Orbit-orbit Interaction Research Articles

Controllable orbital-angular-momentum Hall effect by engineering intrinsic orbit-orbit interaction.

We report both theoretically and experimentally a process of optical intrinsic orbit-orbit interaction with a vortex-antivortex structure nested in a freely propagating light field. The orbit-orbit interaction is originating from the coupling between different vortices and antivortices. Based on this process, we reveal the resultant controllable orbital-angular-momentum Hall effect by considering a typical structure, which comprises a vortex-antivortex pair and another vortex (or antivortex) as a controllable knob. The intrinsic Hall effect can be spatially manipulated by appropriately engineering the orbit-orbit interaction, namely arranging the initial distribution of these elements. This work can find interesting potential applications. For example, it provides an effective technique for controllable paired photon generation.

Scalar Breit interaction for molecular calculations.

Variational treatment of the Dirac-Coulomb-Gaunt or Dirac-Coulomb-Breit two-electron interaction at the Dirac-Hartree-Fock level is the starting point of high-accuracy four-component calculations of atomic and molecular systems. In this work, we introduce, for the first time, the scalar Hamiltonians derived from the Dirac-Coulomb-Gaunt and Dirac-Coulomb-Breit operators based on spin separation in the Pauli quaternion basis. While the widely used spin-free Dirac-Coulomb Hamiltonian includes only the direct Coulomb and exchange terms that resemble nonrelativistic two-electron interactions, the scalar Gaunt operator adds a scalar spin-spin term. The spin separation of the gauge operator gives rise to an additional scalar orbit-orbit interaction in the scalar Breit Hamiltonian. Benchmark calculations of Aun (n = 2-8) show that the scalar Dirac-Coulomb-Breit Hamiltonian can capture 99.99% of the total energy with only 10% of the computational cost when real-valued arithmetic is used, compared to the full Dirac-Coulomb-Breit Hamiltonian. The scalar relativistic formulation developed in this work lays the theoretical foundation for the development of high-accuracy, low-cost correlated variational relativistic many-body theory.

Packing-Shape Effects of Optical Properties in Amplified Spontaneous Emission through Dynamics of Orbit-Orbit Polarization Interaction in Hybrid Perovskite Quantum Dots Based on Self-Assembly.

This paper reports packing-shape effects of amplified spontaneous emission (ASE) through orbital polarization dynamics between light-emitting excitons by stacking perovskite (MAPbBr3) quantum dots (QDs sized between 10 nm and 14 nm) into rod-like and diamond-like aggregates. The rod-like packing shows a prolonged photoluminescence (PL) lifetime (184 ns) with 3 nm red-shifted peak (525 nm) as compared to the diamond-like packing (PL peak, 522 nm; lifetime, 19 ns). This indicates that the rod-like packing forms a stronger interaction between QDs with reduced surface-charged defects, leading to surface-to-inside property-tuning capability with an ASE. Interestingly, the ASE enabled by rod-like packing shows an orbit-orbit polarization interaction between light-emitting excitons, identified by linearly/circularly polarized pumping conditions. More importantly, the polarization dynamics is extended to the order of nanoseconds in the rod-like assembly, determined by the observation that within the ASE lifetime (2.54 ns) the rotating pumping beam polarization direction largely affects the coherent interaction between light-emitting excitons.

Room-Temperature Magnetic Field Effect on Excitonic Photoluminescence in Perovskite Nanocrystals.

Magnetic-field-enhanced spin-polarized electronic/optical properties in semiconductors are crucial for fabricating various spintronic devices. However, this spin polarization is governed by weak spin exchange interactions and easily randomized by thermal fluctuations; therefore, it is only produced at cryogenic temperatures, which severely limits the applications. Herein, a room-temperature intrinsic magnetic field effect (MFE) on excitonic photoluminescence is achieved in CsPbX3 :Mn (X = Cl, Br) perovskite nanocrystals. Through moderate Mn doping, the MFE is enhanced by exciton-Mn interactions, and through partial Br substitution, the MFE is stabilized at room temperature by exciton orbital ordering. The orbital ordering significantly enhances the g-factor difference between electrons and holes, which is evidenced by a parallel orbit-orbit interaction among excitons generated by circular polarized laser excitation. This study provides a clear avenue for engineering spintronic materials based on orbital interactions in perovskites.

