Independent Electron Approximation Research Articles

Real-space tight-binding model for twisted bilayer graphene based on mapped Wannier functions

Twisted multi-layer heterostructures have been considered a platform for studying highly correlated many-particle systems, hosting the emerging phenomena of correlation physics. Electronic structure calculations of such materials which mainly focused on Twisted Bilayer Graphene (TBG) in the framework of the independent-electron approximation, despite the complexity, accurately match the experimental results around the Fermi level. Here, we present a convenient real space π-bands tight-binding model to calculate the band structure of TBG based on the Wannier interlayer hopping parameters obtained from non-twisted bilayer graphene. Our approach is based on mapping hopping parameters onto the real space TBG interlayer couplings, using Radial Basis Function (RBF) interpolation method. This accurate mapping, naturally, transfers all the symmetries and orbital shape features of the bilayer graphene lattice to the TBG lattice and preserves coupling orientation dependencies in addition to distance dependencies. The importance of this fact is explained by showing the effect of the threefold rotation symmetry of AB′ interlayer coupling on the flat band of the TBG band structure. In addition, due to real space study, the model gives us a comprehensive and intuitive view of the role of each interlayer orbital coupling in the TBG band structure and the structural variation relative to twisting.

Ionization and electron capture in O6+ + He collisions at 0.86, 1.5, 1.94 a.u. velocities

Using the projectile-ion-recoil-ion coincidence method, relative cross sections for single-electron capture, single ionization, double-electron capture, transfer ionization and double ionization in collisions of multiply charged O6+ ions with helium atoms have been measured at 0.86, 1.5, 1.94 a.u. velocities. Calculations based on the semi-classical over-barrier model in the framework of independent electron approximation is employed to discuss various competing reaction mechanisms. These results are also compared with other experimental and theoretical results available in the velocity range considered.

Inelastic collisions of fast charged particles with atoms: Bethe asymptotic formulas and shell corrections

The relativistic plane-wave Born approximation is applied to the study of inelastic collisions of charged particles with atoms, by considering atomic wave functions calculated from the independent-electron approximation with the self-consistent Dirac-Hartree-Fock-Slater potential. A database of longitudinal and transverse generalized oscillator strengths (GOSs) has been computed by using accurate numerical methods for all the subshells of the ground-state configurations of the elements with atomic numbers from 1 (hydrogen) to 99 (einsteinium). The calculated GOS do not satisfy the Bethe sum rule; departures from the sum rule are in accordance with previous theoretical estimates. Asymptotic high-energy formulas for the total cross section, the stopping cross section, and the energy-straggling cross section are derived with proper account of the relativistic departure from the Bethe sum rule. The shell correction is calculated as the energy-dependent term that, when added to the asymptotic formula, reproduces the value of the atomic cross section calculated by integrating the energy-loss differential cross section. Shell corrections to the stopping cross section obtained from the present approach are presented and compared with previous estimates.

Quantum decoherence in high-order harmonic generation from solids

For the high-order harmonic generation (HHG) from solids, the dephasing process induced by many-body interactions has been discussed extensively in the studies of using the semiconductor Bloch equations (SBEs). However, the role of dephasing in solid HHG is always ignored in the simulations of using a time-dependent Schr\"odinger equation under the independent electron approximation. To solve this problem, we introduce the imaginary potential to phenomenologically depict the dephasing process in the solid HHG. Compared with the results of experiment and SBEs, the validity of this approach has been verified by the laser intensity- and wavelength-dependent HHG spectra. Diffusion of the quantum wave packet controls the time-frequency characteristic in solid HHG. To obtain semiclassical trajectories whose predictions are consistent with the quantum simulations, we propose an open-trajectory model by relaxing the zero displacement condition in the tunneling and recollision steps. In addition, the quantum decoherence adjusts the chirp of the emission time profile via modulating the coherent overlap between recombined wave packets, which further paves a way to generate an attosecond pulse from solids and probe the dephasing time via the high-harmonic spectroscopy.

Microreversibility and the statistics of currents in quantum transport.

