Direct Coulomb Interaction Research Articles

Anisotropic spin Hamiltonians due to spin-orbit and Coulomb exchange interactions.

Here we correct, extend, and clarify results concerning the spin Hamiltonian ${\mathit{scrH}}_{\mathit{S}}$ used to describe the ground manifold of Hubbard models for magnetic insulators in the presence of spin-orbit interactions. Most of our explicit results are for a tetragonal lattice as applied to some of the copper oxide lamellar systems and are obtained within the approximation that ${\mathit{scrH}}_{\mathit{S}}$ consists of a sum of nearest-neighbor bond Hamiltonians. We consider both a ``generic'' model in which hopping takes place from one copper ion to another and a ``real'' model in which holes can hop from a copper ion to an intervening oxygen 2p band. Both models include orbitally dependent direct and exchange Coulomb interactions involving two orbitals. Our analytic results have been confirmed by numerical diagonalizations for two holes occupying any of the 3d states and, if applicable, the oxygen 2p states. An extension of the perturbative scheme used by Moriya is used to obtain analytic results for ${\mathit{scrH}}_{\mathit{S}}$ up to order ${\mathbf{t}}^{2}$ (t is the matrix of hopping coefficients) for arbitrary crystal symmetry for both the ``generic'' and ``real'' models. With only direct orbitally independent Coulomb interactions, our results reduce to Moriya's apart from some minor modifications. For the tetragonal case, we show to all orders in t and \ensuremath{\lambda}, the spin-orbit coupling constant, that ${\mathit{scrH}}_{\mathit{S}}$ is isotropic in the absence of Coulomb exchange terms and assuming only nearest-neighbor hopping. In the presence of Coulomb exchange, scaled by K, the anisotropy in ${\mathit{scrH}}_{\mathit{S}}$ is biaxial and is shown to be of order ${\mathit{Kt}}^{2}$${\ensuremath{\lambda}}^{2}$. Even when K=0, for systems of sufficiently low symmetry, the anisotropy in ${\mathit{scrH}}_{\mathit{S}}$ is proportional to ${\mathit{t}}^{6}$${\ensuremath{\lambda}}^{2}$ when the direct on-site Coulomb interaction U is independent of the orbitals involved and of order ${\mathit{t}}^{2}$${\ensuremath{\lambda}}^{2}$ otherwise. These latter results apply to the orthorhombic phase of ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$.

Effect of antiferromagnetic spin fluctuations on the phonon-mediated pair interaction in high-T c superconductors

We investigate the effect of electronic correlations on the phonon-mediated part of the pair interaction by including the effect of an exchange interaction U between the electrons in the calculation of the phonon frequencies and the electron-phonon vertices. We employ two RPA models: the first, consisting of a direct Coulomb interaction in addition to U, leads to softer phonons and an enhanced attractive s-wave phonon-induced electron-electron interaction while the second, a pure Hubbard model, yields the opposite effect. The weak-coupling selfconsistency equation for the order parameter in the 2D first Brillouin zone is solved for a tight-binding band. The change of Tc arises primarily from the change of the phonon frequencies rather than from the vertex renormalization.

Maxwell-Bloch formulation for semiconductors: Effects of coherent Coulomb exchange.

A generalized Bloch-Maxwell formulation for laser-field-coupled semiconductors is derived from a two-band model which includes direct Coulomb interactions. The momentum-dependent, microscopic, electron-hole equations of motion in the time-dependent Hartree-Fock approximation and neglecting interband exchange interactions form the starting point for the formulation. A self-consistent set of coupled equations in four dynamical variables for the medium, together with the electric-field amplitude coupled through the Maxwell wave equation in a semiclassical approximation, are obtained to lowest order in the coherent Coulomb exchange interaction and the density-of-states distribution. Intrinsic optical bistability is predicted in a steady state due to a carrier density-dependent redshift of the band edge due explicitly to coherent Coulomb exchange. Integration of the dynamical equations for conditions which correspond to the ultrafast time regime exhibit intrinsic adiabatic inversion, adiabatic following, anomalous Rabi cycling, and unique, as well as fast, optical switching, all of which depend upon the coherent Coulomb exchange interaction.