Anharmonicity in light nuclei near drip lines

Single-particle energy levels of nucleons moving in an anisotropic harmonic oscillator potential along with a spin-orbit and an orbit-orbit interaction have been calculated. The model proposed herein incorporates shapes generated by higher multipolar anisotropies other than the quadruple one. The gaps among the energy levels are strongly dependent on the degree of anisotropy and hence, affect the nucleonic separation energies. For large anisotropies, this characteristic disturbs the occurrences of the usual magic numbers and the sequential ordering of the shells characterized by principal quantum number, N, associated with the elementary shell model. For large asymmetries, the states characterized by higher N, may come down and lie below the energies of the states with lower N and vice versa. This feature of the model provides a natural explanation of intruder states or the island of inversion observed experimentally. For certain choices of the parameters, the large gaps in single nucleonic separation energies could occur at neutron numbers, 10,18,30, and 32 as observed, respectively, in 20Ne, 28Ne, 52Ti, and 54Ti. For neutron as well as proton number 14, the magnitude of this energy gap depends strongly on the choice of the strength of the spin-orbit and orbit-orbit terms. The model provides a simple understanding of the observed fact that some nuclei with proton or neutron number 14 sometimes exhibit this gap but not others. It also provides an interesting insight of having a low-laying (1/2 − ) state in 7He, and confirms the ground state spin and parity of 11Be to be (1/2+) and those of 9He to be (1/2+), both of which have been contentious. This investigation indicated the density distribution, i.e., the shapes of many of nuclei near drip line to be anisotropic having a symmetry about their body-fixed z-axis.

External Field-Tunable Internal Orbit-Orbit Interaction in Flexible Perovskites.

In hybrid metal halide perovskites, electrons carry both orbital and spin momenta through s-p wave function hybridization. This leads to a hypothesis that the orbit-orbit interaction between excitons can occur through orbital magnetic dipoles forming short-range interaction or through orbital polarizations forming long-range interaction to influence optoelectronic properties. This Letter reports an interesting phenomenon: the orbit-orbit interaction can be electrically switched between orbital magnetic dipoles and orbital polarizations in a flexible perovskite (MAPbI3-xClx) solar cell by scanning an external voltage between forward and reverse biases (0.2 and -0.2 V). Essentially, this phenomenon presents an external mechanism for electrically controlling the internal orbit-orbit interaction in hybrid perovskites. It was further observed that this bias-switchable orbit-orbit interaction is sensitive to temperature, becoming negligible when the temperature is decreased from 300 to 250 K. This observation indicates that the mobile ions driven by an external electrical field provide an intrinsic mechanism for electrically switching the orbit-orbit interaction through polarization and spin parameters while applying an external voltage between forward and reverse biases. These results provide a comprehensive understanding of tuning the orbit-orbit interaction in flexible perovskites toward developing orbitronic actions.

Doping Induced Orbit-Orbit Interaction between Excitons While Enhancing Photovoltaic Performance in Tin Perovskite Solar Cells.

Doping has been used as a common method to improve photovoltaic performance in perovskite solar cells (PSCs). This paper reports a new phenomenon that the SnF2 doping can largely increase the exciton-exciton interaction through orbital magnetic dipoles toward increasing dissociation probabilities in lead-free FASnI2Br PSCs. Essentially, when orbit-orbit interaction between excitons occurs, linearly and circularly polarized photoexcitations can inevitably generate different photocurrents, giving rise to a ΔJsc phenomenon. Here, it is found that, when SnF2 doping is used to boost photovoltaic efficiency to 7.61%, the orbit-orbit interaction is increased by a factor of 2.2, shown as the ΔJsc changed from 1.21% to 0.55%. Simultaneously, magnetic field effects of Jsc indicate that increasing orbit-orbit interaction leads to an increase on the spin-orbital coupling in Sn perovskites (FASnI2Br) upon SnF2 doping. This presents a new doping effect occurring in the Sn perovskite solar cell toward enhancing photovoltaic efficiency.

