Spin-orbit Coupling Parameter Research Articles

Comparing the effective enhancement of local and nonlocal spin-orbit couplings on honeycomb lattices due to strong electronic correlations

We investigate the interplay of electronic correlations and spin-orbit coupling (SOC) for a one-band and a two-band honeycomb lattice model. The main difference between the two models concerning SOC is that in the one-band case the SOC is a purely non-local term in the basis of the $p_z$ orbitals, whereas in the two-band case with $p_x$ and $p_y$ as basis functions it is purely local. In order to grasp the correlation effects on non-local spin-orbit coupling, we apply the TRILEX approach that allows to calculate non-local contributions to the self-energy approximatively. For the two-band case we apply dynamical mean-field theory. In agreement with previous studies, we find that for all parameter values in our study, the effect of correlations on the spin-orbit coupling strength is that the bare effective SOC parameter is increased. However, this increase is much weaker in the non-local than in the local SOC case. Concerning the TRILEX method, we introduce the necessary formulas for calculations with broken SU(2) symmetry.

Creating moving gap solitons in spin-orbit-coupled Bose-Einstein condensates

A simple and efficient method to create gap solitons is proposed in a spin-orbit-coupled spin-1 Bose-Einstein condensate. We find that a free expansion along the spin-orbit coupling dimension can generate two moving gap solitons, which are identified from a generalized massive Thirring model. The dynamics of gap solitons can be controlled by adjusting spin-orbit coupling parameters.

Spin polarized quantum oscillations in monolayer InSe induced by magnetic field

We study the quantum capacitance and the Landau levels (LLs) in n-type monolayer InSe subjected to a vertical magnetic field. Starting from a single band k⋅p Hamiltonian, we analytically obtain the LLs by solving the Hamiltonian and find that the LLs have a uniform distribution on the LL index and magnetic field, i.e., the equal LL spacings. Further, the LLs are fully spin polarized under moderate magnetic fields originating from the spin–orbit coupling and Zeeman splitting. The magneto-capacitance peaks show one-to-one correspondence to the LLs, resulting in a perfect square-wave-shaped spin polarization. Our results is useful to detect the effective mass and spin–orbit coupling parameters of n-type monolayer InSe and design spintronics devices based on it.

Magnetoresistance of electrons in quantum ring with Rashba spin-orbit interaction

The influence of Rashba spin-orbit interaction on the transport properties of the two-dimensional quantum ring with finite width has been investigated in the presence of the uniform perpendicular magnetic field. The dependence of magnetoresistance on the magnetic field and Rashba spin-orbit coupling parameter in quantum ring with finite width are investigated. It was shown that in the presence Rashba spin-orbit interaction that the beating pattern is destroyed.

Higher angular momentum pairings in interorbital shadowed-triplet superconductors: Application to Sr2RuO4

Even-parity interorbital spin-triplet pairing emerges as an intriguing candidate in multiorbital superconductors with significant Hund's and spin-orbit coupling. Within such a state, the pairing is dominated by the intraband pseudospin-singlet component via the spin-orbit coupling, distinguishing it from a pure spin triplet and motivating the name, shadowed triplet. With atomic spin-orbit coupling, it was shown that this pairing exhibits an anisotropic $s$-wave character, while higher angular momentum pairing symmetries such as $d$- or $g$-wave have been proposed based on phenomenological analyses in candidate systems. A natural question is then whether higher angular momentum pairings may arise with this form of spin-triplet pairing. Here, we examine the interplay between spin-orbit coupling and the electronic dispersions in correlated metals and demonstrate how they can be realized. We apply this idea to Sr$_{2}$RuO$_{4}$ and determine the competition among different pairing states as multiple spin-orbit coupling parameters are tuned. The presence of both $d$- and $g$-wave pairings, including a $d+ig$ state, are found when momentum-dependent spin-orbit coupling with $d$-wave character is increased. Implications of the theory and future directions are also discussed.

Highly persistent spin textures with giant tunable spin splitting in the two-dimensional germanium monochalcogenides

The ability to control the spin textures in semiconductors is a fundamental step toward novel spintronic devices, while seeking desirable materials exhibiting persistent spin texture (PST) remains a key challenge. The PST is the property of materials preserving a unidirectional spin orientation in the momentum space, which has been predicted to support an extraordinarily long spin lifetime of carriers. Herein, by using first-principles density functional theory calculations, we report the emergence of the PST in the two-dimensional (2D) germanium monochalcogenides (GeMC). By considering two stable formation of the 2D GeMC, namely the pure GeX and Janus Ge2 XY monolayers (X, Y = S, Se, and Te), we observed the PST around the valence band maximum where the spin orientation is enforced by the lower point group symmetry of the crystal. In the case of the pure GeX monolayers, we found that the PST is characterized by fully out-of-plane spin orientation protected by C 2v point group, while the canted PST in the y–z plane is observed in the case of the Janus Ge2 XY monolayers due to the lowering symmetry into C s point group. More importantly, we find large spin–orbit coupling (SOC) parameters in which the PST sustains, which could be effectively tuned by in-plane strain. The large SOC parameter observed in the present systems leads to the small wavelength of the spatially periodic mode of the spin polarization, which is promising for realization of the short spin channel in the spin Hall transistor devices.