For the statistics of currents in quantum transport, microreversibility is shown to provide a way to obtain the statistical cumulants at the order n+1 from the measurement of the cumulants at the order n or lower. This fundamental result is based on relations generalizing the fluctuation-dissipation theorem and the Onsager-Casimir reciprocal relations from linear toward nonlinear transport properties, as a consequence of the time-reversal symmetry of the underlying microscopic Hamiltonian dynamics. The method is demonstrated in detail in the case of multiterminal Aharonov-Bohm rings. Within the independent electron approximation, the cumulant generating function, which fully specifies the statistics of the nonequilibrium currents, is obtained from the scattering matrix of these circuits. The time-reversal symmetry relations are explicitly shown to express the cumulants at equilibrium up to the fourth order in terms of lower-order cumulants and their nonequilibrium responses in the presence of an external magnetic field.

Relativistic Calculation of the Nuclear Recoil Effect on the g Factor of the 2P3/2 State in Highly Charged B-like Ions

The nuclear recoil effect on the $^2 P_{3/2}$-state $g$ factor of B-like ions is calculated to first order in the electron-to-nucleus mass ratio $m/M$ in the range $Z=18$--$92$. The calculations are performed by means of the $1/Z$ perturbation theory. Within the independent-electron approximation, the one- and two-electron recoil contributions are evaluated to all orders in the parameter $\alpha Z$ by employing a fully relativistic approach. The interelectronic-interaction correction of first order in $1/Z$ is treated within the Breit approximation. Higher orders in $1/Z$ are partially taken into account by incorporating the screening potential into the zeroth-order Hamiltonian. The most accurate to date theoretical predictions for the nuclear recoil contribution to the bound-electron $g$ factor are obtained.

Nonlocal annihilation of Weyl fermions in correlated systems

Weyl semimetals (WSMs) are characterized by topologically stable pairs of nodal points in the band structure, that typically originate from splitting a degenerate Dirac point by breaking symmetries such as time reversal or inversion symmetry. Within the independent electron approximation, the transition between an insulating state and a WSM requires the local creation or annihilation of one or several pairs of Weyl nodes in reciprocal space. Here, we show that strong electron-electron interactions may qualitatively change this scenario. In particular, we reveal that the transition to a Weyl semi-metallic phase can become discontinuous, and, quite remarkably, pairs of Weyl nodes with a finite distance in momentum space suddenly appear or disappear in the spectral function. We associate this behavior to the buildup of strong many-body correlations in the topologically non-trivial regions, manifesting in dynamical fluctuations in the orbital channel. We also highlight the impact of electronic correlations on the Fermi arcs.

Релятивистский расчёт эффекта отдачи ядра для g-фактора состояния ^2P-=SUB=-3/2-=/SUB=- многозарядных бороподобных ионов

The nuclear recoil effect on the $^2 P_{3/2}$-state $g$ factor of B-like ions is calculated to first order in the electron-to-nucleus mass ratio $m/M$ in the range $Z=18$--$92$. The calculations are performed by means of the $1/Z$ perturbation theory. Within the independent-electron approximation, the one- and two-electron recoil contributions are evaluated to all orders in the parameter $\alpha Z$ by employing a fully relativistic approach. The interelectronic-interaction correction of first order in $1/Z$ is treated within the Breit approximation. Higher orders in $1/Z$ are partially taken into account by incorporating the screening potential into the zeroth-order Hamiltonian. The most accurate to date theoretical predictions for the nuclear recoil contribution to the bound-electron $g$ factor are obtained.