Extremely Long Spin Lifetime of Light-Emitting States in Quasi-2D Perovskites through Orbit-Orbit Interaction.

This paper reports an extremely long spin relaxation time of optically polarized light-emitting states at room temperature in quasi-2D perovskites [(PEA)2(MA)4Pb5Br16 with n = 5], when the long-range orbit-orbit interaction between excited states is developed through orbital polarization. Our studies found that the quasi-2D perovskite [(PEA)2(MA)4Pb5Br16 with n = 5] demonstrates a long-range orbit-orbit interaction between excited states to conserve the spins of optically polarized light-emitting states, identified by the positive change on photoluminescence intensity (+ΔPL) in steady state upon switching the photoexcitation from linear to circular polarization. Meanwhile, the PL circular polarization (σ+σ+ - σ+σ-) can maintain in nanosecond under fixed photoexcitation (σ+). In contrast, the 2D/3D mixed perovskite (n > 5) shows a short-range orbit-orbit interaction between excited states through orbital magnetic dipoles, identified by the -ΔPL by switching from linear to circular photoexcitation. At the same time, the spin lifetime of light-emitting states becomes undetectable.

Exploring Orbit-Orbit Interaction in Relationship to Photoluminescence Quantum Efficiency in Perovskite Quantum Dots through Rashba Effect.

This study demonstrates the influence of the orbit-orbit interaction on the photoluminescence quantum efficiency (PLQE) of metal halide perovskite quantum dots (QDs) through the Rashba effect. The orbit-orbit interaction between excitons was characterized by using the minimal excitation intensity required to generate a photoluminescence difference (ΔPL) between linearly and circularly polarized photoexcitations. It was observed that changing the surface functionalization from PFOA-OA to PFSH-OAm and OA can largely increase the minimal excitation intensity for generating ΔPL. This indicates that the orbit-orbit interaction is essentially decreased in CsPbBr1I2 QDs with surface functionalization. Simultaneously, the PLQE is increased from 39% to 59 and 72% in CsPbBr1I2 QDs upon surface functionalization. Furthermore, the PL lifetime is decreased with increasing the PLQE in CsPbBr1I2 QDs upon surface functionalization. This phenomenon implies that decreasing the orbit-orbit interaction can essentially weaken the Rashba effect and consequently reduce the disallowed transitions, leading to an enhancement in the PLQE in perovskite QDs.

Mechanically tuning spin-orbit coupling effects in organic-inorganic hybrid perovskites

Organic-inorganic hybrid perovskites have potential applications in flexible electronics based on solution-processing polycrystalline thin-films. This article reports an emerging phenomenon: mechanically tunable spin-orbit coupling (SOC) in flexible perovskite solar cells under elastic bending. Polarization-dependent photocurrent studies show that mechanical bending increases the orbit-orbit interaction, shown as an enhanced SOC, and consequently boosting the intersystem crossing to convert optically generated bright states (which are allowed to recombine) into dark states (which are forbidden to recombine) in flexible perovskite solar cells [PET/ITO/PEDOT:PSS/MAPbI3-xClx/PCBM/PEI/Ag]. Simultaneously, the photocurrent is increased from 15.39 mA/cm2 to 22.0 mA/cm2 by 43% upon such elastic bending with the curvature radius of 4.2 mm. It is further found that introducing mechanical stress leads to both grain boundary interaction and grain deformation shown as the decreased defects at grain boundaries through thermal admittance spectroscopy and the elastic strain verified by X-ray diffraction measurement. The capacitance-frequency characteristics indicate that applying this mechanical stress causes an increase on the bulk polarization by introducing grain boundary interaction and grain deformation. This provides necessary condition to realize mechanically tunable SOC effects in perovskites via electric-magnetic coupling. Essentially, mechanically tunable SOC effects present new mechanisms to control the optoelectronic properties in flexible perovskite electronic devices.

