Electron-electron Coulomb Interaction Research Articles

Spin conversion rates due to dipolar interactions in monoisotopic quantum dots at vanishing spin-orbit coupling

Dipolar interaction between the magnetic moments of electrons is studied as a source for electron spin decay in quantum dots or arrays of quantum dots. This magnetic interaction will govern spin decay, after other sources, such as the coupling to nuclear spins or spin orbit coupling, have been eliminated by a suitable sample design. Electron-electron (Coulomb) interactions, important for magnetic properties, are included. Decomposing the dipolar operator according to the symmetric group of electron permutations allows one to deduce vanishing decay channels as a function of electron number and spatial symmetries of the quantum dot(s). Moreover, we incorporate the possibility of rapid phonon induced spin conserving transitions which crucially affect the temperature dependence of spin decay rates. An interesting result is that a sharp increase of the spin decay rate occurs already at relatively low temperatures.

From independent particles to Wigner localization in quantum dots: The effect of the dielectric environment

The influence of image charges on the electron correlation in two-electron spherical quantum dots is investigated. The image charges induced by the dielectric mismatch between the quantum dot and the surrounding medium can induce a transition from volume to surface states, the latter being localized mainly in the self-polarization potential well. Coulomb interaction and correlation effects in these surface states depend strongly upon the ratio of dielectric constants: If ${\ensuremath{\epsilon}}_{\text{dot}}<{\ensuremath{\epsilon}}_{\mathrm{out}}$ the bare electron-electron Coulomb interaction can be screened by the polarizatization terms, then, the kinetic energy dominates, the correlation energy becomes negligible and the electrons behave almost as independent particles. However, if ${\ensuremath{\epsilon}}_{\text{dot}}>{\ensuremath{\epsilon}}_{\mathrm{out}}$ a strongly enhanced angular correlation can lead to the formation of a Wigner-type molecule even in the high electronic density and small dot-size regimes.

Energy relaxation due to magnetic impurities in mesoscopic wires: Logarithmic approach

The transport in mesoscopic wires with large applied bias voltage has recently attracted great interest by measuring the energy distribution of the electrons at a given point of the wire, in Saclay. In the diffusive limit with negligible energy relaxation that shows two sharp steps at the Fermi energies of the two contacts, which are broadened due to the energy relaxation. In some of the experiments the broadening is reflecting an anomalous energy relaxation rate proportional to $E^{-2}$ instead of $E^{-3/2}$ valid for Coulomb electron-electron interaction, where $E$ is the energy transfer. Later it has been suggested that such relaxation rate can be due to electron-electron interaction mediated by Kondo impurities. In the present paper the latter is systematically studied in the logarithmic approximation valid above the Kondo temperature. In the case of large applied bias voltage Kondo resonances are formed at the steps of the distribution function and they are narrowed by increasing the bias. An additional Korringa energy broadening occurs for the spins which smears the Kondo resonances, and the renormalized coupling can be replaced by a smooth but essentially enhanced average coupling (factor of 8-10). Thus the experimental data can be described by formulas without logarithmic Kondo corrections, but with enhanced coupling. In certain regions of large bias, that averaged coupling depends weakly on the bias. In those cases the distribution function depends only on the ratio of the electron energy and the bias, showing scaling behavior. The impurity concentrations estimated from those experiments and other dephasing experiments can be very different, and a possible explanation considering the surface spin anisotropy due to strong spin-orbit interaction is the subject of our earlier paper.

A short-range correlation energy density functional with multi-determinantal reference

We introduce a short-range correlation density functional defined with respect to a multi-determinantal ref- erence which is meant to be used in a multi-determinantal extension of the Kohn-Sham scheme of density functional theory based on a long-range/short-range decomposition of the Coulomb electron-electron interaction. We construct the local density approximation for this functional and discuss its performance on the He atom.

Exchange instabilities in electron systems: Bloch versus Stoner ferromagnetism

We show that 2D and 3D electron systems with the long-range Coulomb electron-electron interaction could develop ferromagnetic instabilities due to strong exchange effects at low densities. The critical densities in both 2D and 3D systems at which the magnetic instability, which could either be of Stoner type (second-order) or of Bloch type (first-order), are higher than the dispersion instability critical density where effective mass at the Fermi surface diverges. We discuss the theoretical as well as experimental implications of the ferromagnetic instability at low electron densities, particularly in low-disorder semiconductor-based two-dimensional systems.

