Orbital Effects Research Articles

Intrinsic orbital and spin Hall effect in bismuth semimetal

We investigate the intrinsic orbital Hall conductivity (OHC) and spin Hall conductivity (SHC) in a bismuth semimetal, by employing an $sp$-orbital tight-binding model. We report a notable difference between the anisotropy of OHC and SHC whose orbital and spin polarizations lie within the basal plane. We do not observe a substantial correlation between the orbital and spin Berry curvatures with spin-orbit coupling (SOC) at the Fermi energy, disproving the correlation between OHC and SHC in a strong SOC regime. We argue the huge SHC in a Bi semimetal is attributed to its gigantic SOC which strongly affects the hybridization of the $p$ orbitals, despite its relatively small magnitude of OHC. We hope the distinct anisotropy of OHC and SHC provides a feasible means to differentiate between the two effects in experiments.

Large upper critical fields and dimensionality crossover of superconductivity in the infinite-layer nickelate La0.8Sr0.2NiO2

The recently emerging superconductivity in infinite-layer nickelates, with isostructure and isoelectron of cuprates, provides a new platform to explore the pairing mechanism of high-temperature superconductors. In this work, we studied the upper critical field ($H_{\rm{c2}}$) of a high-quality La$_{0.8}$Sr$_{0.2}$NiO$_{2}$ thin film with superconducting transition temperature, $T_{\rm{c}}$ = 18.8 K, using high magnetic field up to 56 T. A very large $H_{\rm{c2}}$, $\sim$ 40 T for $H$ $\Arrowvert$ $c$ and $\sim$ 52 T for $H$ $\Arrowvert$ $ab$, was confirmed, which suggests that infinite-layer nickelates also have great application potential. The anisotropy of $H_{\rm{c2}}$ monotonically decreases from $\sim$ 10 near $T_{\rm{c}}$ to $\sim$ 1.5 at 2 K. Angle dependence of $H_{\rm{c2}}$ confirms the crossover of superconductivity from two-dimensional (2D) to three-dimensional (3D) as the temperature decreases. We discussed that the interstitial orbital effect causes the weakening of anisotropy. The observed abnormal upturning of $H_{\rm{c2}}$ at low temperatures is found to be a universal behavior independent of film quality and rare earth elements. Therefore, it should not be the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state due to the fact that it is in the dirty limit and insensitive to disorder.

Assessing the Effects of Orbital Relaxation and the Coherent-State Transformation in Quantum Electrodynamics Density Functional and Coupled-Cluster Theories.

Cavity quantum electrodynamics (QED) generalizations of time-dependent (TD) density functional theory (DFT) and equation-of-motion (EOM) coupled-cluster (CC) theory are used to model small molecules strongly coupled to optical cavity modes. We consider two types of calculations. In the first approach (termed "relaxed"), we use a coherent-state-transformed Hamiltonian within the ground- and excited-state portions of the calculations, and cavity-induced orbital relaxation effects are included at the mean-field level. This procedure guarantees that the energy is origin-invariant in post-self-consistent-field calculations. In the second approach (termed "unrelaxed"), we ignore the coherent-state transformation and the associated orbital relaxation effects. In this case, ground-state unrelaxed QED-CC calculations pick up a modest origin dependence but otherwise reproduce relaxed QED-CC results within the coherent-state basis. On the other hand, a severe origin dependence manifests in ground-state unrelaxed QED mean-field energies. For excitation energies computed at experimentally realizable coupling strengths, relaxed and unrelaxed QED-EOM-CC results are similar, while significant differences emerge for unrelaxed and relaxed QED-TDDFT. First, QED-EOM-CC and relaxed QED-TDDFT both predict that electronic states that are not resonant with the cavity mode are nonetheless perturbed by the cavity. Unrelaxed QED-TDDFT, on the other hand, fails to capture this effect. Second, in the limit of large coupling strengths, relaxed QED-TDDFT tends to overestimate Rabi splittings, while unrelaxed QED-TDDFT underestimates them, given splittings from relaxed QED-EOM-CC as a reference, and relaxed QED-TDDFT generally does the better job of reproducing the QED-EOM-CC results.

