Presence Of Spin-orbit Coupling Research Articles

Unveiling the Role of Spin Currents on the Giant Rashba Splitting in Single-Layer WSe2.

The Rashba spin splitting in uniaxial, inversion-asymmetric materials has attracted considerable interest for spintronic applications. The most widely used theoretical framework to model such states is Kohn-Sham density functional theory (DFT) in combination with standard (semi)local exchange-correlation density functional approximations (DFAs). However, in the presence of spin-orbit coupling, DFT misses contributions due to modification of the many-body interaction by spin currents J⃗. Inclusion of the latter effects requires a spin current DFT (SCDFT) formulation, which is seldom considered. We investigate the giant Rashba splitting in single-layer WSe2, and we quantify the effect of including spin currents in DFAs of the SCDFT. Crucially, we show that SCDFT allows fully capturing the giant Rashba band splitting in single-layer WSe2, otherwise previously systematically underestimated by standard (semi)local DFAs within the DFT framework. We find the inclusion of J⃗ on the DFA increases the Rashba splitting by about 20%.

2D MnTiX2 (X = F/Cl/Br) monolayers: Robust valley-polarized quantum anomalous Hall insulators with high transition temperatures and wide bandgaps

The valley-polarized quantum anomalous Hall (VP-QAH) materials, which combine valley polarization and the quantum anomalous Hall (QAH) effect, are of both fundamental and technological importance due to their potential applications for nanoscale devices. Here, we explored the stability, magnetic, and topological properties of two-dimensional MnTiX2 (X = F/Cl/Br) monolayers based on first-principles calculations. Our results show that all the structures have robust antiferromagnetic orders with large magnetic anisotropic energies and high transition temperatures (480–670 K). In the absence of spin–orbital coupling (SOC), the MnTiX2 monolayers represent antiferromagnetic quadratic crossing semimetals. In the presence of SOC, the quadratic crossing points of the systems are opened with sizable bandgaps (> 0.5 eV), and they are transformed to be QAH insulators with |C| = 1. Moreover, the MnTiF2 monolayer is found to be a spontaneous VP-QAH semiconductor due to the time reversal symmetry and inversion symmetry being broken. These insights provide an ideal platform for achieving VP-QAH materials for dissipationless transport and quantum computing.

Phonon-mediated spin transport in quantum paraelectric metals

The concept of ferroelectricity is now often extended to include continuous inversion symmetry-breaking transitions in various metals and doped semiconductors. Paraelectric metals near ferroelectric quantum criticality, which we term ‘quantum paraelectric metals,’ possess soft transverse optical phonons which can have Rashba-type coupling to itinerant electrons in the presence of spin-orbit coupling. We find through the Kubo formula calculation that such Rashba electron-phonon coupling has a profound impact on electron spin transport. While the spin Hall effect arising from non-trivial electronic band structures has been studied extensively, we find here the presence of the Rashba electron-phonon coupling can give rise to spin current, including spin Hall current, in response to an inhomogeneous electric field even with a completely trivial band structure. Furthermore, this spin conductivity displays unconventional characteristics, such as quadrupolar symmetry associated with the wave vector of the electric field and a thermal activation behavior characterized by scaling laws dependent on the phonon frequency to temperature ratio. These findings shed light on exotic electronic transport phenomena originating from ferroelectric quantum criticality, highlighting the intricate interplay of charge and spin degrees of freedom.

Density functional theory study on the electronic and optical properties of full-hydrogenated stanene

The lack of a bandgap in stanene severely limits its outstanding characteristics in optoelectronic devices. Using first-principles calculations, we systematically investigate the effects of full hydrogenation and shear deformation on the electronic structure and optical properties of stanene. Hydrogenation exerts a remarkable impact on electronic structure of stanene, enabling surface state transition from quasi-metallic to semiconducting. Shear degrades the structural stability of full-hydrogenated stanene (FHstanene). FHstanene exhibits a tunable bandgap of 1.327[Formula: see text]eV, which can be further reduced to 0.719[Formula: see text]eV through shear deformation. The presence of spin-orbit coupling (SOC) induces band splitting in FHstanene. The maximum optical absorption of FHstanene occurs at 291[Formula: see text]nm, while the reflectance peak is observed at 449[Formula: see text]nm. The variation in bandgap due to deformation results in a redshift in the absorption coefficient and reflectance, and shear deformation increases the reflectance of FHstanene. These findings broaden the application prospects of stanene in novel nano-optoelectronic devices.