A pre-impact model for ionic and atomic desorption induced by fast multicharged projectiles

Desorption induced by highly charged particles is described through a model based on direct Coulomb interaction between the projectile and adsorbed molecules. It is assumed that the emission of ionized and neutral species from metals or insulators is triggered by the electric field of the projectile before its impact on the surface. The projectile interaction with the adsorbate layer induces ionizations or electronic excitations which lead to subsequent desorption through processes such as Coulomb explosion or molecular dissociation, causing the secondary emission of ions or neutral species. The pre-impact desorption (PID) model proposed here is based on a potential-ejection model normally used for projectile velocities below the Bohr velocity. It is considered that surface ionization occurs in a well defined period of time, when over-the-barrier electron emission (or electron promotion) is possible. The model predicts a q 3 cosθ behavior of the desorption yield, q being the projectile charge and θ the angle of incidence. The q 3-dependence has been observed for H + emission induced by keV and MeV energy beams. It also predicts an increase of the induced desorption yield, as the ionization potential of the adsorbed layer decreases. With regard to the yield dependence on the projectile velocity, the pre-impact model predicts a maximum around the Bohr velocity; the detailed description of the projectile-surface interaction may affect the position of this maximum but not the general trend of the function.

Electronic Raman scattering in p-doped GaAs/Ga1-xAlxAs quantum-well structures: Scattering mechanisms and many-particle interactions.

By means of resonance Raman spectroscopy we have investigated intersubband transitions of quasi-two-dimensional (2D) hole gases in p-type modulation-doped GaAs/${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum-well structures. The observed excitations have an essentially single-particle character due to Landau damping of collective excitations and due to single-particle scattering by energy-density fluctuations under conditions of extreme resonance. In samples with well widths of typically 100\char21{}200 \AA{} and 2D hole densities \ensuremath{\rho}\ensuremath{\sim}${10}^{11}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$, we observe a characteristic variation of intersubband-transition energies with laser frequency in depolarized and in polarized scattering configurations. This variation is caused by the nonparabolic subband dispersion of the 2D single-particle hole subbands. Experiments under variation of p, by illuminating the sample with photons that have energies above the band gap of the ${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As barriers, allow an estimate of the relative strengths of direct and exchange Coulomb interactions. From these experiments a greater relative strength of the exchange interaction, in comparison to that found for 2D electron gases, can be deduced.

Temperature and many-body effects on the intersubband transition in a GaAs/Al0.3Ga0.7As multiple quantum well.

Temperature and many-body effects on the intersubband transition in a GaAs/${\mathrm{Al}}_{0.3}$${\mathrm{Ga}}_{0.7}$As multiple quantum well are studied using the infrared-absorption technique and the envelope-function-approximation method. In order to explain the measured peak position energy of the intersubband transition and its blueshift observed by decreasing temperature and/or increasing the two-dimensional electron-gas density, a theoretical model is developed which is based on a nonparabolic-anisotropic envelope-function-approximation (NAEFA) method. This model takes into account the many-body corrections, in particular, temperature-dependent electron-electron intrasubband and intersubband exchange and direct Coulomb interaction energies as well as the depolarization and excitonlike shifts within the framework of Zaluzny's implementation of Ando's formalism [Phys. Rev. B 43, 4511 (1991)]. Temperature-dependent effective masses, nonparabolicity, conduction-band offsets, the Fermi level, and line-shape broadening are also incorporated in the present NAEFA calculations. Our theory provides a qualitative explanation for the magnitude of the measured temperature blueshift. Additional support for many-body effects is obtained by utilizing the persistent photoeffect measurements.

Confined excitons in a semiconductor quantum dot in a magnetic field

Magnetic field effects in a semiconductor quantum dot (QD) are studied theoretically. Magneto-optical effects originating from electron-hole pairs in the lowest and the higher excited states are discussed. The theory is based on the effective-mass approximation with the following effects taken into account: the direct Coulomb interaction, the electron-hole exchange interaction, and the valence-band mixing effect. A calculation is performed with a numerical diagonalization method. The transition from the quantum confined Zeeman effect for a weak magnetic field to the quantum confined Paschen-Back effect for a strong magnetic field is discussed. Special attention is paid to a magnetic field dependence of the optical transition probabilities which is found to be a pronounced effect for a CdSe QD, where the confinement by a potential and a magnetic field have competing contributions.

Surface ionization by ion impact at grazing incidence

We have calculated the energy distribution of electrons produced by ionization of bulk electrons in grazing H + surface collisions. In this first approach we assume a direct ion-surface Coulomb interaction, describe the solid within the jellium approximation, and consider nonparallel ion trajectories near the surface. In agreement with experimental results, the energy distributions present a maximum around 3 eV, strongly dependent on the observation angle and projectile energy.

Many-electron effects on transport through two-dimensional quantum structures

A two-dimensional Thomas–Fermi–Dirac–von Weizsacker formalism is derived using a local density approximation to study ballistic transport in quantum structures. The effective potential of the two-dimensional system is calculated by minimizing the energy using a conjugate gradient technique. This method enables us to study the effects of exchange and correlation, in addition to the direct Coulomb interaction, on quantum transport. We have applied this method to calculate the transport property of a T-shaped two-dimensional quantum wire in the presence of the effective potential.

