-metal dichalcogenides

We present a model of the electronic properties of monolayer transition-metal dichalcogenides based on a tight binding approach which includes the effects of strain and curvature of the crystal lattice. Mechanical deformations of the lattice offer a powerful route for tuning the electronic structure of the transition-metal dichalcogenides, as changes to bond lengths lead directly to corrections in the electronic Hamiltonian while curvature of the crystal lattice mixes the orbital structure of the electronic Bloch bands. We first present an effective low energy Hamiltonian describing the electronic properties near the K point in the Brillouin zone, then present the corrections to this Hamiltonian due to arbitrary mechanical deformations and curvature in a way which treats both effects on an equal footing. This analysis finds that local area variations of the lattice allow for tuning of the band gap and effective masses, while the application of uniaxial strain decreases the magnitude of the direct band gap at the K point. Additionally, strain induced bond length modifications create a fictitious gauge field with a coupling strength that is smaller than that seen in related materials like graphene. We also find that curvature of the lattice leads to the appearance of both an effective in-plane magnetic field which couples to spin degrees of freedom and a Rashba-like spin-orbit coupling due to broken mirror inversion symmetry.

One-dimensional spin texture of Bi(441): Quantum spin Hall properties without a topological insulator

The high index (441) surface of bismuth has been studied using Scanning Tunnelling Microscopy (STM), Angle Resolved Photoemission Spectroscopy (APRES) and spin-resolved ARPES. The surface is strongly corrugated, exposing a regular array of (110)-like terraces. Two surface localised states are observed, both of which are linearly dispersing in one in-plane direction ($k_x$), and dispersionless in the orthogonal in-plane direction ($k_y$), and both of which have a Dirac-like crossing at $k_x$=0. Spin ARPES reveals a strong in-plane polarisation, consistent with Rashba-like spin-orbit coupling. One state has a strong out-of-plane spin component, which matches with the miscut angle, suggesting its {possible} origin as an edge-state. The electronic structure of Bi(441) has significant similarities with topological insulator surface states and is expected to support one dimensional Quantum Spin Hall-like coupled spin-charge transport properties with inhibited backscattering, without requiring a topological insulator bulk.

Wigner-localized states in spin-orbit-coupled bosonic ultracold atoms with dipolar interaction

We investigate the occurence of Wigner-localization phenomena in bosonic dipolar ultracold few-body systems with Rashba-like spin-orbit coupling. We show that the latter strongly enhances the effects of the dipole-dipole interactions, allowing to reach the Wigner-localized regime for strengths of the dipole moment much smaller than those necessary in the spin-orbit-free case.

Topological states in a one-dimensional fermi gas with attractive interaction.

We describe a novel topological superfluid state, which forms in a one-dimensional Fermi gas with Rashba-like spin-orbit coupling, a Zeeman field, and intrinsic attractive interactions. In spite of total number conservation and the presence of gapless excitations, Majorana-like zero modes appear in this system and can be linked with interfaces between two distinct phases that naturally form at different regions of the harmonic trap. As a result, the low lying collective excitations of the system, including the dipole oscillations and the long-wavelength phonons are all doubly degenerate. While backscattering from point impurities can lead to a splitting of the degeneracies that scales algebraically with the system size, the smooth confining potential can only cause an exponentially small splitting. We show that the topological state can be uniquely probed by a pumping effect induced by a slow sweep of the Zeeman field from a high initial value down to zero. The effect is expected to be robust to introducing a finite temperature as long as it is much smaller than the interaction induced single particle gap in the final state of the sweep.

