Long-range coulomb interaction of electrons of 4f orbitals in impurity centers Yb3+: KZnF3, CsCaF3, and Sm3+: CaF2

Expressions for calculating the matrix elements of the Coulomb interaction of f electrons of the isolated ion with an infinite crystal lattice have been obtained. The contribution of this interaction to the parameters of the crystal field in impurity centers Yb³⁺: KZnF₃, CsCaF₃, and Sm³⁺: CaF₂ has been calculated.     

Electrostatic model of band-gap renormalization and the photoluminescence line shape in a GaAs/AlGaAs two-dimensional layer at a high excitation level

An electrostatic model for calculating the band-gap renormalization in a two-dimensional (2D) semiconductor layer (quantum well) due to the Coulomb interaction between nonequilibrium charge carriers has been proposed. Consideration is given only to the first quantum-well energy levels for electrons and heavy holes. The exchange and correlation energies are calculated for the first time taking into account the charge-carrier potential energyfluctuations created by electrons and holes along the 2D layer. A relationship for the screened Coulomb potential along the 2D layer is derived, which, within the extremely narrow quantum-well approximation, transforms into the known expression. The band-gap renormalization and the photoluminescence line shape for the GaAs 2D layer in an Al_xGa_1?x As matrix are computed depending on the concentration of nonequilibrium electrons and holes. The calculated band-gap renormalization is in agreement with the available experimental data at a high photoexcitation of the quantum well when the electrons and holes form the 2D plasma.     

Charge-transfer transitions and optical spectra of chromites

Specific features of charge-transfer states and charge-transfer transitions of the O_2p → Cr_3d type in octahedral complexes (CrO₆)^9? have been considered in the cluster approximation. Reduced matrix elements of the electric-dipole moment operator on many-electron wave functions, which are the initial and final states for charge-transfer transitions, are calculated. The results are parameterized, and the relative intensities of different allowed charge-transfer transitions in the absence of mixing of different charge-transfer configurations with identical symmetry are calculated. This mixing is taken into account within the Tanabe-Sugano theory, and the true energies and intensities of many-electron charge-transfer transitions are obtained. The Coulomb interaction between 2p electrons of O^2? ligands and 3d electrons of the central Cr³⁺ ion in (CrO₆)^9? cluster is considered. The influence of this interaction on the optical spectra is found to be insignificant. Simulation of the optical spectra of chromium oxides has shown the presence of a band of complex charge-transfer transitions composed of 33 lines with a total width of about 8 eV. The model spectrum is in adequate agreement with the experimental data, which indicates limited applicability of the widespread view that charge-transfer transition spectra have a simple structure.     

Tc of superconducting alloys with narrow energy bands

The vertex equation for a Cooper pair is solved for T_c of an A—B alloy, assuming a single-site interaction between electrons. The result depends on the partial densities of state N_A(O), N_B(O), the intra-atomic Coulomb repulsions, and the attractive interaction which contains the normal-mode density g(z) and the matrix elements of the ion-potential gradients between two electrons at one and the same site.     

Electronic structure and magnetism of YbRhSn

The electronic band structure of YbRhSn has been calculated using the self-consistent full potential nonorthogonal local orbital minimum basis scheme based on the density functional theory. We investigated the electronic structure with the spin-orbit interaction and on-site Coulomb potential for the Yb-derived 4f orbitals to obtain the correct ground state of YbRhSn. The exchange interaction between local f electrons and conduction electrons play an important role in the heavy fermion characters of them. The fully relativistic band structure scheme shows that spin-orbit coupling splits the 4f states into two manifolds, the 4f_7/2 and the 4f_5/2 multiplet.     

Pressure induced phase transition in rare earth mono-antimonides

Pressure induced structural phase transition of mono-antimonides of lanthanum, cerium, praseodymium and neodymium (LnSb, Ln=La, Ce, Pr and Nd) has been studied theoretically using an inter-ionic potential with modified ionic charge which parametrically includes the effect of Coulomb screening by the delocalized f electrons of rare earth (RE) ion. The anomalous structural properties of these compounds have been interpreted in terms of the hybridization of f electrons with the conduction band and strong mixing of f states of Ln ion with the p orbital of neighbouring antimonide ion. All the four compounds are found to undergo from their initial NaCl (B₁) phase to body centered tetragonal (BCT) phase at high pressure and agree well with the experimental results. The body centered tetragonal phase is viewed as distorted CsCl structure and is highly anisotropic with c/a=0.82. The transition pressure of LnSb compounds is observed to increase with decreasing lattice constant in NaCl phase. The nature of bonds between the ions is predicted by simulating the ion-ion (Ln-Ln and Ln-Sb) distances at high pressure. The calculated values of elastic constants are also reported.     