Excitation, ionization, neutralization and anionic production in collisions of C+, N+ and CnN+ (n = 1–3) with He atoms at 2.2 a.u. velocity; cross sections and dissociation branching ratios

We present measurements of absolute cross sections for projectile ionization and electron capture for C+, N+ and CnN+ (n = 1–3) projectiles impinging on He atoms with velocity v = 2.2 a.u. Single and multiple electron processes are considered, as well as projectile dissociative excitation in the case of incident molecular cations. The measurements are compared to Classical Trajectory Monte Carlo (CTMC) calculations for C+, N+ + He collisions in the framework of the independent electron approximation. CnN+ + He systems are described by means of the independent atom and electron (IAE) model which represents the molecule as a set of independent atoms. The impact parameter probabilities for excitation, ionization and electron transfer in C, C+, N–He collisions, underlying the IAE calculations, are also obtained by means of CTMC computations. A good agreement is generally found between measured and calculated cross sections, except for anionic production of C− and CnN−. The internal energy deposit due to electron excitation in CnN+ is also calculated with the IAE/CTMC model and compared to semi-empirical estimates based on either measured dissociation branching ratios for C2N+ and C3N+ (IdBarkach et al 2018 Mol. Astrophys. 12 25) or measured fragments kinetic energy release for CN+. Finally, measured dissociation branching ratios of excited CnN− and CnNQ+ species, with 1 ≤ n ≤3 and 0 ≤ Q ≤ 4, are reported.

Fully differential cross sections for ionization of by ion impact: classical and quantum effects

Single ionization of molecular ions by impact of bare ions is theoretically studied. Fully differential cross sections are calculated by employing the prior version of the continuum distorted wave-eikonal initial state model within an independent electron approximation. It is shown in this work that, under certain conditions there can exist a competition between classical and quantum mechanisms in the ionization reaction that gives rise to the suppression of characteristic classical structures, namely the binary and recoil peaks, from the ionization angular spectra. The existence of destructive quantum interferences due to the coherent emission of electrons from the neighbourhood of both molecular centres may be held as the responsible for the suppression of these classical signatures. Different behaviours are observed depending on whether the ground (gerade) or the first excited (ungerade) states of the target are analysed. Different values of the projectile nuclear charge and collision geometries are considered when calculating FDCS.

Single- and multiple-electron processes in water molecules colliding with proton beams

Single- and multiple-electron removal processes (ionization, capture and transfer-ionization) from water molecules by the impact of protons have been studied. A prior version of the three-body continuum distorted wave-eikonal initial state (3B-CDW-EIS) approximation within the independent electron approximation is used to calculate transition probabilities as a function of the impact parameter and consequently pure and net absolute cross sections for the collisions under consideration. A unitarization procedure is employed to avoid possible overestimation of the 3B-CDW-EIS single-particle impact parameter probabilities at intermediate collision energies. Multiple-electron transitions are determined using a statistical multinomial distribution. A critical analysis of the validity of this type of distribution for describing pure single-electron processes is presented. The results are compared with other theoretical calculations and available experimental data at impact energies from 50 keV to 5 MeV. New physical insights into the reactions studied are introduced.

Time-dependent Hartree-Fock study of electron-hole interaction effects on high-order harmonic generation from periodic crystals

We investigate the multielectron effects on high-harmonic generation from solid-state materials using the time-dependent Hartree-Fock theory. We find qualitative change in harmonic spectra, in particular, multiple-plateau formation at significantly lower laser intensities than within the independent-electron approximation. We reveal its origin in terms of interband polarization, i.e, electron-hole polarization, enabling interband excitation at remote crystal momenta via Coulomb potential.

Double differential cross sections for liquid water ionization by fast electron impact

In this work we study theoretically the single ionization of liquid water by impact of energetic electrons. A realistic description of the wavefunction for an isolated water molecule in the liquid phase is made by means of a Wannier orbital formalism. We develop a first order model within the framework of an independent electron approximation in which the relaxation of the target is not taken into account. The double differential cross sections are computed and compared with experimental data and theoretical calculations for gas phase.

Full-Potential Simulation of X-ray Raman Scattering Spectroscopy.

We present a new ab initio way to calculate X-ray Raman scattering spectra within the independent electron approximation. Our approach avoids any approximation about the shape of the used potential and leads to good agreement between experiment and theory. We show that the momentum transfer dependence in two typical cases, the F K-edge in LiF and the B and N K-edges in hexagonal BN, is well-reproduced. A more in-depth analysis of the electronic states and of the local atomic structure around the absorbing atoms is at hand.