Luminescence Intensity Ratio Thermometry with Er3+: Performance Overview

The figures of merit of luminescence intensity ratio (LIR) thermometry for Er3+ in 40 different crystals and glasses have been calculated and compared. For calculations, the relevant data has been collected from the literature while the missing data were derived from available absorption and emission spectra. The calculated parameters include Judd–Ofelt parameters, refractive indexes, Slater integrals, spin–orbit coupling parameters, reduced matrix elements (RMEs), energy differences between emitting levels used for LIR, absolute, and relative sensitivities. We found a slight variation of RMEs between hosts because of variations in values of Slater integrals and spin–orbit coupling parameters, and we calculated their average values over 40 hosts. The calculations showed that crystals perform better than glasses in Er3+-based thermometry, and we identified hosts that have large values of both absolute and relative sensitivity.

Shadowed triplet pairings in Hund's metals with spin-orbit coupling

Hund's coupling in multiorbital systems allows for the possibility of even-parity orbital-antisymmetric spin-triplet pairing, which can be stabilized by spin-orbit coupling (SOC). While this pairing expressed in the orbital basis is uniform and spin-triplet, it appears in the band basis as a pseudospin-singlet, with the momentum dependence determined by the SOC and the underlying triplet character remaining in the form of interband pairing active away from the Fermi energy. Here, we examine the role of momentum-dependent SOC in generating nontrivial pairing symmetries, as well as the hidden triplet nature associated with this interorbital pairing, which we dub a "shadowed triplet". Applying this concept to Sr$_{2}$RuO$_{4}$, we first derive several forms of SOC with $d$-wave form factors from a microscopic model, and subsequently we show that for a range of SOC parameters, a pairing state with $s+id_{xy}$ symmetry can be stabilized. Such a pairing state is distinct from pure spin-singlet and -triplet pairings due to its unique character of pseudospin-energy locking. We discuss experimental probes to differentiate the shadowed triplet pairing from conventional pseudospin-triplet and -singlet pairings.

Электронные состояния и персистентные токи в кольцах с неоднородным спин-орбитальным взаимодействием Рашбы

The paper considers one-dimensional isolated quantum rings in a perpendicular magnetic field, in which Rashba spin-orbit coupling parameter changes along the ring. Electronic spectra and persistent currents of such ring structures are calculated for different values of the structure parameters and the magnitude of the magnetic flux. It is shown that the inhomogeneity of the Rashba parameter leads to anticrossing of energy levels and smoothing of the dependence of the persistent charge current on the flux. The influence of inhomogeneity on the spin persistent current turns out to be more significant: the projection of the spin current on the ring axis ceases to be preserved when moving along the ring; additional extrema or zeros appear on the dependence of the absolute value of the spin current on the magnetic flux for a given number of electrons in the ring.

Landau levels in spin-orbit coupling proximitized graphene: Bulk states

We study the magnetic-field dependence of Landau levels in graphene proximitized by large spin-orbit coupling materials, such as transition-metal dichalcogenides or topological insulators. In addition to the Rashba coupling, two types of intrinsic spin-orbit interactions, uniform (Kane-Mele type) and staggered (valley Zeeman type), are included, to resolve their interplay with magnetic orbital effects. Employing a continuum model approach, we derive analytic expressions for low-energy Landau levels, which can be used to extract local orbital and spin-orbit coupling parameters from scanning probe spectroscopy experiments. We compare different parameter regimes to identify fingerprints of relative and absolute magnitudes of intrinsic spin-orbit coupling in the spectra. The inverted band structure of graphene proximitized by WSe$_2$ leads to an interesting crossing of Landau states across the bulk gap at a crossover field, providing insights into the size of Rashba spin-orbit coupling. Landau level spectroscopy can help to resolve the type and signs of the intrinsic spin-orbit coupling by analyzing the symmetry in energy and number of crossings in the Landau fan chart. Finally, our results suggest that the strong response to the magnetic field of Dirac electrons in proximitized graphene can be associated with extremely large self-rotating magnetic moments.