Two-Photon Up-Conversion Photoluminescence Realized through Spatially Extended Gap States in Quasi-2D Perovskite Films.

A new approach to generate a two-photon up-conversion photoluminescence (PL) by directly exciting the gap states with continuous-wave (CW) infrared photoexcitation in solution-processing quasi-2D perovskite films [(PEA)2 (MA)4 Pb5 Br16 with n = 5] is reported. Specifically, a visible PL peaked at 520 nm is observed with the quadratic power dependence by exciting the gap states with CW 980 nm laser excitation, indicating a two-photon up-conversion PL occurring in quasi-2D perovskite films. Decreasing the gap states by reducing the n value leads to a dramatic decrease in the two-photon up-conversion PL signal. This confirms that the gap states are indeed responsible for generating the two-photon up-conversion PL in quasi-2D perovskites. Furthermore, mechanical scratching indicates that the different-n-value nanoplates are essentially uniformly formed in the quasi-2D perovskite films toward generating multi-photon up-conversion light emission. More importantly, the two-photon up-conversion PL is found to be sensitive to an external magnetic field, indicating that the gap states are essentially formed as spatially extended states ready for multi-photon excitation. Polarization-dependent up-conversion PL studies reveal that the gap states experience the orbit-orbit interaction through Coulomb polarization to form spatially extended states toward developing multi-photon up-conversion light emission in quasi-2D perovskites.

Practical theoretical expressions for ions embedded in Debye and quantum plasmas

An accurate theoretical expression is proposed for the atomic structure under external confinement. The analysis is based on the tensor expression for the Breit-Pauli Hamiltonian in which the Racah wave functions are expanded in terms of the linear combinations of the multi-Slater wave functions. The variables are separated into radial and angular parts, where the variational parameters in the trial wave functions are obtained by solving the radial Schrödinger equation and the expressions of the angular part are worked out using an irreducible theory of complex system. Relativistic corrections are derived directly, which are treated as a sum of five terms: mass correction, one-body Darwin correction, two-body Darwin correction, spin-spin contact interaction correction, and orbit-orbit interaction correction. Energies and radiative decay rates of Be-like Fe22+ and Kr32+ ions in the presence of two kinds of plasma environments are presented for demonstration purposes, one is the Debye plasma which is described by a standard Debye-Hückel potential and the other is the quantum plasma which is treated under an exponential cosine screened Coulomb potential. Independent self-consistent calculations within the fully relativistic frame by incorporating the above two potentials are also performed using the Flexible Atomic Code to verify the validity of the proposed expressions. Results are given over a wide range of screening lengths. Relativistic effects in energy spectra are studied for the first time and are found to be rather important, especially in the high-Z system. Comparisons between our two sets of results and other theoretical predictions when available are made. Some behavior of the respective properties with respect to the plasma shielding strength is discussed. The present study should be beneficial for the analysis of spectra in astrophysical and fusion plasmas.

Influence of plasma shielding effect on ground state and excited state energies of Ar<sup>16+</sup>

A systematical knowledge of the atomic properties in plasma is of great interest for various research areas, such as the explanation of the X-ray radiation from universe, plasma diagnostics, extreme ultraviolet (EUV) and X-ray sources and so on. Among these researches, the detailed information about how the plasma influences the atomic energy level and transition spectrum are crucial for understanding the X-ray emission mechanism and the state of plasma. An analytic calculation method of treating the non-relativistic energy and its relativistic corrections for the multi-electron atoms embedded in weakly coupled plasma is developed based on the Rayleigh-Ritz variation method. The systematical investigations are performed for the ground state 1s<sup>2</sup> <sup>1</sup>S, single excited states 1sns <sup>1,2</sup>S (<i>n</i> = 2−5), 1s<i>n</i>p <sup>1,3</sup>P (<i>n</i> = 2−5) and double excited state 2s2p <sup>1</sup>P of Ar<sup>16+</sup> ion in weak coupled plasma. The analytic formulas for calculating the non-relativistic energy and its relativistic correction energy are derived, which include mass correction, one and two-body Darwin correction, spin-spin contact interaction and orbit-orbit interaction. All the angular integration spin sums involved in the problem are worked out explicitly by using the irreducible theory. The influence of plasma on non-relativistic energy and relativistic correction energy are discussed. The results show that the mass correction and the one-body Darwin correction are the main ones among the terms of relativistic correction, and are three orders of magnitude greater than the other relativistic terms. The plasma shielding effect mainly affects the non-relativistic energy, and has little effect on the relativistic correction. At the same time, it has a more significant selectivity for the electronic configuration. Further research shows that the influence of plasma on the energy of the outer shell electron is greater than that of the inner shell electron. With the increase of the plasma shielding parameters, the outer shell electron extends outward, and the higher the excited state, the greater the degree of extension is. This work should be useful for astrophysical applications where such a plasma environment exists.