Electronic structure and magnetism of CeCoGe3

The electronic band structure of CeCoGe₃ has been calculated using the self-consistent full potential nonorthogonal local orbital minimum basis scheme based on density functional theory. We investigated the electronic structure with the spin-orbit interaction and on-site Coulomb potential for the Ce-derived 4f orbitals to obtain the correct ground state of CeCoGe₃. The exchange interaction between local f electrons and conduction electrons play an important role in their heavy fermion characters. The fully relativistic band structure scheme shows that spin-orbit coupling splits the 4f states into two manifolds, the 4f_7/2 and the 4f_5/2 multiplets.     

First-principles calculation of the energy of compressed calcium

The energy of a calcium crystal with a simple cubic lattice as a function of the ratio (t/U) between two internal parameters of the Hubbard model has been calculated using the Hubbard model for the s bands, equations of motion, and direct algebraic method. The electronic spectra have been calculated for the 4s band of the crystal in two principal symmetry directions of the first Brillouin zone. The calculations have been performed at temperatures T ₁ = 0 K and T ₂ = 1000 K. All calculations have been carried out for different interaction energies U of s electrons, one angle, and their different concentrations n in the range 0 ≤ n ≤ 2. The calculations have demonstrated that the dependences of the energy and electronic spectra in this compressed state are very smooth. The occupation of the Ca 4s band is in good agreement with the results of the pioneering calculations of compressed Ca (and a number of other metals), which were carried out by Gandel’man and his colleagues in the Wigner-Seitz spherical cell approximation. It has been shown that the performed analysis accurately reproduces the data obtained on the superconductivity in terms of the Bardeen-Cooper-Schrieffer theory if the 4s band is half-occupied.     

Unified calculations of the optical and electron paramagnetic resonance spectral data for Ce ion in Y3Ga5O12 crystal

Seven crystal field energy levels (obtained from the optical spectra) and three g factors g_x, g_y and g_z (obtained from electron paramagnetic resonance (EPR) spectra) for Ce³⁺ ion in Y₃Ga₅O₁₂ crystal are calculated together by diagonalizing a complete energy matrix. The Hamiltonian of this energy matrix includes all the interactions for 4f¹ ion Ce³⁺ in rhombic crystal field and under an external magnetic field, and so the optical and EPR data can be studied in a unified way. The calculated crystal field energy levels are in better agreement with the experimental values than the calculated values in the previous paper, and the g factors (which have not been calculated previously) are explained reasonably. The results are discussed.     

EPR,ENDOR and optical spectroscopy of Yb3+ ion in KZnF3 single crystals

The paramagnetic center of tetragonal symmetry formed by the Yb³⁺ ion in the KZnF₃ crystal has been studied using methods of EPR, ENDOR and optical spectroscopy. The location of the impurity ion and the structural model of the complex differing from the model of the Yb³⁺ center in KMgF₃ have been established. The empirical scheme of the energy levels of the Yb³⁺ ion has been found. The parameters of its interaction with the crystal electrostatic field and the hyperfine interaction with ligands of the nearest environment have been determined. The parameters of the crystal field were used for the analysis of the distortions of the crystal lattice in the vicinity of Yb³⁺. The parameters of the transferred hyperfine interaction have been calculated for the distances between Yb³⁺ and F⁻ ions of the nearest environment obtained taking into account the found distortions. They are in good agreement with the experimental values.     

The influence of Coulomb interaction on transport through mesoscopic two-barrier structures

We investigate the influence of the Coulomb interaction on the energy spectrum of a finite number of electrons in a geometrically confined quantum mechanical system. The spectrum is calculated numerically using the Slater determinants of the one-electron states as basis set. It is found to be dominated by the Coulomb repulsion when the system is large. Coulomb and exchange matrix elements for a given combination of four one-electron states are of the same order of magnitude. As a consequence, the energy difference between the ground states of the (N+1)- and theN-electron system is an order of magnitude smaller than each of the matrix elements, although being much larger than the separation of the one-electron energy levels. We discuss the importance of the interaction effects for the explanation of the recently observed resonant behavior of the electronic transport through quantum dots.     

Electronic Structure of Amorphous SiO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> with Variable Composition

The heights of barriers for the injection of electrons and holes from silicon in SiO_x have been calculated in the tight binding approximation without any fitting parameters. The dependence of the electronic structure of silicon-enriched amorphous silicon oxide SiO_x on the degree of enrichment has been found. The calculations have been performed with the parameterization of the matrix elements of the tight binding Hamiltonian proposed in our previous work. This parameter involves a change in the localization region of valence electrons of an insulated atom at its introduction into a solid. It has been shown that the inclusion of this change makes it possible to calculate the electronic structure without fitting parameters using the parameters of individual atoms as initial data. This circumstance allows the calculation in the absolute energy scale with zero corresponding to the energy of the electron in vacuum.     