Ground State and Its Topological Properties of Three-Dimensional Spin-Orbit Coupled Degenerate Fermi Gases

Three-dimensional (3D) degenerate Fermi gases in the presence of spin-orbit coupling, inducing various kinds of physical findings and phenomena, have attracted tremendous attention in these years. We investigate the 3D spin-orbit coupled degenerate Fermi gases in theory and first present the analytic expression of their ground state. Our study provides an innovative perspective into understanding of the topological properties of 3D unconventional superconductors, and describes the topological phase transitions in trivial and topological phase areas. Further, such a system is provided with a richer set of Cooper pairings than traditional superconductors. The dual Cooper pairs with same spin directions emerge and exhibit peculiar behaviors, leading to topological phase transitions. Our study and discussion can be generalized to some other types of unconventional superconductors and areas of optical lattices.

Ferromagnetic ordering of magnetic impurities mediated by supercurrents in the presence of spin-orbit coupling

Ferromagnetic ordering of magnetic impurities mediated by supercurrents in the presence of spin-orbit coupling

Tunability of Andreev levels in a spin-active Ising superconductor/half-metal Josephson junction

We study the Andreev levels, supercurrent and tunnelling conductance in a clean Ising superconductor (ISC)/half-metal (HM)/ISC Josephson junction (JJ) with spin-active interfaces using Bogoliubov–de Gennes equations. We theoretically demonstrate the effect of spin mixing, spin flipping processes and spin–orbit coupling (SOC) of the ISC on Andreev bound states spectra, the current phase relation and tunnelling conductance in a transparent and opaque barrier limit. We witness an additional splitting of the Andreev levels due to the SOC of the ISC and transition for different barrier magnetic moments. Also, different φ-junctions can be achieved by tuning the strength of the barrier magnetic moment and spin mismatch angle. Moreover, a possible transition can also be achieved for a SOC stronger than the chemical potential of the ISC using suitable control parameters. The tunnelling conductance is found to be dependent on the spin mismatch angle. A finite subgap conductance is also observed, indicating different probabilities of Andreev reflected electrons and holes in the presence of SOC. Furthermore, anomalous Andreev levels are observed for different HM length scales, signifying their role in the tunability of the φ-phase JJ.

Tunnel-magneto resistance of double-barrier tunnel junctions in the presence of spin-orbit coupling within spin-filter barriers

The tunnel magneto-resistance ratio is investigated for double-barrier tunnel junctions with spin-filter (magnetic insulators) barriers. The transmission probability is calculated in the tight-binding model by the non-equilibrium Green's function formalism considering spin-orbit coupling within barriers. The formation of resonant states inside a non-magnetic spacer gives rise to an enhancement in tunnel magneto-resistance ratio. Double spin-filter tunnel junctions have also shown a higher tunnel magneto-resistance ratio compared to that in double-barrier magnetic tunnel junctions. These findings will be valuable to improve the performance of spintronics devices.

Quantum phases of rotating Raman spin–orbit-coupled dipolar Bose–Einstein condensates with Lee–Huang–Yang correction

We investigate the ground-state phases and spin textures of rotating binary dipolar Bose–Einstein condensates with Lee–Huang–Yang (LHY) correction and Raman-induced spin–orbit coupling (SOC) in a harmonic trap. Without rotation and SOC, the enhanced LHY correction can lead to structural phase transitions of the system. In the presence of SOC, a phase diagram as a function of the Raman coupling and LHY correction strengths is given. It is shown that the system exhibits rich and exotic quantum phases including quantum droplet (QD) phase with hidden vortex–antivortex pairs, droplet-stripe coexistence phase with hidden vortex–antivortex cluster, QD phase with visible triangular vortex lattice, annular stripe phase containing Anderson–Toulouse coreless vortex, and annular phase with vortex–antivortex pair necklace. In particular, for the rotation case, with the variation of Raman coupling strength the system displays complicated ground-state structures, such as layered structure of droplet necklaces and annular stripe with hidden layered vortex necklace and antivortex necklace, toroidal stripe phase with hidden antivortex necklace, and composite phase of visible square antivortex lattice and annular stripe. Furthermore, the system sustains fascinating novel spin textures and skyrmion excitations, including triangular half-antiskyrmion lattice, alternating meron-antimeron necklace, double-layer half-skyrmion necklace, and triangular half-skyrmion lattice.

