Presence Of Spin-orbit Interaction Research Articles

Spin-orbit coupling effects in single-layer phosphorene

The electronic band structure of monolayer phosphorene is thoroughly studied by considering the presence of spin-orbit interaction. We employ a multiorbital Slater-Koster tight-binding approach to derive effective k·p-type Hamiltonians that describes the dominant spin-orbit coupling (SOC) effects of the Rashba and intrinsic origin at the high Γ and S high symmetry points in phosphorene. In the absence of SOC effects a minimal admixture of pz and py atomic orbitals suffices to reproduce the well-known anisotropy of highest valence and the lowest conduction bands at the Γ point, consistent with density functional theory (DFT) and k·p methods. In contrast, the inclusion of the px and s atomic orbitals are rather crucial for an adequate description of the SOC effects in phosphorene at low energies, particularly at the S point. We introduce useful analytical expressions for the Rashba and intrinsic SOC parameters in terms of the relevant Slater-Koster integrals. In addition, we report simple formulas for the interband dipole strengths, revealing the nature of the strong anisotropic behavior of its lower bands. Our findings can be useful for further studies of electronic and spin transport properties in monolayer phosphorene and its nanoribbons. Published by the American Physical Society 2024

Reactive Hall and Edelstein effects in a tight-binding model with spin-orbit coupling

The reactive Hall constant RH, described by reactive (nondissipative) conductivities, is analyzed within linear response theory in the presence of spin-orbit interaction. Within a two-dimensional tight-binding model the effect of Van Hove singularities is studied. Along the same line a formulation of the Edelstein constant is proposed and studied as a function of coupling parameters and fermion filling. Published by the American Physical Society 2024

Spin orbit induced anisotropic giant effective g factor and reduced effective mass in non-magnetic Sn1−xSrxTe mixed crystal

The binary and ternary telluride systems containing europium as one of the magnetic components exhibit a higher effective g factor and much lower effective mass due to strong spin-orbit and s/p-f hybridized interaction mediated by the dopant impurity. In this communication, we have exploited the same for a ternary mixed crystal Sn1−xSrxTe, with strontium as the non-magnetic counterpart of europium. We have derived a functional equation within the framework of effective mass representation, accounting for both spin-orbit interaction and the presence of a magnetic field. In the context of k→⋅π→ model, at first, two MW (Mitchell-Wallis) band edge states are diagonalized properly, and subsequently, the off-band edge states are treated using perturbation up to the k2 level. We derived the formulas for the effective g factor and effective mass by employing Green's function method, considering the presence of spin-orbit interaction, magnetic field, and Sr impurity and assuming band inversion model as applicable to Sn1−xSrxTe system. Finally, we conduct a comprehensive examination of the effective g factor, effective mass, and their respective anisotropies in Sn1−xSrxTe considering their dependence on carrier concentration and impurity levels at T=300K. We present extremely elevated effective g factor; g=2230, for n−Sn1−xSrxTe and g=2160, for p−Sn1−xSrxTe respectively with large anisotropies and correspondingly low effective mass mc,v=0.003m0 around x=0.014 in the concentration range 0.01×1019 cm−3 to 0.1×1019 cm−3. Irrespective of the unsaturated electronic shell of Sr, the existence of strong spin-orbit interaction refers to the strong coupling of band edge states across the band minima triggered by substitutional impurity. The occurrence of a substantial effective g factor and low effective mass is unique in such non-magnetic Sn1−xSrxTe mixed crystal ever reported.