Dissection of electron correlation in strong-field sequential double ionization using a classical model.

Recent experiments on strong-field sequential double ionization (SDI) have reported several observations which are regarded as evidence of electron correlation, querying the validity of the standard independent electron approximation for SDI. Here we theoretically study SDI with a classical ensemble model. The experimental results are well reproduced with this model. Back tracing of the ionization process shows that these results are ascribed to the subcycle ionization dynamics of the two electrons, not the evidences of the electron correlation in SDI. Thus, the previously reported observations are not enough to claim the breakdown of the independent electron approximation in SDI.

Anharmonic effects in atomic hydrogen: Superconductivity and lattice dynamical stability

We present first-principles calculations of metallic atomic hydrogen in the 400-600 GPa pressure range in a tetragonal structure with space group $I4_1/amd$, which is predicted to be its first atomic phase. Our calculations show a band structure close to the free-electron-like limit due to the high electronic kinetic energy induced by pressure. Bands are properly described even in the independent electron approximation fully neglecting the electron-electron interaction. Linear-response harmonic calculations show a dynamically stable phonon spectrum with marked Kohn anomalies. Even if the electron-electron interaction has a minor role in the electronic bands, the inclusion of electronic ex- change and correlation in the density response is essential to obtain a dynamically stable structure. Anharmonic effects, which are calculated within the stochastic self-consistent harmonic approxima- tion, harden high-energy optical modes and soften transverse acoustic modes up to a 20% in energy. Despite a large impact of anharmonicity has been predicted in several high-pressure hydrides, here the superconducting critical temperature is barely affected by anharmonicity, as it is lowered from its harmonic 318 K value only to 300 K at 500 GPa. We atribute the small impact of anharmoncity on superconductivity to the absence of softened optical modes and the fairly uniform distribution of the electron-phonon coupling among the vibrational modes.

Unconventional Magnetism and Band Gap Formation in LiFePO4: Consequence of Polyanion Induced Non-planarity.

Oxygen plays a critical role in strongly correlated transition metal oxides as crystal field effect is one of the key factors that determine the degree of localization of the valence d/f states. Based on the localization, a set of conventional mechanisms such as Mott-Hubbard, Charge-transfer and Slater were formulated to explain the antiferromagnetic and insulating (AFI) phenomena in many of these correlated systems. From the case study on LiFePO4, through density-functional calculations, we demonstrate that none of these mechanisms are strictly applicable to explain the AFI behavior when the transition metal oxides have polyanions such as (PO4)3−. The symmetry-lowering of the metal-oxygen complex, to stabilize the polyanion, creates an asymmetric crystal field for d/f states. In LiFePO4 this field creates completely non-degenerate Fe-d states which, with negligible p-d and d-d covalent interactions, become atomically localized to ensure a gap at the Fermi level. Due to large exchange splitting, high spin state is favored and an antiferromagnetic configuration is stabilized. For the prototype LiFePO4, independent electron approximation is good enough to obtain the AFI ground state. Inclusion of additional correlation measures like Hubbard U simply amplifies the gap and therefore LiFePO4 can be preferably called as weakly coupled Mott insulator.

Characteristics of ground state electronic structures of ionized atoms and rules of their orbital competitions