Cone-beam CT sampling incompleteness: analytical and empirical studies of emerging systems and source-detector orbits.

Motivated by emerging cone-beam computed tomography (CBCT) systems and scan orbits, we aim to quantitatively assess the completeness of data for 3D image reconstruction-in turn, related to "cone-beam artifacts." Fundamental principles of cone-beam sampling incompleteness are considered with respect to an analytical figure-of-merit [FOM, denoted ] and related to an empirical FOM (denoted ) for measurement of cone-beam artifact magnitude in a test phantom. A previously proposed analytical FOM [, defined as the minimum angle between a point in the 3D image reconstruction and the x-ray source over the scan orbit] was analyzed for a variety of CBCT geometries. A physical test phantom was configured with parallel disk pairs (perpendicular to the -axis) at various locations throughout the field of view, quantifying cone-beam artifact magnitude in terms of (the relative signal modulation between the disks). Two CBCT systems were considered: an interventional C-arm (Cios Spin 3D; Siemens Healthineers, Forcheim Germany) and a musculoskeletal extremity scanner; Onsight3D, Carestream Health, Rochester, United States)]. Simulations and physical experiments were conducted for various source-detector orbits: (a)a conventional 360deg circular orbit, (b)tilted and untilted semi-circular (196deg) orbits, (c)multi-source (three x-ray sources distributed along the axis) semi-circular orbits, and (d)a non-circular (sine-on-sphere, SoS) orbit. The incompleteness of sampling [] and magnitude of cone-beam artifacts () were evaluated for each system and orbit. The results show visually and quantitatively the effect of system geometry and scan orbit on cone-beam sampling effects, demonstrating the relationship between analytical and empirical . Advanced source-detector orbits (e.g., three-source and SoS orbits) exhibited superior sampling completeness as quantified by both the analytical and the empirical FOMs. The test phantom and metric were sensitive to variations in CBCT system geometry and scan orbit and provided a surrogate measure of underlying sampling completeness. For a given system geometry and source-detector orbit, cone-beam sampling completeness can be quantified analytically (in terms arising from Tuy's condition) and/or empirically (using a test phantom for quantification of cone-beam artifacts). Such analysis provides theoretical and practical insight on sampling effects and the completeness of data for emerging CBCT systems and scan trajectories.

Electronic structures and Aharonov–Bohm effect in higher-order topological Dirac Semimetal nanoribbons with strong confinements

Electronic structures and magnetotransport properties of topological Dirac semimetal (TDSM) nanoribbons are studied by adopting the tight-binding lattice model and the Landauer–Büttiker formula based on the non-equilibrium Green’s function. For concreteness, the TDSM material Cd3As2 grown along the experimentally accessible [110] crystallographic direction is taken as an example. We found that the electronic structures of the TDSM nanoribbon depend on both the strength and direction of the magnetic field (MF). The transversal local charge density (LCD) distribution of the electronic states in the TDSM nanoribbon is moved gradually from the center toward the hinge of each surface as a [010] direction MF strength is increased, forming the two-sided hinge states. However, one-sided surface states are generated in the TDSM nanoribbon when a [001] direction MF is applied. As a result, one-sided hinge states can be achieved once a tilted MF is placed to the TDSM nanoribbon. The underlying physical mechanism of the desired one-sided hinge states is attributed to both the orbital and Zeeman effects of the MF, which is given by analytical analyses. In addition, typical Aharonov–Bohm interference patterns are observed in the charge conductance of the two-terminal TDSM nanoribbon with a tilted MF. This conductance behaviour originates from the unique interfering loop shaped by the one-sided hinge states. These findings may not only further our understanding on the external-field-induced higher-order (HO) topological phases but also provide an alternative method to probe the HO boundary states.