Reversible metal-insulator transition in SrIrO3 ultrathin layers by field effect control of inversion symmetry breaking

SrIrO3 is a correlated semimetal with narrow t2g d-bands of strong mixed orbital character resulting from the interplay of the spin-orbit interaction due to heavy iridium atoms and the band folding induced by the lattice structure. In ultrathin layers, inversion symmetry breaking, occurring naturally due to the presence of the substrate, opens new orbital hopping channels, which in presence of spin-orbit interaction causes deep modifications in the electronic structure. Here, we show that in SrIrO3 ultrathin films the effect of inversion symmetry breaking on the band structure can be externally manipulated in a field effect experiment. We further prove that the electric field toggles the system reversibly between a metallic and an insulating state with canted antiferromagnetism and an emergent anomalous Hall effect. This is achieved through the spin-orbit driven coupling of the electric field generated in an ionic liquid gate to the electronic structure, where the electric field controls the band structure rather than the usual band filling, thereby enabling electrical control of the effective role of electron correlations. The externally tunable antiferromagnetic insulator, rooted in the strong spin-orbit interaction of iridium, may inspire interesting applications in spintronics.

Spin-transport across a two-dimensional metal-semiconductor interface with infinite potential in presence of spin-orbit interactions: Double refraction and spin-filtering effect

The spin-transport across a two-dimensional metal-semiconductor junction with a Dirac-delta function potential at the interface and the Rashba and Dresselhaus spin-orbit interactions in the semiconductor region is studied exactly using discontinuous boundary conditions and the spin-polarized reflected and refracted current density and differential conductance are calculated. It is shown that in the presence of an infinite interface potential, an increase in the incident electron's energy reduces the spin splitting. It is also shown that the reflected and refracted coefficients, the spin-polarized currents and the corresponding differential conductance depend strongly on the spin-orbit interactions. The reflected spin polarization, however, becomes zero due to the infinite potential. The Rashba coupling enhances the refracted spin polarization while the Dresselhaus coupling reduces it. Thus, the maximum in polarization occurs at small values of Dresselhaus coupling and large values Rashba coupling. Interestingly, though the presence of delta-potential at the interface does not change the splitting angle between the spin-up and spin-down electrons, it causes a constant shift in the spin polarization.

Influence of Magnetic Field on Electron Energy Levels in Semconductor Quantum Dots in the Presence of Spin-Orbit Interactions

Energy levels of electrons in semiconductor quantum dots are obtained within the framework of perturbation theory taking into account the Rashba and Dresselhaus spin-orbit interactions and an external magnetic field. The circular quantum dots are simulated by a new smooth confinement potential of a finite depth and width. The dependence of energy levels on a constant uniform magnetic field and potential parameters is presented.

Relativistic Density Functional NMR Tensors Analyzed with Spin-free Localized Molecular Orbitals.

The implementation of fast relativistic methods based on density functional theory, in conjunction with localized molecular orbital (LMO) based analysis, allows straightforward interpretations of NMR parameters in terms of contributions from core shells, lone pairs, and bonds, for compounds containing elements from across the periodic table. We present a conceptual review of a frequently used LMO analysis of NMR parameters calculated in the presence of spin-orbit interactions and other relativistic effects. An accompanying example focuses on the 15 N shielding in a heavy metal complex.

Formula omitted] electronic structure and strain-dependence of the crystal field splitting and inter-band transition energy of W–InN

In this paper, we study the electronic structure of wurtzite Indium Nitride (W–InN) using a k→∙π→ theory. Here π→ is the relativistic momentum operator. It is based on an eight-band model; three valence bands and one conduction band, each Kramers’ split by spin-orbit interaction. We diagonalize the k→∙π→ Hamiltonian following a two-band model, where each valence band is treated separately with the conduction band by using a suitable basis set in the presence of spin-orbit interaction. Effects of other valence bands on the dispersion of a given valence band are incorporated using second order perturbation theory. Valence band dispersions are plotted and compared with a previous calculation and our own results obtained by using a different method. Agreement is found to be satisfactory. Electronic and hole effective masses are calculated and compared with previously reported values, which are substantially different from each other. Fair agreement is noticed. Discrepancies are discussed. Effect of strain is calculated on the electronic structure by calculating the crystal field energy and transition energy for small variations of strain. Although results could not be compared with any previous calculation, due presumably to their absence in literature, trends and systematics are found to be in accord with the same found in case of other wurtzite semiconductors.