The Coexistence of Superconductivity and Topological Order in Van der Waals InNbS2.

The research on systems with coexistence of superconductivity and nontrivial band topology has attracted widespread attention. However, the limited availability of material platforms severely hinders the research progress. Here, it reports the first experimental synthesis and measurement of high-quality single crystal van der Waals transition-metal dichalcogenide InNbS2 , revealing it as a topological nodal line semimetal with coexisting superconductivity. The temperature-dependent measurements of magnetization susceptibility and electrical transport show that InNbS2 is a type-II superconductor with a transition temperature Tc of 6 K. First-principles calculations predict multiple topological nodal ring states close to the Fermi level in the presence of spin-orbit coupling. Similar features are also observed in the as-synthesized BiNbS2 and PbNbS2 samples. This work provides new material platforms ANbS2 (A = In, Bi, and Pb) and uncovers their intriguing potential for exploring the interplay between superconductivity and band topology.

SOiCISCF: Combining SOiCI and iCISCF for Variational Treatment of Spin-Orbit Coupling.

It has recently been shown that the SOiCI approach [Zhang, N.; J. Phys.: Condens. Matter 2022, 34, 224007], in conjunction with the spin-separated exact two-component relativistic Hamiltonian, can provide very accurate fine structures of systems containing heavy elements by treating electron correlation and spin-orbit coupling (SOC) on an equal footing. Nonetheless, orbital relaxations/polarizations induced by SOC are not yet fully accounted for due to the use of scalar relativistic orbitals. This issue can be resolved by further optimizing the still real-valued orbitals self-consistently in the presence of SOC, as done in the spin-orbit coupled CASSCF approach [Ganyushin, D.; et al. J. Chem. Phys. 2013, 138, 104113] but with the iCISCF algorithm [Guo, Y.; J. Chem. Theory Comput. 2021, 17, 7545-7561] for large active spaces. The resulting SOiCISCF employs both double group and time reversal symmetries for computational efficiency and the assignment of target states. The fine structures of p-block elements are taken as showcases to reveal the efficacy of SOiCISCF.

Identifying Rashba–Dresselhaus splittings from first-principle calculations: A brief overview

The present review is aimed to understand the Rashba and Dresselhaus effects from the first-principle calculations. A brief overview of first-principle density functional theory (DFT) and its global acceptance have been discussed. The discussions of the Rashba–Dresselhaus splittings, spin textures and understanding the effects from first-principle DFT calculations have been highlighted. Rashba and Dresselhaus effects have gained much attention in recent era for their highly promising applications in spintronics. In the presence of spin-orbit coupling and inherent non-centrosymmetry, while BiTeCl, TiS2Se, rhombohedral CsPbF3 and BiCoO3 compounds show large values of Rashba parameter ([Formula: see text] of [Formula: see text], 1.10, 1.05 and 0.74[Formula: see text]eVÅ, respectively, the single-layered semiconductor nanostructure InSb, rhombohedral BiFeO3 and Ag2BiO3 systems however depict promising values of Dresselhaus parameter ([Formula: see text] of [Formula: see text], 0.50 and 0.15[Formula: see text]eVÅ, respectively. The future of Rashba–Dresselhaus effects and their advancements in spintronics have also been enlightened in this paper. We believe that this study will not only help to understand the Rashba–Dresselhaus effects from first-principle calculations, but can also augment their applications in next generation spintronic devices.

Existence of nodal-arc and its evolution into Weyl-nodes in the presence of spin-orbit coupling in TaAs & TaP

In this work, we report the existence of nodal-arc, which acts as the building block of all the nodal-rings in TaAs & TaP. This nodal-arc is found to be capable of generating all the nodal-rings in these materials upon the application of space-group symmetry operations including time-reversal symmetry. The arcs are obtained to be dispersive with the energy spread of ∼109 (∼204) meV in TaAs (TaP). Also, the orbitals leading to bands-inversion and thus the formation of nodal-arcs are found to be Ta-5d & As-4p (P-3p) in TaAs (TaP). The area of nodal-rings is found to be highly sensitive to the change in hybridization-strength, where the increase in hybridization-strength leads to the decrease in the area of nodal-rings. In the presence of spin–orbit coupling (SOC), all the points on these arcs get gaped-up and two pairs of Weyl-nodes are found to evolve from them. Out of the two pair, one is found to be situated close to the joining point of the two arcs forming a ring. This causes the evolution of each nodal-ring into three pairs of Weyl-nodes. The coordinates of these Weyl-nodes are found to be robust to the increase in SOC-strength from ∼0.7–3.5 eV. All the results are obtained at the first-principle level. This work provides a clear picture of the existence of nodal-arc due to accidental degeneracy and its evolution into Weyl-nodes under the effect of SOC.