Spin–orbit effects in cluster chemistry: Considerations and applications for rationalization of their properties

Relativistic effects are usually taken into account in heavy-element-containing species, bringing to the scientific community stimulating cases of study. Scalar and spin–orbit effects are required to properly evaluate both the geometrical and electronic structures of such species, where, generally, scalar corrections are included. In order to take into account the spin–orbit term resulting from the interaction between the spatial and spin coordinates, double-valued point groups of symmetry are required, leading to total angular momenta (j) functions and atomic or molecular spinors, instead of pure orbital-angular momenta (l) and atomic or molecular orbitals. Here, we reviewed the role of spin–orbit coupling in bare and ligand-protected metallic clusters, from early to current works, leading to a more comprehensive relativistic quantum chemistry framework. As a result, the electronic structure is modified, leading to a variation in the calculated molecular properties, which usually improves the agreement between theory and experiment, allowing furthering rationalize of experimental results unexpected from a classical inorganic chemistry point of view. This review summarizes part of the modern application of spin–orbit coupling in heavy-elements cluster chemistry, where further treatment on an equal footing basis along with the periodic table is encouraged in order to incorporate such term in the general use vocabulary of both experimental and theoretical chemist and material scientist.

Probing electron localization during molecular dissociation by femtosecond strong-field ion momentum spectroscopy

The study of molecular valence electron dynamics and their coupling with nuclear motion is one of the frontiers of ultrafast physics and ultrafast chemistry. With time-resolved strong-field ion momentum spectroscopy, we study electron valence and nucleus wavepacket evolution on a femtosecond timescale. Two orientation-dependent bond-breaks of N2O molecules from the same electronic state are studied, and the influence of orbital hybridization and polarization effect during molecular breaking is analyzed based on the measured time-resolved asymmetric Pzsum distributions, allowing a visual representation of electron localization during the dissociation of molecules into ions and atoms. Comparison of experimental and theoretical results on orientation-dependent dissociation dynamics allows us to understand how nuclear motions evolve during fragmentation and to control ultrafast molecular reactions.

Orbital Fulde-Ferrell-Larkin-Ovchinnikov state in an Ising superconductor.

In superconductors possessing both time and inversion symmetries, the Zeeman effect of an external magnetic field can break the time-reversal symmetry, forming a conventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state characterized by Cooper pairings with finite momentum1,2. In superconductors lacking (local)inversion symmetry, the Zeeman effect may still act as the underlying mechanism of FFLO states by interacting with spin-orbit coupling (SOC). Specifically, the interplay between the Zeeman effect and Rashba SOC can lead to the formation of more accessible Rashba FFLO states that cover broader regions in the phase diagram3-5. However, when the Zeeman effect is suppressed because of spin locking in the presence of Ising-type SOC, the conventional FFLO scenarios are no longer effective. Instead, an unconventional FFLO state is formed by coupling the orbital effect of magnetic fields with SOC, providing an alternative mechanism in superconductors with broken inversion symmetries6-8. Here we report the discovery of such an orbital FFLO state in the multilayer Ising superconductor 2H-NbSe2. Transport measurements show that the translational and rotational symmetries are broken in the orbital FFLO state, providing the hallmark signatures of finite-momentum Cooper pairings. We establish the entire orbital FFLO phase diagram, consisting of a normal metal, a uniform Ising superconducting phase and a six-fold orbital FFLO state. This study highlights an alternative route to achieving finite-momentum superconductivity and provides a universal mechanism to preparing orbital FFLO states in similar materials with broken inversion symmetries.

Spin–orbit effects on the electronic and optical properties of lead iodide

Lead iodide (PbI2) has gained much interest due to its direct electronic gap in the visible range and layered crystal structure. It has thereby been considered as a promising material for applications in atomically thin optoelectronic devices. In this work, we present a detailed investigation of the effect of spin–orbit coupling (SOC) that arises from the presence of heavy atoms on the electronic and optical properties of PbI2 using first-principles calculations based on density-functional theory and many-body perturbation theory. We find that SOC not only alters the bandgap but also induces the mixing of orbital characters, resulting in a significant change in the overall band structure and charge carrier effective masses. Moreover, the band orbital mixing caused by SOC results in the dramatic change in optical transition matrix elements and, correspondingly, the absorption spectrum. Our experimentally measured absorption spectra validate the calculation results and demonstrate the importance of SOC in the optical processes of PbI2. Our findings provide insights that are important for the potential use of PbI2 as a material platform for visible optoelectronic devices.