Giant effective g factor and anisotropy in Sn1−xEuxTe: Contribution from spin-orbit and s/p − f hybridization

We consider the effective equation of motion starting from the fundamental six-level double group basis as stated by Mitchell-Wallis under effective mass representation in the presence of spin-orbit interaction, external magnetic field, and impurity. Here, the hybridized exchange type interactions due to magnetic impurities with carrier and external magnetic field are incorporated in the k⃗⋅π⃗ perturbation technique. Finally, we perform a systematic analysis of the effective g factor and its anisotropy in Sn1−xEuxTe as functions of carrier concentration and impurity at T = 300 K. We report very high values of effective g factor; g = 1028 for n − Sn1−xEuxTe and g = 997 for p − Sn1−xEuxTe with large anisotropies around x = 0.02 as compared to Pb1−xEuxTe in the concentration range 0.01 × 1019cm−3 to 0.1 × 1019cm−3. Our calculated results and trends are very similar to others’ work, previously reported for similar systems. The presence of a large effective g factor renders this material a potential choice for spintronics applications.

Energy levels of an electron in a circular quantum dot in the presence of spin-orbit interactions

The two-dimensional circular quantum dot in a double semiconductor heterostructure is simulated by a new axially symmetric smooth potential of finite depth and width. The presence of additional potential parameters in this model allows us to describe the individual properties of different kinds of quantum dots. The influence of the Rashba and Dresselhaus spin-orbit interactions on electron states in quantum dot is investigated. The total Hamiltonian of the problem is written as a sum of unperturbed part and perturbation. First, the exact solution of the unperturbed Schrödinger equation was constructed. Each energy level of the unperturbed Hamiltonian was doubly degenerated. Further, the analytical approximate expression for energy splitting was obtained within the framework of perturbation theory, when the strengths of two spin-orbit interactions are close. The numerical results show the dependence of energy levels on potential parameters.

Rydberg series of dark excitons and the conduction band spin-orbit splitting in monolayer WSe2

Strong Coulomb correlations together with multi-valley electronic bands in the presence of spin-orbit interaction are at the heart of studies of the rich physics of excitons in monolayers of transition metal dichalcogenides (TMD). Those archetypes of two-dimensional systems promise a design of new optoelectronic devices. In intrinsic TMD monolayers the basic, intravalley excitons, are formed by a hole from the top of the valence band and an electron either from the lower or upper spin-orbit-split conduction band subbands: one of these excitons is optically active, the second one is dark, although possibly observed under special conditions. Here we demonstrate the s-series of Rydberg dark exciton states in tungsten diselenide monolayer, which appears in addition to a conventional bright exciton series in photoluminescence spectra measured in high in-plane magnetic fields. The comparison of energy ladders of bright and dark Rydberg excitons is shown to be a method to experimentally evaluate one of the missing band parameters in TMD monolayers: the amplitude of the spin-orbit splitting of the conduction band.

Evidence for spin-orbit and e−e Coulomb interaction from a magnetotransport study on CaCu3Ru4O12 thin films

$\mathrm{Ca}{\mathrm{Cu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$ (CCRO) is considered a $d$-electron-based heavy-fermion metallic system with intriguing electronic properties. The magnetotransport measurements on metallic CCRO thin films reveal weak antilocalization (WAL) effects; however, it is not straightforward to infer whether the same originates from $e\text{\ensuremath{-}}e$ Coulomb interaction (EEI), spin-orbit interaction (SOI), or both present in CCRO. By evaluating quantum correction to sheet conductance for CCRO metallic thin films in the two-dimensional limit, it is observed that SOI gives rise to a dominant contribution to negative magnetoconductance (MC) in the weak-field regime. Based on weak localization (WL) and WAL analysis, SOI and inelastic scattering lengths (${l}_{so}$ and ${l}_{\ensuremath{\phi}}$) are obtained to be 30 and 74 nm, respectively, which indicates that WAL $({l}_{so}<{l}_{\ensuremath{\phi}})$ remains at play. The anisotropic effect of SOI is reflected in the field-direction-dependent in-plane and out-of-plane MC measurements. The presence of the EEI contribution is evidenced from (i) the linear increment (positive slope) of sheet conductance with $ln(T)$ in the quantum interference regime [only the WAL effect should otherwise show a negative slope with $ln(T)]$ and (ii) $ln(T)$ dependence of the Hall coefficient with a negative slope. Further, in the high-magnetic-field regime where WL or WAL is not valid, MC follows $ln(B)$-type behavior, indicating the presence of EEI. These findings have implications for the basic understanding of quantum magnetotransport properties in the presence of SOI and EEI in CCRO.