AN INVESTIGATION OF SPIN-ORBIT COUPLING OF [Eu(NO3)3 (2 pb)2]∙CH3COCH3 COMPLEX

In this study, Eu metal investigated from lanthanides. Eu(NO3)3(2pb)2]CH3COCH3 (Eu(III)Nitrate -2-(2-pyridyl)benzimidazole.Acetone) complex was structurally optimized by using the Gaussian program. Geometric structure, molecular geometry, optimized geometric parameters, bond length, and bond angle of the complex were calculated using the SDD basis set of (DFT/B3LYP). HOMO, LUMO, and Energy differences were calculated using the DFT method. The spin-orbit coupling parameter of the complex was theoretically calculated. Magnetic susceptibility analysis was performed using this value

Spin–Orbit Coupling-Induced Effective Interactions in Superconducting Nanowires in the Strong Correlation Regime

In the second order of the operator form of the perturbation theory, the effective interactions in a superconducting nanowire have been obtained at the strong electron correlations, when the spin–orbit coupling parameter is comparable with the hopping integral. Using the exact diagonalization technique, in short nanowires with the open boundary conditions at the strong Coulomb repulsion, the excitations corresponding to the Majorana edge states with the energy below the value of a bulk superconducting gap have been demonstrated.

High-harmonic generation in spin-orbit coupled systems

We study high-harmonic generation in two-dimensional electron systems with Rashba and Dresselhaus spin-orbit coupling and derive harmonic generation selection rules with the help of group theory. Based on the bandstructures of these minimal models and explicit simulations we reveal how the spin-orbit parameters control the cutoff energy in the high-harmonic spectrum. We also show that the magnetic field and polarization dependence of this spectrum provides information on the magnitude of the Rashba and Dresselhaus spin-orbit coupling parameters. The shape of the Fermi surface can be deduced at least qualitatively and if only one type of spin-orbit coupling is present, the coupling strength can be determined.

(2+1) -dimensional sonic black hole from a spin-orbit-coupled Bose-Einstein condensate and its analog Hawking radiation

We study the properties of a $2+1$ dimensional Sonic black hole (SBH) that can be realised, in a quasi-two-dimensional two-component spin-orbit coupled Bose-Einstein condensate (BEC). The corresponding equation for phase fluctuations in the total density mode that describes phonon field in the hydrodynamic approximation is described by a scalar field equation in $2+1$ dimension whose space-time metric is significantly different from that of the SBH realised from a single component BEC that was studied experimentally, and, theoretically meticulously in literature. Given the breakdown of the irrotationality constraint of the velocity field in such spin-orbit coupled BEC, we study in detail how the time evolution of such condensate impacts the various properties of the resulting SBH. By time evolving the condensate in a suitably created laser-induced potential, we show that such a sonic black hole is formed, in an annular region bounded by inner and outer event horizon as well as elliptical ergo-surfaces. We observe amplifying density modulation due to the formation of such sonic horizons and show how they change the nature of analogue Hawking radiation emitted from such sonic black hole by evaluating the density-density correlation at different times, using the truncated Wigner approximation (TWA) for different values of spin-orbit coupling parameters. We finally investigate the thermal nature of such analogue Hawking radiation.

Zero-field spin splitting in AlInN/GaN heterostructures

GaN-based heterostructures are of technical interest in spintronic applications. This paper reports the study of the magnetotransport properties of AlInN/GaN heterostructures with the indium composition of 17%. The quantum Hall effect is observed at low temperatures, accompanied by the Shubnikov–de Haas (SdH) oscillations of the longitudinal magnetoresistance. In the SdH oscillations, weak beating patterns appear up at high magnetic field, which is indicative of the presence of the zero-field spin splitting. Together with the beating patterns, the weak antilocalization effect is also observed. From this effect, the dephasing rate and the spin–orbit scattering time are extracted. From the extracted spin–orbit scattering time, we obtained a spin–orbit coupling parameter of α=8.6×10−13 eV m, comparable to the reported values in AlGaN/GaN heterostructures. This suggests that AlInN/GaN heterostructures provides an alternative to AlGaN/GaN heterostructures for spintronic applications.