Superconductivity in noncentrosymmetricBaAl4derived structures

Ternary intermetallics Ep-T-X, crystallizing in ordered variants of the ${\mathrm{BaAl}}_{4}$ structure type, have been investigated systematically with respect to their formation and stability. For this, a comprehensive overview of the ${\mathrm{BaAl}}_{4}$ derivative structure types including group-subgroup relations was established. Special emphasis was laid on compounds where inversion symmetry is missing in the respective crystal structures and where superconductivity is observed at low temperatures. ${\mathrm{EpTX}}_{3}$ compounds crystallize in the noncentrosymmetric ${\mathrm{BaNiSn}}_{3}$ structure type (space-group $I4mm$; $a\ensuremath{\approx}0.4$ and $c\ensuremath{\approx}1$ nm), an ordered ternary derivative of ${\mathrm{BaAl}}_{4}$. Superconductivity below 3 K was found for seven members of this series, as evidenced from heat capacity and electrical resistivity measurements. Although the Rashba-like spin-orbit coupling in noncentrosymmetric systems can enable a mixture of spin-singlet and spin-triplet pairs in the superconducting condensate, the experimental data basically indicate a predominant $s$-wave superconducting state in all of these compounds. For this family of compounds, fully relativistic density functional theory (DFT) calculations of the electronic structure and phonon properties were done. Despite the different size of spin-orbit coupling depending on the actual choice of elements for Ep, T, and X that result in different spin-orbit splittings of the Fermi surfaces, the experimental observation of a prevalent spin-singlet pairing in the superconducting phases of the ${\mathrm{EpTX}}_{3}$ compounds is supported.

Spin-orbit coupled fermions in ladderlike optical lattices at half filling

We study the ground-state phase diagram of two-component fermions loaded in a ladder-like lattice at half filling in the presence of spin-orbit coupling. For repulsive fermions with unidirectional spin-orbit coupling along the legs we identify a N\'{e}el state which is separated from rung-singlet and ferromagnetic states by Ising phase transition lines. These lines cross for maximal spin-orbit coupling and a direct Gaussian phase transition between rung-singlet and ferro phases is realized. For the case of Rashba-like spin-orbit coupling, besides the rung singlet phases two distinct striped ferromagnetic phases are formed. In case of attractive fermions with spin-orbit coupling at half-filling for decoupled chains we identify a dimerized state that separates a singlet superconductor and a ferromagnetic states.

Effects of the Rashba-like spin–orbit coupling in ferromagnetic superconductors

Interplay between ferromagnetism and superconductivity in ferromagnetic superconductors has been studied by considering the Rashba-like spin–orbit coupling (RSOC). The electron band is splited into two pseudospin bands due to the RSOC and intrinsic magnetization. Quasiparticles in the pseudospin bands are assumed to form A1-phase-like p-wave Cooper pairs, and thus a mixed spin singlet–triplet superconducting state is induced. The singlet and triplet superconducting gaps in electron representation can be obtained from the quasiparticles pairing order parameters. It suggests that the magnetization is suppressed by the RSOC, whereas both the spin-singlet gap and the ratio of the singlet- to triplet-gaps are enhanced with increasing RSOC.

Domain wall dynamics driven by spin transfer torque and the spin–orbit field

We have studied current-driven dynamics of domain walls when an in-plane magnetic field is present in perpendicularly magnetized nanowires using an analytical model and micromagnetic simulations. We model an experimentally studied system, ultrathin magnetic nanowires with perpendicular anisotropy, where an effective in-plane magnetic field is developed when current is passed along the nanowire due to the Rashba-like spin–orbit coupling. Using a one-dimensional model of a domain wall together with micromagnetic simulations, we show that the existence of such in-plane magnetic fields can either lower or raise the threshold current needed to cause domain wall motion. In the presence of the in-plane field, the threshold current differs for positive and negative currents for a given wall chirality, and the wall motion becomes sensitive to out-of-plane magnetic fields. We show that large non-adiabatic spin torque can counteract the effect of the in-plane field.

Condensate fraction of a resonant Fermi gas with spin-orbit coupling in three and two dimensions

We study the effects of laser-induced Rashba-like spin-orbit coupling along the Bardeen-Cooper-Schrieffer--Bose-Einstein condensate (BCS-BEC) crossover of a Feshbach resonance for a two-spin-component Fermi gas. We calculate the condensate fraction in three and two dimensions and find that this quantity characterizes the crossover better than other quantities, like the chemical potential or the pairing gap. By considering both the singlet and the triplet pairings, we calculate the condensate fraction and show that a large-enough spin-orbit interaction enhances the singlet condensate fraction in the BCS side while suppressing it on the BEC side.