Ionized atoms widely exist in plasmas, and studies of properties of ionized atoms are the foundations of frontier science researches such as astrophysics and controlled nuclear fusions. For example, the information about the ground configurations of atoms is required for accurately calculating the physical quantities such as energy levels and dynamical processes. The configurations for different ionized atoms can be obtained with the photo-electron energy spectrum experiment, however it is very time-consuming to obtain so many data of all ions. Therefore the more economical theoretical study will be of great importance. As is well known, the configurations of neutral atoms can be determined according to Mendeleev order while those of highly ionized atoms are hydrogen-like due to the strong Coulombic potential of their nuclei. Then with the variations of ionization degree and atomic number along the periodic table, there would appear the interesting competitions between electronic orbitals. Although some theoretical results exist for ions 3 Z 118, 3 Ne 105 (where Z is the atomic number and Ne is the electron number), there are many errors in the results for highly ionized atoms. Therefore, the ground configurations of ionized atoms and their orbital competitions still deserve to be systematically studied. Based on the independent electron approximation, we calculate the energy levels of all possible competition configurations of all the neutral and ionized atoms in the extended periodic tables (2 Z 119) by Dirac-Slater method. Then the ground configurations are determined by calculating the chosen lowest total energy. The advantages of Dirac- Slater method are as follows. 1) It has been shown that the Dirac-Slater calculation is accurate enough for studying the ground properties of atoms, such as the 1st threshold, and that higher accuracy will be obtained for highly ionized atoms, because the electron correlation becomes less important. 2) Furthermore, with Dirac-Slater method we can obtain the localized self-consistent potential, thereby we can study the orbital competition rules for different atoms. Using the three of our designed atomic orbital competition graphs, all of our calculated ground configurations for over 7000 ionized atoms are conveniently expressed. We systematically summarize the rules of orbital competitions for different elements in different periods. We elucidate the mechanism of orbital competition (i.e., orbital collapsing) with the help of self-consistent atomic potential of ionized atoms. Also we compare the orbital competition rules for different periods of transition elements, the rare-earth and transuranium elements with the variation of the self-consistent filed for different periods. On this basis, we summarize the relationship between the orbital competitions and some bulk properties for some elements, such as the superconductivity, the optical properties, the mechanical strength, and the chemistry activities. We find that there exist some abnormal orbital competitions for some lowly ionized and neutral atoms which may lead to the unique bulk properties for the element. With the ground state electronic structures of ionized atoms, we can construct the basis of accurate quasi-complete configuration interaction (CI) calculations, and further accurately calculate the physical quantities like the energy levels, transition rates, collision cross section, etc. Therefore we can meet the requirements of scientific researches such as the analysis of high-power free-electron laser experiments and the accurate measurement of the mass of nuclei.

Theory and calculation of the atomic photoeffect

Abstract The so-called elementary theory of the atomic photoeffect is presented in a form that is suited for practical numerical calculation of subshell cross sections and angular distributions of emitted photoelectrons. Atomic states are described within the independent-electron approximation, with bound and free one-electron orbitals that are solutions of the Dirac equation with the Dirac–Hartree–Fock–Slater self-consistent potential of the ground-state configuration. Detailed derivations are given of subshell cross sections for both excitation to discrete bound levels and ionization. In the case of ionization, the cross section differential in the direction of the photoelectron is obtained for partially polarized photons, with the polarization specified by means of the Stokes parameters. The theoretical formulas have been implemented in a computer program named photacs that calculates tables of excitation and ionization cross sections for any element and subshell. Numerical calculations are practicable for excitations to final states with the principal quantum number up to about 20 and for ionization by photons with energy up to about 2 MeV. Elaborate extrapolation schemes for determining the subshell cross section for excitation to bound levels with larger principal quantum numbers and for ionization by photons with higher energies are described. The effect of the finite width of atomic energy levels is accounted for by convolving the calculated subshell cross-section with a Lorentzian profile.

Dynamic electron correlation in interactions of light with matter formulated inb⃗space

Scattering of beams of light and matter from multi-electron atomic targets is formulated in the position representation of quantum mechanics. This yields expressions for the probability amplitude, a(b), for a wide variety of processes. Here the spatial parameter b is the distance of closest approach of incoming particles traveling on a straight line with the center of the atomic target. The correlated probability amplitude, a(b), reduces to a relatively simple product of single electron probability amplitudes in the widely used independent electron approximation limit, where the correlation effects of the Coulomb interactions between the atomic electrons disappear. As an example in which a(b} has an explicit dependence on b}, we consider transversely finite vortex beams of twisted photons that lack the translational invariance of infinite plane-wave beams. Some experimental considerations and future applications are briefly considered.