Orbital degrees of freedom and electron correlation in optical absorption of metallic LaSrMnO

The optical absorption in ferromagnetic metal La_1-xSr_xMnO₃ is anomalous; it has a wide-range absorption up to about 1 eV even at zero temperature. Since 3d electrons in La_1-xSr_xMnO₃ partially fill doubly degenerate e_g orbitals, the orbital degrees of freedom are crucial to understand this metallic system. We argue that the interband transition within e_g orbitals is important in the optical absorption. The optical spectrum is modified also by the inter-orbital Coulomb interaction. We have examined perturbatively the effect of the Coulomb interaction on the spectrum. Available experiments are discussed by comparing with the present results. Received: 13 February 1998 / Accepted: 17 March 1998     

Dependence of electrical and magnetic properties of the AuCu-1 alloy on its atomic ordering

Electrical resistivity and magnetic susceptibility studies have shown that atomic ordering in theα ₁ phase of the AuCu-1 alloy is accompanied by a decrease in the Fermi energy, in the Debye characteristic temperature, and in the Young modulus. The behavior of conduction electrons in the ordered AuCu-1 alloy is appreciably affected by the interaction of such electrons with ions in the crystal lattice.     

Some dynamical properties of a two-dimensional Wigner crystal

Results for the static part of the ground state energy of the square and hexagonal two-dimensional Wigner lattices are given. The hexagonal lattice has the lower energy. Phonon dispersion curves and the vibrational zeropoint energy are calculated for the hexagonal lattice. The dielectric susceptibility tensor of a two-dimensional Wigner crystal χ_αβ(q) has been determined in the long wavelength limit in the presence of a static magnetic field perpendicular to the crystal, and explicit expressions have been obtained for the hexagonal lattice. Applying the analysis developed by Chiu and Quinn, the results for the susceptibility have been used to obtain the dispersion relation for the plasma oscillations in the electron crystal on the assumption that the crystal is embedded in a dielectric medium. The dispersion curves have been calculated for differing magnitudes of the applied magnetic field.     

The electronic structure of CuCl: An “ab initio” Hartree-Fock SCF-MO study of the CuCl43− cluster

Results from restricted Hartree-Fock SCF-MO calculations on the CuCl₄^3? cluster occurring in solid CuCl are reported. The chemical bonding is discussed on the basis of a population analysis of the ground state orbitals. Calculations on the first ionized states show the Cu 3d electrons to be less tightly bound than the Cl 3p electrons in contrast to Koopmans' theorem predictions and in agreement with experiment. The high degree of localization of the 3d hole orbitals obtained is in conflict with earlier estimates of d-bond covalency. It is suggested that the “Ham effect” rather than covalency is responsible for the reduced spin orbit splitting that can be deduced from the observed exciton absorption. The potential surface for a Cu⁺ ion moving in the field of neighbouring Cl^? ions, has been determined from calculations on the CuCl₄^3? cluster in which the metal ion has been displaced towards a face, an edge or a vertex of the surrounding tetrahedron. The vibration frequency and the activation energy for the diffusion of Cu⁺ ions obtained are in fair agreement with the experimental data. These results support the viewpoint that the anomalous change in scattering intensity with temperature observed in X-ray and neutron diffraction studies is due to the presence of a substantial fraction of the Cu⁺ ions on interstitial lattice sites.     

Interpretation of the optical and EPR spectra of the Cr<Superscript>3+</Superscript> ion in a lithium niobate crystal

The optical and EPR spectra of the Cr³⁺ γ-center in a lithium niobate crystal are interpreted, and the energy levels of the ground-state spin quadruplet and all the experimentally revealed doublet states are described. The parameters of the Coulomb Hamiltonian for the spin-orbit interaction of electrons and their interaction with an electrostatic field of the crystal are determined. It is found that the crystal field acting on the paramagnetic ion is relatively strong and has trigonal symmetry. The Cr³⁺ ion embedded in the crystal is characterized by considerable changes in the interactions associated with the excited configurations.     

Lattice dynamics of LaMnO3: Coupling of the lattice and orbital degrees of freedom

The lattice dynamics of regular LaMnO₃ is calculated within a shell model with pairwise interionic interaction potentials and with a Jahn-Teller (JT) contribution included into the energy and dynamic matrix of the crystal. A correlation is made between Raman spectral lines and lattice vibrations. The positions of some lines in the Raman spectrum are found to depend heavily on the linear JT coupling constant V _e . The effect of the JT coupling on the phonon density of states of LaMnO₃ is investigated.     

Electronic structure and magnetic susceptibility of monoclinic α-plutonium

The electronic structure of the α-phase of plutonium has been calculated by the band methods with allowance for the spin-orbit interaction and Coulomb correlations in the complete matrix form (the LDA + U + SO method). The strong spin-orbit interaction of the 5 f electrons is manifested in the splitting of the calculated density of the 5f states, which makes a small contribution at the Fermi level on the order of the contribution from the 6d states. Using the results of the ab initio calculations, the spin and orbit contributions to the magnetic susceptibility of α-plutonium have been determined. Along with the impurity contribution, they describe well the experimental data on the susceptibility of this plutonium phase to a temperature of 300 K.