Link of the <i>Zitterbewegung</i> with the spin conductivity and the spin-textures of multiband systems

The report carried out detailed first‐principle calculations of Mercury chalcogenides (HgX; X = Te, Se and S) using density functional theory, verifying the bulk band inversion property with different exchange‐correlation functionals. The Wannier function method is used to study the non‐trivial topology of HgX systems, spin Berry curvature, and intrinsic spin Hall conductivity. Quantized intrinsic spin Hall conductivity is observed in the HgX systems. Large intrinsic spin Hall conductivity is found in the systems due to a strong spin Berry curvature accumulation near the triply degenerate points in the Brillouin zone. Calculation shows that the intrinsic spin Hall conductivity for all three HgX systems has stable plateaus, with Mercury Telluride having a maximum width of up to 1.05 eV. The maximum intrinsic spin Hall conductivity of –931/e () is obtained in mercury sulfide, higher than the reported values for spin Hall conductivity and the plateau width in typical topological insulators such as , , and as well as in transition metal pnictides (TaX, X = As, P and N) and transition metal iridates.

Multiple-$Q$ spin textures, such as magnetic bubble and skyrmion lattices, can be driven into motion by external stimuli. The motion of spin textures affects the electronic states. Here we show that to describe correctly the electronic dynamics, the momentum space needs to be transcended to higher dimensions by including the ancillary dimensions associated with phason modes of the translational motion of the spin textures. The electronic states have non-trivial topology characterized by the first and second Chern numbers in the high dimensional hybrid momentum space. This gives rise to an anomalous electric charge transport due to the motion of spin textures. By deforming the spin textures, a nonlinear response associated with the second Chern number can be induced. The charge transport is derived from the semi-classical equation of motion of electrons that depends on the Berry curvature in the hybrid momentum space. Our results suggest that the motion of multiple-$Q$ spin textures has significant effects on the electronic dynamics and provides a new platform to explore high dimensional topological physics.

The intrinsic spin Hall conductivity is calculated for a two-dimensional electronic gas (2DEG) in presence of strain, Rashba coupling, and an external in-plane applied magnetic field. The conduction electrons of [001] oriented quantum well (QW) are used to model the 2DEG. For a stress applied in the growth direction of QW the intrinsic dc spin Hall conductivity is not dependent on the strain and the in-plan applied magnetic field, and it has the universal value $e∕8\ensuremath{\pi}$.

Recent experiments on strongly correlated bilayer quantum Hall systems strongly suggest that, contrary to the usual assumption, the electron spin degree of freedom is not completely frozen either in the quantum Hall or in the compressibles states that occur at filling factor $\ensuremath{\nu}=1$. These experiments imply that the quasiparticles at $\ensuremath{\nu}=1$ could have both spin and pseudospin textures; i.e., they could be ${\mathit{CP}}^{3}$ Skyrmions. Using a microscopic unrestricted Hartree-Fock approximation, we compute the energy of several crystal states with spin, pseudospin, and mixed spin-pseudospin textures around $\ensuremath{\nu}=1$ as a function of interlayer separation $d$ for different values of tunneling $({\ensuremath{\Delta}}_{SAS})$, Zeeman $({\ensuremath{\Delta}}_{Z})$, and bias $({\ensuremath{\Delta}}_{b})$ energies. We show that in some range of these parameters, crystal states involving a certain amount of spin depolarization have lower energy than the fully spin-polarized crystals. We study this depolarization dependence on $d$, ${\ensuremath{\Delta}}_{SAS}$, ${\ensuremath{\Delta}}_{Z}$, and ${\ensuremath{\Delta}}_{b}$ and discuss how it can lead to the fast NMR relaxation rate observed experimentally.

We report a systematic study on the intrinsic spin Hall conductivity (ISHC) of bilayer ${\mathrm{PtTe}}_{2}$ and explore the connection between the stacking order and ISHC. We find that by changing the stacking mode, ISHC can be manipulated from positive to negative values. Such strong stacking-dependent ISHC originates from the interlayer coupling, in which Te atoms in the upper and lower layers can form either van der Waals or covalentlike quasibonding depending on the stacking modes. Thus ISHC can be effectively tuned by changing the stacking order. These results not only allow us to establish fundamental understanding of ISHC in bilayer ${\mathrm{PtTe}}_{2}$ dependent on the stacking mode but also provide guidelines for the application of bilayer ${\mathrm{PtTe}}_{2}$ in next-generation spintronic devices.