Higher-order magnetic skyrmions in nonuniform magnetic fields

For a two-dimensional Hubbard model with spin-orbit Rashba coupling in external magnetic field the structure of effective spin interactions is studied in the regime of strong electron correlations and at half-filling. It is shown that in the third order of perturbation theory, the scalar and vector chiral spin-spin interactions of the same order arise. The emergence of the latter is due to orbital effects of magnetic field. It is shown that for nonuniform fields, scalar chiral interaction can lead to stabilization of axially symmetric skyrmion states with arbitrary topological charges. Taking into account the hierarchy of effective spin interactions, an analytical theory on the optimal sizes of such states, the higher-order magnetic skyrmions, is developed for axially symmetric magnetic fields of the form $h(r)\ensuremath{\sim}{r}^{\ensuremath{\beta}}$ with $\ensuremath{\beta}\ensuremath{\in}\mathbb{R}$.

Algebraic Diagrammatic Construction Theory for Simulating Charged Excited States and Photoelectron Spectra.

Charged excitations are electronic transitions that involve a change in the total charge of a molecule or material. Understanding the properties and reactivity of charged species requires insights from theoretical calculations that can accurately describe orbital relaxation and electron correlation effects in open-shell electronic states. In this Review, we describe the current state of algebraic diagrammatic construction (ADC) theory for simulating charged excitations and its recent developments. We start with a short overview of ADC formalism for the one-particle Green's function, including its single- and multireference formulations and extension to periodic systems. Next, we focus on the capabilities of ADC methods and discuss recent findings about their accuracy for calculating a wide range of excited-state properties. We conclude our Review by outlining possible directions for future developments of this theoretical approach.

Hydrogen Bonding, π-Stacking, and Aurophilic Interactions in Two Dicyanoaurate(I)-based Manganese(II) Complexes with Auxiliary Bis-Pyridine Ligands.

The relevance of hydrogen-bonding, π-π stacking and aurophilic interactions in the solid-state of two new heterobimetallic (AuI-MnII) complexes is analyzed in this manuscript. They are discrete complexes of formulae [Mn(bipy)2(H2O){Au(CN)2}][Au(CN)2] and [Mn(dmbipy)2{Au(CN)2}]·H2O, (bipy = 2,2'-bipyridine and dmbipy = 5,5'-dimethyl-2,2'-bipyridine), which are based on dicyanidoaurate(I) groups and 2,2'-bipyridyl-like co-ligands. They have been synthesized in good yields and X-ray characterized. In both compounds, aurophilic, OH···N hydrogen bonding and π-π interactions governed the supramolecular assemblies in the solid state. These contacts with special emphasis on the aurophilic interactions have been studied using density functional theory calculations and characterized using the quantum theory of atoms-in-molecules and the noncovalent interaction plot. The aurophilic contacts have been also rationalized from an orbital point of view using the natural bond orbital methodology, evidencing stabilization energies up to 5.7 kcal/mol. Moreover, the interaction energies have been decomposed using the Kitaura-Morokuma energy decomposition analysis, confirming the importance of electrostatic and orbital effects.

Catalytic mechanism of in-situ Ni/C co-incorporation for hydrogen absorption of Mg

Ni and carbon materials exhibit remarkable catalysis for the hydriding reaction of Mg. But the underlying mechanism of Ni/C hybrid catalysis is still unclear. In this work, density functional theory (DFT) calculation is applied to investigate the effect of Ni/C co-incorporation on the hydriding reaction of Mg crystal. The morphology and crystal structure of the Ni/C co-incorporated Mg sample show that the co-incorporated structure is credible. The transition state searching calculation suggests that both the incorporations of Ni and C are beneficial for the H2 dissociation. But Ni atom has a dramatic improvement for H2 dissociation and makes the H diffusion become limiting step of the hyriding reaction. The Ni dz2 orbit and H s orbit accept the electrons and combine together compactly, while the Ni dxy orbit is half-occupied. The catalytic effect of Ni on H2 dissociation can be ascribed to the bridging effect of Ni dxy orbit. The incorporation of C can weaken the over-strong interaction between Ni and H which hindered the H diffusion on Mg(0001). The Ni/C co-incorporated Mg(0001) shows the best performance during hyriding reaction compared with the clean and single incorporated Mg(0001).