Studyof the Spin-Orbit Interaction Effects on Energy Levels and the Absorption Coefficients of Spherical Quantum Dotand Quantum Anti-Dotunderthe Magnetic Field

In this study, the energy levels of spherical quantum dot (QD) and spherical quantum anti-dot (QAD) with hydrogenic impurity in the center, in the presence of spin-orbit interaction (SOI) and weak external magnetic field have been studied. To this aim, solving the Schrodinger equation for the discussed systems by using the finite difference method, the wave functions and energies of these systems are calculated. Then the effect of the external magnetic field, system radius size and height of potential barrier on the energy levels and also the linear, nonlinear and total absorption coefficients, (ACs), of the mentioned systems are studied. Numerical results show that the SOI in both models causes a split of 2p level into two sub-levels of 2p_(1/2)and 2p_(3/2) where the low index indicates the total angular momentum J. Also, considering the electron spin, under an applied magnetic field, the 1s and 2p levels split into two sub-levels and six sub-levels, respectively. Furthermore, in this research, it is proved that energy changes are significantly different as a function of radius size and height of the potential barrier in QD and QAD models and the ACs of these systems behave differently according to the incident photon energy at the same condition.

Comment on “Spin-orbit interaction and spin selectivity for tunneling electron transfer in DNA”

The observation of chiral-induced spin selectivity (CISS) in biological molecules still awaits a full theoretical explanation. In a recent Rapid Communication, Varela et al. [Phys. Rev. B 101, 241410(R) (2020)] presented a model for electron transport in biological molecules by tunneling in the presence of spin-orbit interactions. They then claimed that their model produces a strong spin asymmetry due to the intrinsic atomic spin-orbit strength. As their Hamiltonian is time-reversal symmetric, this result contradicts a theorem by Bardarson [J. Phys. A: Math. Theor. 41, 405203 (2008)], which states that such a Hamiltonian cannot generate a spin asymmetry for tunneling between two terminals (in which there are only a spin-up and a spin-down channels). Here we solve the model proposed by Varela et al. and show that it does not yield any spin asymmetry, and therefore cannot explain the observed CISS effect.

Analytic Expressions for Orbital Angular Momentum Modal Crosstalk in a Slightly Elliptical Fiber

Assuming weakly guiding approximation, we examine orbital angular momentum (OAM) mode mixing on account of ellipticity in a fiber and derive a complete set of analytic expressions for spatial crosstalk, using scalar perturbation theory that incorporates fully the existing degeneracy between a spatial OAM mode and its degenerate partner characterized by a topological charge of opposite sign. These expressions, consequently, include an explicit formula for calculating the 2 pi walk-off length over which an input OAM mode converts into its degenerate partner, and back into itself. We further explore the applicability of the derived expressions in the presence of spin-orbit interaction. The expressions constitute a useful mathematical tool in the analysis and design of fibers for spatially-multiplexed mode transmissions. Their utility is demonstrated with application to a few mode and a multimode step-index fiber.