In this paper, we present a comprehensive theoretical investigation of layer-resolved electronic properties in five-layer magnetic tunnel junction systems with systematically tunable Rashba spin-orbit coupling (SOC) strengths. Using an extended tight-binding (TB) model combined with non-equilibrium Green’s function methods, we calculate spin texture patterns, spectral function distributions, and Berry curvature landscapes across the interface and adjacent layers with SOC parameters [Formula: see text]/t ranging from 0.1 to 0.3. Our results reveal a systematic decrease in topological protection, evidenced by Chern number reduction from 1.222 to 0.694 in the primary interface layer as SOC strength increases. The persistent radial spin texture maintains characteristic vortex-like structures indicative of robust spin-momentum locking, while Berry curvature hotspots demonstrate alternating positive and negative regions that create dipole moments scaling with SOC strength. Significantly, we identify an optimal SOC regime ([Formula: see text]) that balances enhanced quantum effects with preserved topological robustness. The interface-dominated phenomena exhibit substantial proximity effects extending into adjacent layers, with correlated but attenuated electronic structure modifications. Spectral weight redistributions reveal momentum-dependent energy splitting characteristics of Rashba systems, while the evolution of Berry curvature landscapes provides insights into the geometric phase structure governing anomalous transport phenomena. These findings establish fundamental design principles for engineering multilayer spintronics.

Using first-principles calculations within density functional theory, we investigate the intrinsic spin Hall effect in monolayers of group-VI transition-metal dichalcogenides MX2 (M = Mo, W and X = S, Se). MX2 monolayers are direct band-gap semiconductors with two degenerate valleys located at the corners of the hexagonal Brillouin zone. Because of the inversion symmetry breaking and the strong spin-orbit coupling, charge carriers in opposite valleys carry opposite Berry curvature and spin moment, giving rise to both a valley- and a spin-Hall effect. The intrinsic spin Hall conductivity (ISHC) in p-doped samples is found to be much larger than the ISHC in n-doped samples due to the large spin-splitting at the valence band maximum. We also show that the ISHC in inversion-symmetric bulk dichalcogenides is an order of magnitude smaller compared to monolayers. Our result demonstrates monolayer dichalcogenides as an ideal platform for the integration of valleytronics and spintronics.

We theoretically show that two distinctive spin textures manifest themselves\naround saddle points of energy bands in a monolayer NbSe$_2$ under external\ngate potentials. While the density of states at all saddle points diverge\nlogarithmically, ones at the zone boundaries display a windmill-shaped spin\ntexture while the others unidirectional spin orientations. The disparate\nspin-resolved states are demonstrated to contribute an intrinsic spin Hall\nconductivity significantly while their characteristics differ from each\nother.Based on a minimal but essential tight-binding approximation reproducing\nfirst-principles computation results, we established distinct effective Rashba\nHamiltonians for each saddle point, realizing the unique spin textures\ndepending on their momentum. Energetic positions of the saddle points in a\nsingle layer NbSe$_2$ are shown to be well controlled by a gate potential so\nthat it could be a prototypical system to test a competition between various\ncollective phenomena triggered by diverging density of states and their spin\ntextures in low-dimension.\n

This systematic study on the intrinsic spin Hall conductivity (SHC) of BiTeI aims to explore the role of hydrostatic pressure in controlling the topological properties and SHC. It was found that the sign of transverse spin Hall conductivity tensors σxyz, σxzy, and σzxy in BiTeI is reversed due to the topological transition under hydrostatic pressure. The change in sign originates from the variation in spin Berry curvature near A in the Brillouin zone, which is caused by Te-p and I-p orbital hybridization induced by the interplay coupling under hydrostatic pressure in BiTeI. Thus, SHC could be effectively tuned by changing the hydrostatic pressure. These results not only allow us to establish a fundamental understanding of SHC in BiTeI depending on the pressure but also provide guidelines for applying BiTeI in next-generation spintronic devices.

We analytically calculate the intrinsic spin-Hall conductivities (ISHCs) ( and ) in a clean, two-dimensional system with generic k-linear spin–orbit interaction. The coefficients of the product of the momentum and spin components form a spin–orbit matrix . We find that the determinant of the spin–orbit matrix describes the effective coupling of the spin sz and orbital motion Lz. The decoupling of spin and orbital motion results in a sign change of the ISHC and the band-overlapping phenomenon. Furthermore, we show that the ISHC is in general unsymmetrical (), and it is governed by the asymmetric response function , which is the difference in band-splitting along two directions: those of the applied electric field and the spin-Hall current. The obtained non-vanishing asymmetric response function also implies that the ISHC can be larger than e/8π, but has an upper bound value of e/4π. We will show that the unsymmetrical properties of the ISHC can also be deduced from the manifestation of the Berry curvature in the nearly degenerate area. On the other hand, by investigating the equilibrium spin current, we find that determines the field strength of the SU(2) non-Abelian gauge field.