Magnetic orbit-orbit interaction involving electrons and the nucleus orbiting around the center of mass in 1S and 1P Rydberg states of helium. Finite-nuclear-mass calculations with explicitly correlated Gaussian functions.

An finite-nuclear-mass (FNM) approach is employed to describe the magnetic orbit-orbit interaction of the electrons and the nucleus orbiting around the center of mass of the helium atom in 1S and 1P Rydberg states. The calculations are performed using explicitly correlated Gaussian functions to expand the states’ wave functions. The non-linear parameters of the Gaussians are optimized using a variational approach employing the analytical energy gradient. An FNM and INM (infinite-nuclear-mass) approaches are used in the optimization and compared.

Relativistic effects on the energy levels and radiative properties of He-like ions immersed in Debye plasmas

Systematic investigations are performed for the energy levels and radiative properties for selected He-like C4+, Ne8+, Ar16+, and Kr34+ ions embedded in weakly coupled plasmas. For the conditions in which the Coulomb coupling parameter is small, the standard Debye model is adopted to describe the plasma screening effects. Within the relativistic framework, the modified version of the Flexible Atomic Code computations is carried out by considering a Debye-Hückel potential, in which the plasma screening is taken into account for both the electron-nucleus and electron-electron (e-e) interactions. An independent calculation for various Debye lengths is also presented using the multiconfiguration Dirac-Fock method for comparison purposes. For the nonrelativistic treatment, the analytical solution of the Schrödinger equation with the Debye screened potential is proposed. The variation method is developed with Slater wave function as a trial wave function that contains the variational parameters. An exact analytical expression of relativistic corrections such as the mass-velocity correction, the one/two-body Darwin correction, the spin-spin contact interaction correction, and the orbit-orbit interaction correction is derived. Differences among our three kinds of calculated energy levels and transition properties are analyzed in terms of the nuclear charge and/or the Debye length. Systematic trend is observed for all the properties under study with respect to increased screening. The influence of relativistic effects is also investigated in detail and found to play an important role in these systems. Our results are compared with available results from other theoretical calculations and the experimental values in the literature, and a good agreement is achieved. This work should be useful for astrophysical applications where such plasma environments exist.

Construction of Breit quark potential in coordinate space and mass splits of meson and quarkonium

Construction of a valid interaction potential function between quarks is a crucial issue in hadronic physics and also one of the frontier issues. Non-relativistic Breit potential is a common model to describe the interaction between quarks. It is used to successfully calculate the bound states of quarks and quark scatterings. These spur people to improve it. As is well known, the full Breit potential function, which includes the color-Coulomb term, the mass term, the orbit-orbit interaction term, the spin-spin interaction term, the spin-orbit interaction term, the tensor force term, and the constant term, contains singularity factors. How to eliminate the singularity factors is the most urgent task for developing Breit potential model. In this paper, we carry out a replacement method to eliminate the singularity factors in the full Breit quark potential function in coordinate space. Except for the color-Coulomb term and the constant term, remaining terms in the Breit quark potential function are all reconstructed. The replacement of (r) 3 e-r/8 is applied to the mass term and the spin-spin interaction term. The replacement of 1/r (1-e-r)/r is applied to the obit-obit interaction term. The replacement of 1/r3[1-(1+r)e-r]/r3 is applied to the spin-obit interaction term and the tensor force term. We calculate mass splits of heavy mesons and quarkonium species by using the reconstructed potential function and test the validity of the reconstructed potential function. The screening mass used in the calculations is not a simple constant but a variable relating to the quark mass mi and mj. It is found that the simple screening-mass expression cannot give the accurate value of B-meson mass, although it may give the mass splits of light mesons. However, the calculated results of the mass splits of the light mesons -, the heavy mesons, c-J/, b-(1s), c0-c2, etc., are highly consistent with the experimental data only when the screening mass is taken to be the Laurent series, =c-3(a+0.512)-3+ c-2(a+0.512)2 +c-1(a+0.512)-1+c0+c1(a+0.512) with respect to the average quark mass a=(mi+mj)/2. In this case, the mass accuracy of other mesons, especially the six D mesons, is improved significantly. Our calculated results indicate that a valid quark potential model, which gives not only the mass values of light mesons accurately but also the mass splits of heavy quarkonium species, is thus constructed in this paper.