Magnetic Second-Order Topological Insulators in 2H-Transition Metal Dichalcogenides.

The transition metal dichalcogenides, 2H-VX2 (X = S, Se, Te), are identified astwo-dimensional second-order topological insulator (SOTI) with a ferromagnetic ground state by first-principles calculations. The 2H-VX2 (X = S, Se, Te) materials have a nontrivial band gap in two spin channels is found and exhibit topologically protected corner states with spin-polarization. These corner states only accommodate the quantized fractional charge (e/3). And the charge is bound at the corners of the nanodisk geometry 2H-VX2 (X = S, Se, Te) in real space. The corner states are robust against symmetry-breaking perturbations, which makes them more easily detectable in experiments. Further, it is demonstrated that the SOTI properties of 2H-VX2 (X = S, Se, Te) materials can be maintained in the presence of spin-orbit coupling and are stable against magnetization. Overall, the results reveal 2H-VX2 (X = S, Se, Te) as an ideal platform for the exploration of magnetic SOTI and suggest its great potential in experimental detection.

Emergent topological quantum orbits in the charge density wave phase of kagome metal CsV3Sb5

The recently discovered kagome materials AV3Sb5 (A = K, Rb, Cs) attract intense research interest in intertwined topology, superconductivity, and charge density waves (CDW). Although the in-plane 2 × 2 CDW is well studied, its out-of-plane structural correlation with the Fermi surface properties is less understood. In this work, we advance the theoretical description of quantum oscillations and investigate the Fermi surface properties in the three-dimensional CDW phase of CsV3Sb5. We derived Fermi-energy-resolved and layer-resolved quantum orbits that agree quantitatively with recent experiments in the fundamental frequency, cyclotron mass, and topology. We reveal a complex Dirac nodal network that would lead to a π Berry phase of a quantum orbit in the spinless case. However, the phase shift of topological quantum orbits is contributed by the orbital moment and Zeeman effect besides the Berry phase in the presence of spin-orbital coupling (SOC). Therefore, we can observe topological quantum orbits with a π phase shift in otherwise trivial orbits without SOC, contrary to common perception. Our work reveals the rich topological nature of kagome materials and paves a path to resolve different topological origins of quantum orbits.

Spin-orbit coupling-enhanced valley ordering of malleable bands in twisted bilayer graphene on WSe2

Recent experiments in magic-angle twisted bilayer graphene have revealed a wealth of novel electronic phases as a result of interaction-driven spin-valley flavour polarisation. In this work, we investigate correlated phases due to the combined effect of spin-orbit coupling-enhanced valley polarisation and the large density of states below half filling of the moiré band in twisted bilayer graphene coupled to tungsten diselenide. We observe an anomalous Hall effect, accompanied by a series of Lifshitz transitions that are highly tunable with carrier density and magnetic field. The magnetisation shows an abrupt change of sign near half-filling, confirming its orbital nature. While the Hall resistance is not quantised at zero magnetic fields—indicating a ground state with partial valley polarisation—perfect quantisation and complete valley polarisation are observed at finite fields. Our results illustrate that singularities in the flat bands in the presence of spin-orbit coupling can stabilise ordered phases even at non-integer moiré band fillings.

Flavor symmetry breaking in spin-orbit coupled bilayer graphene

Recent experimental discovery of flavor symmetry breaking metallic phases in Bernal-stacked bilayer graphene points to the strongly interacting nature of electrons near the top (bottom) of its valence (conduction) band. Superconductivity was also observed in between these symmetry breaking phases when the graphene bilayer is placed under a small in-plane magnetic field or in close proximity to a monolayer WSe$_2$ substrate. Here we address the correlated nature of the band edge electrons and obtain the quantum phase diagram of their many-body ground states incorporating the effect of proximity induced spin-orbit coupling. We find that in addition to the spin/valley flavor polarized half and quarter metallic states, two types of intervalley coherent phases emerge near the phase boundaries between the flavor polarized metals. Both spin-orbit coupling and in-plane magnetic field disfavor the spin-unpolarized valley coherent phase. Our findings suggest possible competition between intervalley coherence and superconducting orders, arising from the intriguing correlation effects in bilayer graphene in the presence of spin-orbit coupling.