Influence of the Direct Coulomb Interactions on the Resistivity in NdPb3

In order to investigate the influence of the 4f electrons on the scattering processes we measured resistivity of the NdPb3 in the temperature range 7-300 K. As a result, we could compare the experimentally determined magnetic contribution to the resistivity with the theoretically calculated ones for the exchange and quadrupolar scattering. The results may confirm that the direct Coulomb interactions between 4f and conduction electrons predominate.

Dynamical conductivity of a two-layered structure with electron-acoustic phonon coupling

The frequency-dependent conductivity (resistivity) of two isolated parallel electron layers is calculated. The authors take into account both the direct electron-electron interaction and the coupling between electrons through phonon exchange. It is found that the interlayer momentum relaxation due to the direct Coulomb interaction and the phonon exchange interaction has the same dependence on the layer separation. The results for the conductivity rests on the Kubo formula for conductivity and the Green function formalism. The numerical results for the temperature dependence of sigma 12 in the DC limit is presented. Furthermore, they have calculated the frequency dependence of sigma 12 in the zero-temperature limit.

Collective inter-subband excitations of electron gas in quantum wells in infrared absorption, Raman scattering and nonlinear optical processes

We discuss the role of collective inter-subband excitations of electron gases confined in quantum wells in infrared absorption, resonant Raman scattering and nonlinear optical processes. First, exchange as well as direct Coulomb interaction are invoked in a theoretical model to calculate the shift of the collective inter-subband modes from the single particle excitation energy. We then formulate the coupling of the collective inter-subband charge density mode to the electromagnetic field. The coupling mechanisms via exchange and direct Coulomb scattering for resonant Raman processes are discussed. An experiment is designed that can differentiate between the two mechanisms, based on their dependence on wavefunction overlap. Finally, we discuss nonlinear optical processes involving inter-subband transitions and collective excitations.

Temperature-dependent electronic structure and magnetic behavior of Mott insulators.

We investigate the temperature-dependent electronic and magnetic properties of transition-metal monoxides by use of a theoretical model that takes into account the 3d subbands of the transition metal and the oxygen 2p subbands. Characteristic properties of these Mott insulators are caused by strong 3d-electron correlations, described by intra-atomic Coulomb interactions and characterized by three different coupling constants: U, U\ifmmode\bar\else\textasciimacron\fi{}, and J. The intraband coupling U turns out to be decisive for the appearance of spontaneous antiferromagnetism. U\ifmmode\bar\else\textasciimacron\fi{} is a direct interband Coulomb interaction responsible for a nonuniform occupation of the 3d subbands, and therewith decisive for the insulator properties of these materials. The interband exchange J describes an effective electron-magnon interaction and polarizes magnetically inactive subbands. The self-consistent solution of our model yields a quasiparticle density of states that contains three nonconnected energy regions with predominantly 3d character: two below, and one above, the chemical potential \ensuremath{\mu}. The insulator gap is practically temperature independent, persisting for arbitrary T\ensuremath{\gg}${\mathit{T}}_{\mathit{N}}$. A necessary condition for the insulating behavior is an integral number ${\mathit{n}}_{3\mathit{d}}$\ensuremath{\ge}5 of 3d electrons. The antiferromagnetism is caused by 10-${\mathit{n}}_{3\mathit{d}}$ exactly half-filled 3d subbands, while ${\mathit{n}}_{3\mathit{d}}$-5 subbands are completely filled. The magnetic moment remains stable for arbitrarily high temperatures. The temperature dependence of the sublattice magnetization is caused by a ``kinetic Heisenberg exchange.'' The 2p-3d hybridization plays only a minor role with respect to the magnetic and insulating properties of Mott insulators, but becomes decisive for the nature of the band gap and the interpretation of photoemission data. Our model calculation correctly predicts MnO, FeO, CoO, NiO, and CuO to be antiferromagnetic insulators, while VO turns out to be a nonmagnetic metal.

Direct Coulomb and phonon-mediated coupling between spatially separated electron gases.

Momentum transfer due to electron-electron interaction between two quasi-two-dimensional electron gases, whose edges are separated by a distance d, is studied at low temperatures (T). The coupling between the gases results from the direct Coulomb (screened) interaction and from the interaction mediated by virtual phonon exchange. The former has a ${\mathit{T}}^{2}$ dependence and varies approximately as ${\mathit{d}}^{\mathrm{\ensuremath{-}}4}$ for large d. The latter depends very weakly on d and, combined with the former, accounts extremely well for the T and d dependences of the relaxation time as measured by Gramila et al. [Phys. Rev. Lett. 66, 1216 (1991)].