Large-momentum tail of one-dimensional Fermi gases with spin-orbit coupling

We study the contacts, large-momentum tail, radio-frequency spectroscopy, and some other universal relations for an ultracold one-dimensional (1D) two-component Fermi gas with spin-orbit coupling (SOC). Different from previous studies, we find that the $q^{-8}$ tail in the spin-mixing (off-diagonal) terms of the momentum distribution matrix is dependent on the two SOC parameters in the laboratory frame for 1D systems, where $q$ is the relative momentum. This tail can be observed through time-of-flight measurement as a direct manifestation of the SOC effects on the many-body level. Besides the traditional 1D even-wave scattering length, we find that two new physical quantities must be introduced due to the SOC. Consequently, two new adiabatic energy relations with respect to the two SOC parameters are obtained. Furthermore, we derive the pressure relation and virial theorem at short distances for this system. To find how the SOC modifies the large-momentum behavior, we take the SOC parameters as perturbations since the strength of the SOC should be much smaller than the corresponding strength scale of the interatomic interactions. In addition, by using the operator product expansion method, we derive the asymptotic behavior of the large-momentum distribution matrix up to the $q^{-8}$ order and find that the diagonal terms of the distribution matrix include the contact of traditional 1D even-wave scattering length as the leading term and the SOC modified terms beyond the leading term, the off-diagonal term is beyond the subleading term and is corrected by the SOC parameters. We also find that the momentum distribution matrix shows spin-dependent and anisotropic features. Furthermore, we calculate the momentum distribution matrix in the laboratory frame for the experimental implication.

Determination of spin-orbit scattering lifetime at the interface of LaAlO3/SrTiO3 from the superconducting upper critical fields

This paper presents results on the coexistence of fluid and superfluidity phases or the interface superconductivity in LaAlO3/SrTiO3. The orbital nature of an electron largely affects its spin-orbit interaction, which can be determined independently either from the weak-localization model in normal state or from the upper critical fields in superconducting state. A discrepancy in the extracted spin-orbit coupling parameters is uncovered

Bowing of transport gap in hybrid halide perovskite alloys (CH3NH3Sn1−xPbxI3): Which band is responsible?

Apart from being a unique material for efficient solar cells, hybrid halide perovskites possess more mysteries than ever. An anomalous bandgap behavior in CH3NH3Sn1−xPbxI3 alloys has been reported recently [Hao et al., J. Am. Chem. Soc. 136, 8094 (2014)], in which the composition-dependent optical bandgap follows nonmonotonic and nonlinear characteristics instead of a linear trend or Vegard's law; the bandgap of the intermediate compounds was lower than that of the end members. In this article, we study composition-dependent conduction and valence band energies through scanning tunneling spectroscopy to deliberate on the role of the two bands in the bandgap bowing phenomenon and the underlying mechanism. We observe a nonlinear behavior of the two bands with respect to the alloy composition, leading to an anomalous behavior in the transport gap as well. We confirm that two competing events, namely, a spin–orbit coupling parameter appearing due to inclusion of a high-Z material and structural distortion affecting molecular orbitals responsible for the formation of the valence and the conduction bands, result in bandgap bowing in CH3NH3Sn1−xPbxI3 alloys.

Эффективные взаимодействия, индуцированные спин-орбитальной связью в сверхпроводящих нанопроволоках в режиме сильных корреляций

Abstract In the second order of the operator form of the perturbation theory, the effective interactions in a superconducting nanowire have been obtained at the strong electron correlations, when the spin–orbit coupling parameter is comparable with the hopping integral. Using the exact diagonalization technique, in short nanowires with the open boundary conditions at the strong Coulomb repulsion, the excitations corresponding to the Majorana edge states with the energy below the value of a bulk superconducting gap have been demonstrated.

Electronic Properties of Bulk and Single-Layer MoS2 Using ab Initio DFT: Application of Spin-Orbit Coupling (SOC) Parameters

Two dimensional (2D) materials are currently gaining a lot of interest due to excellent properties that are different from their bulk structures. Single and few-layered of Transition metal dichalcogenides (TMDCs) have a bandgap that ranges between 1-2 eV, which is used for FET devices or any optoelectronic devices. Within TMDCs, a ton of consideration is focused on Molybdenum Disulfide (MoS2) because of its promising band gap-tuning and transition between direct to indirect bandgap properties relies upon its thickness. The density functional theory (DFT) calculations with different functionals and spin-orbit coupling (SOC) parameters were carried out to study the electronic properties of bulk and monolayer MoS2. The addition of SOC brought about a noteworthy change in the profile of the band energy, explicitly the splitting of the valence band maximum (VBM) into two sub-bands. The indirect bandgap in bulk MoS2 ranges from 1.17- 1.71eV and that of the monolayer bandgap was 1.6 – 1.71eV. The calculated parameters were compared to the obtained experimental and theoretical results. The obtained density of states (DOS) can be used in explaining the nature of bandgap in both the bulk and monolayer MoS2. These electronic characteristics are important for applications in material devices and energy-saving applications