This study proposes oxygen vacancy engineering as an effective strategy to achieve efficient charge-to-spin conversion in heavy-metal oxides, establishing a novel theoretical framework for semiconductor spintronics devices. Using first-principles calculations, we systematically investigate the impact of oxygen vacancy on the intrinsic spin Hall conductivity (ISHC) and spin Hall angle (SHA) of room-temperature-stable monoclinic WO3. Incorporating oxygen vacancies raises the Fermi level into the conduction band, significantly enhancing ISHC from zero to near 10 3 magnitude. At low vacancy concentrations, WO3 achieves exceptional charge-to-spin conversion efficiency (i.e. SHA) up to 72.6%, whereas elevated concentrations induce disproportionate enhancement in charge conductivity relative to ISHC gains, consequently reducing SHA. The cubic-like structure of WO3 ensures that oxygen vacancy positions exert negligible influence on ISHC magnitude. These findings establish WO3 as a promising spintronics material, demonstrating the dual functionality of oxygen vacancies as enhancers of both charge conductivity and spin current. The synergistic integration of defect engineering with heavy-metal oxides opens new pathways for spintronics device applications.

We study the ground-state topology and quasiparticle properties in bosonic Mott insulators with two- dimensional spin-orbit couplings in cold atomic optical lattices. We show that the many-body Chern and spin-Chern number can be expressed as an integral of the quasihole Berry curvatures over the Brillouin zone. Using a strong-coupling perturbation theory, for an experimentally feasible spin-orbit coupling, we compute the Berry curvature and the spin Chern number and find that these quantities can be generated purely by interactions. We also compute the quasiparticle dispersions, spectral weights, and the quasimomentum space distribution of particle and spin density, which can be accessed in cold-atom experiments and used to deduce the Berry curvature and Chern numbers.

While the metastable $\ensuremath{\beta}$ (A15) phase of tungsten has one of the largest spin Hall angles measured, the origin of this high spin Hall conductivity is still unclear. Since large concentrations of oxygen and nitrogen are often used to stabilize $\ensuremath{\beta}$ tungsten, it is not obvious whether the high spin Hall conductivity is due to an intrinsic or extrinsic effect. In this work, we have examined the influence of O and N dopants on the spin Hall conductivity and spin Hall angle of $\ensuremath{\beta}$-W. Using multiple first-principles approaches, we examine both the intrinsic and extrinsic (skew-scattering) contributions to spin Hall conductivity. We find that intrinsic spin Hall conductivity calculations for pristine $\ensuremath{\beta}$-W are in excellent agreement with experiment. However, when the effect of high concentrations (11 at.%) of O or N interstitials on the electronic structures is taken into account, the predicted intrinsic spin Hall conductivity is significantly reduced. Skew-scattering calculations for O and N interstitials in $\ensuremath{\beta}$-W indicate that extrinsic contributions have a limited impact on the total spin Hall conductivity. However, we find that the spin-flip scattering at O and N impurities can well explain the experimentally found spin-diffusion length within the range of 1--5 nm. To explain these findings, we propose that dopants (O and N) help to stabilize $\ensuremath{\beta}$-W grains during film deposition and afterwards segregate to the grain boundaries. This process leads to films of relatively pristine small $\ensuremath{\beta}$-W grains and grain boundaries with high concentrations of O or N scattering sites. This combination provides high spin Hall conductivity and large electrical resistance, leading to high spin Hall angles. This work shows that engineering grain-boundary properties in other high spin Hall conductivity materials could provide an effective way to boost the spin Hall angle.

We report a comprehensive study on the intrinsic spin Hall conductivity (SHC) of semimetals MoTe2 and WTe2 by ab initio calculation. Large SHC and desirable spin Hall angles have been discovered, due to the strong spin orbit coupling effect and low charge conductivity in semimetals. Diverse anisotropic SHC values, attributed to the unusual reduced-symmetry crystalline structure, have been revealed. We report an effective method on SHC optimization by electron doping, and exhibit the mechanism of SHC variation respect to the energy shifting by the spin Berry curvature. Our work provides insights into the realization of strong spin Hall effects in 2D systems.

Intrinsic spin Hall conductivities are calculated for strong spin-orbit Bi(1-x)Sb(x) semimetals, from the Kubo formula and using Berry curvatures evaluated throughout the Brillouin zone from a tight-binding Hamiltonian. Nearly crossing bands with strong spin-orbit interaction generate giant spin Hall conductivities in these materials, ranging from 474 (ℏ/e)(Ω cm)^{-1} for bismuth to 96 (ℏ/e)(Ω cm)^{-1} for antimony; the value for bismuth is more than twice that of platinum. The large spin Hall conductivities persist for alloy compositions corresponding to a three-dimensional topological insulator state, such as Bi(0.83)Sb(0.17). The spin Hall conductivity could be changed by a factor of 5 for doped Bi, or for Bi(0.83)Sb(0.17), by changing the chemical potential by 0.5 eV, suggesting the potential for doping or voltage tuned spin Hall current.