Spin-Orbit and Zeeman Effects on the Electronic Properties of Single Quantum Rings: Applied Magnetic Field and Topological Defects.

Within the framework of effective mass theory, we investigate the effects of spin-orbit interaction (SOI) and Zeeman splitting on the electronic properties of an electron confined in GaAs single quantum rings. Energies and envelope wavefunctions in the system are determined by solving the Schrödinger equation via the finite element method. First, we consider an inversely quadratic model potential to describe electron confining profiles in a single quantum ring. The study also analyzes the influence of applied electric and magnetic fields. Solutions for eigenstates are then used to evaluate the linear inter-state light absorption coefficient through the corresponding resonant transition energies and electric dipole matrix moment elements, assuming circular polarization for the incident radiation. Results show that both SOI effects and Zeeman splitting reduce the absorption intensity for the considered transitions compared to the case when these interactions are absent. In addition, the magnitude and position of the resonant peaks have non-monotonic behavior with external magnetic fields. Secondly, we investigate the electronic and optical properties of the electron confined in the quantum ring with a topological defect in the structure; the results show that the crossings in the energy curves as a function of the magnetic field are eliminated, and, therefore, an improvement in transition energies occurs. In addition, the dipole matrix moments present a non-oscillatory behavior compared to the case when a topological defect is not considered.

Magneto-responsive optics in a chiral crystal with thermally triggered reversible phase transitions between chiral space groups.

Herein, a chiral charge transfer crystal that exhibits reversible phase transition between chiral space groups has been fabricated. When the phase switches from left-handed to right-handed chiral space group, more pronounced orbital angular momentum effects will be generated, where magneto-responsive optics are the opposite for chiral enantiomers. Moreover, circularly polarized light could enhance the chiral orbit of the crystal with the same spiral orientation to let spin have a better ability to resist external magnetic field. Thus, the magnetic field dependence of transmission and photoluminescence of chiral crystals are strongly dependent on the polarized state of incident light. Furthermore, by studying the coupling among spin, orbit, and circular photon, we obtained that the chiral orbit plays a key role in the coupling between the spin and circular photon. It is expected that this work could promote further exploration of organic chiral magneto-optical crystals in potential applications of sensing.

Hall Effect at the Focus of an Optical Vortex with Linear Polarization.

The tight focusing of an optical vortex with an integer topological charge (TC) and linear polarization was considered. We showed that the longitudinal components of the spin angular momentum (SAM) (it was equal to zero) and orbital angular momentum (OAM) (it was equal to the product of the beam power and the TC) vectors averaged over the beam cross-section were separately preserved during the beam propagation. This conservation led to the spin and orbital Hall effects. The spin Hall effect was expressed in the fact that the areas with different signs of the SAM longitudinal component were separated from each other. The orbital Hall effect was marked by the separation of the regions with different rotation directions of the transverse energy flow (clockwise and counterclockwise). There were only four such local regions near the optical axis for any TC. We showed that the total energy flux crossing the focus plane was less than the total beam power since part of the power propagated along the focus surface, while the other part crossed the focus plane in the opposite direction. We also showed that the longitudinal component of the angular momentum (AM) vector was not equal to the sum of the SAM and the OAM. Moreover, there was no summand SAM in the expression for the density of the AM. These quantities were independent of each other. The distributions of the AM and the SAM longitudinal components characterized the orbital and spin Hall effects at the focus, respectively.

Secondary Orbital Effect Involving Fluorine is Responsible for Substrate-Controlled Diastereodivergence in the Catalyzed syn-aza-Henry Reaction of α-Fluoronitroalkanes.