A two-dimensional kagome magnet with tunable topological phases

Kagome magnets have garnered a lot of investigation due to their plentiful topological states and promising, strong correlated phenomena. However, there have been few reports of two-dimensional (2D) van der Waals kagome magnets. Here, we suggest a stable 2D van der Waals kagome material, V3Br8, which exhibits a ferromagnetic ground state with a Curie temperature of 89 K. Near the Fermi level, there is only a set of three kagome bands from one spin species, which possesses Van Hove singularities at the M point and a Weyl point at the K point. It is interesting that its ground state is gapless at the K point and maintains a 2D Weyl half semimetal state even in the presence of spin-orbit coupling, while when the magnetization rotates from the in-plane direction of the ground state to the out-of-plane direction, the spin-orbit coupling will open an energy gap at the K point, resulting in a topological phase transition to a quantum anomalous Hall effect state. We further demonstrate that the tensile strain can optimize the band structure and raise the Curie temperature to above 100 K. In addition, a Li atom intercalated V3Br8 (V3Br8Li) is revealed to be a stable structure that can successfully tune the Fermi level to the Weyl point while maintaining the ferromagnetic ground state. Moreover, V3Br8Li displays an out-of-plane magnetism, producing the quantum anomalous Hall effect . Our findings provide a solid foundation for future research into topological states and singular effects in 2D kagome magnets.

Topological semimetal phases in a family of monolayer X3YZ6 (X=Nb,Ta, Y=Si,Ge,Sn, Z=S,Se,Te) with abundant nodal lines and nodes

The electronic and topological properties of single-layer X3YZ6 (X=Nb,Ta, Y=Si,Ge,Sn, Z=S,Se,Te) materials have been studied with the aid of first principles calculations. This kind of materials belong to topological semimetals (TMs) with abundant nodal lines and nodes. Considering their similar properties, we focus on the analysis of Ta3SnTe6 and Ta3SiSe6. The presence of spin–orbit coupling (SOC) leads to the transition from type-I nodal lines to Dirac points as well as the disappear of type-II Dirac points. The three-dimensional (3D) plot of the band structure reproduces vividly the characteristics of nodes and nodal lines. The appearance of the flat bands in (110) edge states further confirm their nontrivial topological properties. We also explore the relationship among different nodal lines (nodes), crystal symmetry and SOC. The type-I nodal lines are protected by Mz and Mỹ symmetry in the absence of SOC. Symmetry breaking leads to band splitting even in the presence of SOC. The single-layer X3YZ6 can be used as candidates for two-dimensional (2D) Dirac materials and provide a platform for further study of interesting physical phenomena.

Nodal-line and triple point fermion induced anomalous Hall effect in the topological Heusler compound Co2CrGa

Magnetic topological semimetals have interesting anomalous behavior and can be manipulated by tuning the symmetry-protected nodal crossings. ${\mathrm{Co}}_{2}$-based full Heusler compounds serve as a fertile playground where various novel topological properties can be investigated. In this paper, we present a systematic investigation of the anomalous Hall effect (AHE) in the ferromagnetic Heusler compound ${\mathrm{Co}}_{2}\mathrm{CrGa}$ using combined experimental and theoretical studies. The anomalous Hall resistivity ${\ensuremath{\rho}}_{yx}^{A}$ is observed to scale nearly quadratically with the longitudinal resistivity ${\ensuremath{\rho}}_{xx}$, and further experimental analysis suggests that the AHE in ${\mathrm{Co}}_{2}\mathrm{CrGa}$ should be dominated by the intrinsic Karplus-Luttinger Berry phase mechanism. Experimental results also reveal that the anomalous Hall conductivity (AHC) is as large as $\ensuremath{\sim}569$ S/cm at 10 K with an intrinsic contribution of $\ensuremath{\sim}526$ S/cm and the observed AHC is nearly temperature independent. In addition to the large AHC, we also found an exceptionally large anomalous Hall angle of $\ensuremath{\sim}8.5$% and a large anomalous Hall factor of $\ensuremath{\sim}0.23 {\mathrm{V}}^{\ensuremath{-}1}$ simultaneously at room temperature. First-principles calculations suggest that the Berry curvature originates from a gapped nodal line and that Weyl nodes which are generated from the triple point near the Fermi level ${E}_{F}$ in the presence of spin-orbit coupling are responsible for the observed large AHC in this compound.