Studies of surface states in Bi2Se3 induced by the BiSe substitution in the crystal subsurface structure

We present a systematic theoretical study of bismuth selenide electronic structure in the presence of spin-orbit interaction. It is confirmed that the inversion of Bi pz and Se pz states in the bulk band structure is induced by spin-orbit coupling. The energy gap in the bulk electronic structure is closed by pz states associated mainly with Bi atoms from the first quintuple layer. We elucidate the influence of Bi substitution in the fifth atomic layer on the local density of electronic states in the top quintuple layer. Finally, we describe how it develops into the additional p states in the surface electronic structure, which produce the triangular protrusion observed in Scanning Tunnelling Microscopy measurements and characteristic narrow features in Scanning Tunnelling Spectroscopy results.

Quantum spin Hall effect, thermoelectric performance, and optical properties of XBi (X = Sc, Y) monolayers

Abstract The investigations of quantum spin Hall effect and the edge states manipulation of two dimensional topological insulators are very salient for the practical applications and fundamental sciences. The high thermoelectric efficiency of these materials has also been confirmed, recently. So, in this study the first-principles calculations are implemented based on density functional theory in the presence of spin orbit interaction, to evaluate the topological phase transition and thermoelectric performance of XBi (X = Sc, Y) monolayers under in-plane strains. It is found that the compressive in-plane strains and spin orbit interaction, which host considerable effects on the electronic structure, can cause the topologically nontrivial phase and high thermoelectric performance. The topological state of XBi monolayers is confirmed with the Z2 topological invariant calculation. These results provide these monolayers for the novel thermoelectric and nanoelectronics quantum devices and topological phenomena. Also some optical properties of XBi monolayers are calculated and investigated under in-plane strains. The results show the considerable transparency and reflectivity of these monolayers near zero energy.

Levitons in helical liquids with Rashba spin-orbit coupling probed by a superconducting contact

We consider transport properties of a single edge of a two-dimensional topological insulators, in presence of Rashba spin-orbit coupling, driven by two external time-dependent voltages and connected to a thin superconductor. We focus on the case of a train of Lorentzian-shaped pulses, which are known to generate coherent single-electron excitations in two-dimensional electron gas, and prove that they are minimal excitations for charge transport also in helical edge states, even in the presence of spin-orbit interaction. Importantly, these properties of Lorentzian-shaped pulses can be tested computing charge noise generated by the scattering of particles at the thin superconductor. This represents a novel setup where electron quantum optics experiments with helical states can be implemented, with the superconducting contact as an effective beamsplitter. By elaborating on this configuration, we also evaluate charge noise in a collisional Hong-Ou-Mandel configuration, showing that, due to the peculiar effects induced by Rashba interaction, a non-vanishing dip at zero delay appears.

Superadiabatic spin-preserving control of a single-spin qubit in a double quantum dot with spin–orbit interaction

A protocol for controlling the localization of an electron with a fixed projection of spin between two quantum dots in a material with spin-orbit (SO) interaction is studied. Due to SO coupling, the manipulation of the electron shuttling between both quantum dots also leads to a mixing between spin projections near to the avoided crossing of levels. We use a transitionless quantum driving approach, neglecting SO interaction, to analytically design simple electric and magnetic pulses able to rapidly drive the electron along an adiabatic Landau–Zener manifold. We show that the same fields in the presence of SO interaction can also give a fast high-fidelity transition between the qubit states. The performance of the proposed protocol is assessed in the presence of SO interactions of typical semiconductor materials. It is shown that it provides a fast and efficient spin-conserving method for controlling the electron position in a double quantum dot.

Double quantum dot scenario for spin resonance in current noise

We show that interference between parallel currents through two quantum dots, in presence of spin orbit interactions and strong on-site Coulomb repulsion, leads to resonances in current noise at the corresponding Larmor frequencies. An additional resonance at the difference of Larmor frequencies is present even without spin-orbit interaction. The resonance lines have strength comparable to the background shot noise and therefore can account for the numerous observations of spin resonance in STM noise with non-polarized leads. We solve also several other models that show similar resonances.