Orbit-orbit relativistic correction calculated with all-electron molecular explicitly correlated Gaussians.

An algorithm for calculating the first-order electronic orbit-orbit magnetic interaction correction for an electronic wave function expanded in terms of all-electron explicitly correlated molecular Gaussian (ECG) functions with shifted centers is derived and implemented. The algorithm is tested in calculations concerning the H2 molecule. It is also applied in calculations for LiH and H3+ molecular systems. The implementation completes our work on the leading relativistic correction for ECGs and paves the way for very accurate ECG calculations of ground and excited potential energy surfaces (PESs) of small molecules with two and more nuclei and two and more electrons, such as HeH-, H3+, HeH2+, and LiH2+. The PESs will be used to determine rovibrational spectra of the systems.

Relativistic Electron Vortex Beams in a Laser Field.

The orbital angular momentum Hall effect and the spin Hall effect of electron vortex beams (EVBs) have been studied for the EVBs interacting with a laser field. In the scenario of a paraxial beam, the cumulative effect of the orbit-orbit interaction of EVBs and laser fields drives the orbital Hall effect, which in turn produces a shift of the center of the beam from that of the field-free case towards the polarization axis of the photons. In addition, for nonparaxial beams one can also perceive a similar shift of the center of the beam owing to the spin Hall effect involving spin-orbit interaction. Our analysis suggests that the shift in the paraxial beams will always be larger than that in the nonparaxial beams.

Orbit-orbit interaction and photonic orbital Hall effect in reflection of a light beam

We examine the orbit—orbit interaction when a paraxial beam with intrinsic orbital angular momentum (IOAM) reflects at an air—glass interface. The orbital-dependent splitting of the beam intensity distribution arises due to the interaction between IOAM and extrinsic orbital angular momentum (EOAM). In addition, we find that the beam centroid shows an orbital-dependent rotation when seen along the propagation axis. However, the motion of the beam centroid related to the orbit—orbit interaction undergoes a straight line trajectory with a small angle inclining from the propagation axis. Similar to a previously developed spin-dependent splitting in the photonic spin Hall effect, the orbital-dependent splitting could lead to the photonic orbital Hall effect.

Excited-state energies and fine structure of highly charged lithiumlike ions

The full-core-plus-correlation method (FCPC) is extended to calculate the energies and fine structures of 1${s}^{2}nd$ and 1${s}^{2}nf$ ($n\ensuremath{\le}5$) states for the lithiumlike systems with high nuclear charge from $Z$ $=$ 41 to 50. In calculating energy, the higher-order relativistic contribution is estimated under a hydrogenic approximation. The nonrelativistic energies and wave functions are calculated by the Rayleigh-Ritz method. The mass polarization and the relativistic corrections including the kinetic energy correction, the Darwin term, the electron-electron contact term, and the orbit-orbit interaction are calculated perturbatively as the first-order correction. The quantum-electrodynamics contributions to the energy and to the fine-structure splitting are estimated by using the effective nuclear charge formula. The excited energies, the fine structures, and other relevant term energies are given and compared with the data available in the literature.