The fluorine atom is a powerful, yet enigmatic influence on chemical reactions. True to form, fluorine was recently discovered to effect diastereodivergence in an enantioselective aza-Henry reaction, resulting in a very rare case of syn-β-amino nitroalkane products. More bewildering was the observation of an apparent hierarchy of substituents within this substrate-controlled behavior: Ph>F>alkyl. These cases have now been examined comprehensively by computational methods, including both non-fluorinated and α-fluoro nitronate additions to aldimines catalyzed by a chiral bis(amidine) [BAM] proton complex. This study revealed the network of non-covalent interactions that dictate anti- (α-aryl) versus syn-selectivity (α-alkyl) using α-fluoronitronate nucleophiles, and an underlying secondary orbital interaction between fluorine and the activated azomethine.

Quantum theory of the intrinsic orbital magnetoelectric effect in itinerant electron systems at finite temperatures

Magnetization can be induced by an electric field in systems without inversion symmetry $\mathcal{P}$ and time-reversal symmetry $\mathcal{T}$. This phenomenon is called the magnetoelectric (ME) effect. The spin ME effect has been actively studied in multiferroics. The orbital ME effect also exists and has been mainly discussed in topological insulators at zero temperature. In this paper, we study the intrinsic orbital ME response in metals at finite temperature using the Kubo formula. The intrinsic response originates from the Fermi sea and does not depend on the dissipation. Especially in systems with $\mathcal{PT}$ symmetry, the extrinsic orbital ME effect becomes zero, and the intrinsic ME effect is dominant. We apply the response tensor obtained in this work to a $\mathcal{PT}$-symmetric model Hamiltonian with antiferromagnetic loop current order, demonstrating that the intrinsic ME effect is enhanced around the Dirac points.

Orbital magnetoelectric effect in nanoribbons of transition metal dichalcogenides

The orbital magnetoelectric effect (OME) generically refers to the appearance of an orbital magnetization induced by an applied electric field. Here, we show that nanoribbons of transition metal dichalcogenides (TMDs) with zigzag (ZZ) edges may exhibit a sizeable OME activated by an electric field applied along the ribbons' axis. We examine nanoribbons extracted from a monolayer (1L) and a bilayer (2L) of MoS$_2$ in the trigonal (H) structural phase. Transverse profiles of the induced orbital angular momentum accumulations are calculated to first order in the longitudinally applied electric field. Our results show that close to the nanoribbon's edge-state crossings energy, the orbital angular momentum accumulations take place mainly around the ribbons' edges. They have two contributions: one arising from the orbital Hall effect (OHE) and the other consists in the OME. The former is transversely anti-symmetric with respect to the principal axis of the nanoribbon, whereas the latter is symmetric, and hence responsible for the resultant orbital magnetization induced in the system. We found that the orbital accumulation originating from the OHE for the 1L-nanoribbon is approximately half that of a 2L-nanoribbon. Furthermore, while the OME can reach fairly high values in 1L-TMD nanoribbons, it vanishes in the 2L ones that preserve spatial inversion symmetry.The microscopic features that justify our findings are also discussed.

A relativistic relationship between parity-violating nuclear spin-rotation tensors and parity-violating NMR shielding tensors.

The nuclear-spin-dependent parity-violation contributions to the nuclear magnetic resonance shielding and nuclear spin-rotation tensors (σPV and MPV, respectively) are known to be formally related to one another in the non-relativistic regime. In this work, the polarization propagator formalism and the linear response within the elimination of small components model are used to show a new and more general relationship between them, which is valid within the relativistic framework. The full set of the zeroth- and first-order relativistic contributions to σPV and MPV are also given here for the first time, and these results are compared with previous findings. According to four-component relativistic calculations, the electronic spin-orbit effects are the most significant ones for the isotropic values of σPV and MPV in the H2X2 series of molecules (with X = O, S, Se, Te, and Po). When only scalar relativistic effects are taken into account, the non-relativistic relationship between σPV and MPV does hold. However, when the spin-orbit effects are taken into consideration, this old non-relativistic relationship breaks down, and therefore, the new one must be considered.