6p1/2,3/2nf J=1-5 autoionizing series of barium.

The 6pnf series of barium converging to both 6${\mathit{p}}_{1/2}$ and 6${\mathit{p}}_{3/2}$ limits were investigated in a two-step pulsed-laser experiment. From 6s5d $^{3}$${\mathit{D}}_{1,2,3}$ metastable atoms, discharge populated in an atomic beam, 11 out of the full manifold of 12 autoionizing 6${\mathit{p}}_{1/2,3/2}$nf J=1--5 Rydberg series were excited via selected 5d6p J=0--4 doubly excited intermediate states. For each value of the total angular momentum J, the data were analyzed using R-shifted multichannel-quantum-defect theory. The autoionization rates of the different series compare well with a model for autoionization based upon only a direct Coulomb interaction mechanism with neglect of exchange effects. The multiplet level structure of the 6pnf configuration for a particular n Rydberg manifold was analyzed in terms of Slater integrals. The level ordering of 6pnf J substates could only be explained by including a large exchange parameter. Some 6pnp series were also observed, in particular 6${\mathit{p}}_{3/2}$${\mathit{np}}_{3/2}$ J=3.

Hole superconductivity: Review and some new results

We review recent work on a mechanism proposed to explain high T c superconductivity in oxides as well as superconductivity of conventional materials. It is based on pairing of hole carriers through their direct Coulomb interaction, and gives rise to superconductivity because of the momentum dependence of the repulsive interaction in the solid state environment. In the regime of parameters appropriate for high T c oxides this mechanism leads to characteristic signatures that should be experimentally verifiable. In the regime of “conventional superconductors” most of these signatures become unobservable, but the characteristic dependence of T c on band filling survives. New features discussed here include the demonstration that superconductivity can result from repulsive interactions even if the gap function does not change sign and the inclusion of a self-energy correction to the hole propagator that reduces the range of band filling where T c is not zero.

Large exchange interactions in the electron gas of GaAs quantum wells.

Inelastic-light-scattering measurements show that exchange Coulomb interactions in the two-dimensional electron gas of GaAs microstructures are more important than previously anticipated. Small-wave-vector spectra from modulation-doped quantum wells exhibit unexpected single-particle intersubband transitions in addition to collective spin-density and charge-density modes. From the measured spectral energies the direct and exchange intersubband Coulomb interactions are determined and found to be of comparable strengths.

Hydrogen-induced ordering of Cs atoms on the Pd(110)-(1 x 2)Cs surface.

${\mathrm{H}}_{2}$ adsorption on the Pd(110)-(1\ifmmode\times\else\texttimes\fi{}2)Cs surface has been studied with use of low-energy electron diffraction, thermal-desorption spectroscopy, and vibrational-electron-energy-loss spectroscopy. It is reported for the first time that H atoms induce ordering of the Cs atoms to form the c(2\ifmmode\times\else\texttimes\fi{}4) structure. Strong evidence exists that the ordering results from the direct Coulomb interaction between H and Cs. A structural model of the Pd(110)-c(2\ifmmode\times\else\texttimes\fi{}4)Cs/H patch is proposed.

A Model for Lattice Dynamics of Lanthanides

AbstractA simple model is proposed for studying the lattice dynamics of h.c.p. rare earth metals. The interaction between core‐core and (f, d)shells–(f, d)shells via conduction electrons is considered through a screened‐Coulomb potential. The direct Coulomb interaction between cores and (f, d)shell electrons is essentially short‐range and is, therefore, described through a non‐central type interaction extending upto the third neighbours.

Functional formulation of microscopic theory of exciton polaritons

Exact results obtained from quantum field theory in its functional formulation are used to construct a microscopic theory of exciton polaritons in semiconductors. It is shown that the polariton spectrum is determined by the poles of the two-particle Green's function that describes both the direct Coulomb electron-hole interaction as well as the exchange electron-hole interaction. By means of higher Legendre transformations the Bethe-Salpeter equation for the two-particle Green's function is obtained from Schwinger's equations. The polariton spectrum and the permittivity tensor are determined from the solution of the Bethe-Salpeter equation. The nontrivial normalization condition obtained in the paper for the wave functions of the polaritons has made it possible for the first time to connect their energy and momentum to the Minkowski tensor for the energy and momentum densities of the electromagnetic field in a dispersive medium.