Intermolecular electrostatic energies using density fitting

A method is presented to calculate the electron-electron and nuclear-electron intermolecular Coulomb interaction energy between two molecules by separately fitting the unperturbed molecular electron density of each monomer. This method is based on the variational Coulomb fitting method which relies on the expansion of the ab initio molecular electron density in site-centered auxiliary basis sets. By expanding the electron density of each monomer in this way the integral expressions for the intermolecular electrostatic calculations are simplified, lowering the operation count as well as the memory usage. Furthermore, this method allows the calculation of intermolecular Coulomb interactions with any level of theory from which a one-electron density matrix can be obtained. Our implementation is initially tested by calculating molecular properties with the density fitting method using three different auxiliary basis sets and comparing them to results obtained from ab initio calculations. These properties include dipoles for a series of molecules, as well as the molecular electrostatic potential and electric field for water. Subsequently, the intermolecular electrostatic energy is tested by calculating ten stationary points on the water dimer potential-energy surface. Results are presented for electron densities obtained at four different levels of theory using two different basis sets, fitted with three auxiliary basis sets. Additionally, a one-dimensional electrostatic energy surface scan is performed for four different systems (H2O dimer, Mg2+-H2O, Cu+-H2O, and n-methyl-formamide dimer). Our results show a very good agreement with ab initio calculations for all properties as well as interaction energies.

Evidence for strong electron-phonon coupling inMgCNi3

The title compound is investigated by specific heat measurements in the normal and superconducting state supplemented by upper critical field transport, susceptibility and magnetization measurements. From a detailed analysis including also full potential electronic structure calculations for the Fermi surface sheets, Fermi velocities and partial densities of states the presence of both strong electron-phonon interactions and considerable pair-breaking has been revealed. The specific heat and the upper critical field data can be described to first approximation by an effective single band model close to the clean limit derived from a strongly coupled predominant hole subsystem with small Fermi velocities. However, in order to account also for Hall-conductivity and thermopower data in the literature, an effective general two-band model is proposed. This two-band model provides a flexible enough frame to describe consistently all available data within a scenario of phonon mediated s-wave superconductivity somewhat suppressed by sizeable electron-paramagnon or electron-electron Coulomb interaction. For quantitative details the relevance of soft phonons and of a van Hove type singularity in the electronic density of states near the Fermi energy is suggested.

Quantum effects on charge order

Charge ordering in strongly correlated 1/4-filled systems, such as charge transfer organic conductors and transition metal oxides, is discussed from a theoretical point of view. Strong electron-electron Coulomb interaction especially that between neighboring molecules induces Wigner crystal-type charge order, which competes with another insulating state due to strong correlation in these systems, i.e., the dimer Mott insulating state. Based on such idea, new aspects of the charge ordering phenomenon are pointed out, where full quantum mechanical treatments are required. One case is the interplay between electron-phonon interaction leading to a novel co-existence of charge order and spin-Peierls lattice distortion, and the other is the effect of geometrical frustration resulting in a quantum melting of the charge order.

Re-examination of the NDDO approximation and introduction of a new model beyond it

The NDDO (neglect of diatomic differential overlap) approximation, a widely used basis for many semi-empirical molecular orbital (MO) approaches, is re-examined based on non-empirical frozen-core calculations on small molecules. An improvement going beyond the NDDO approximation is proposed. Our study shows that under the NDDO approximation, when the remaining non-DDO-type two-electron repulsion integrals (TERIs) are calculated using the basis set from the Löwdin orthogonalization of the valence atomic orbitals, the resulting total energies are much higher than those from the corresponding frozen-core ab initio calculations. On the other hand, when the remaining non-DDO TERIs are calculated using non-orthogonal valence atomic orbitals (similar to the Roby model), for most of the molecules calculated, the total energies are significantly lower than those from the corresponding ab initio calculations. Furthermore, we also find that for some molecules, the total energies thus calculated are higher than the corresponding ab initio results. The nonsystematic variation of the absolute errors in the total energy calculations is due to the fact that the core-electron and the electron-electron interactions are not treated in a balanced way in the NDDO approximation. A new model, which overcomes the deficiencies in the NDDO model, is proposed. In this model, a first-order correction term is added to the electron-electron Coulomb interactions, thereby improving the balance between the core-electron and the electron-electron interactions. Non-empirical test calculations show that the total energies from the new model are consistently higher than those from the ab initio calculation but closer to the ab initio results. We expect that the proposed new model would be useful in developing new high-quality semi-empirical MO approaches.

A closer look at electron-electron correlation in laser-induced non-sequential double ionization

The S-matrix formalism for non-sequential double ionization (NSDI) in a rescattering scenario is further explored with two objectives in mind. First, two different forms of the electron-electron correlation are compared: the Coulomb repulsion and a three-body contact interaction including the ion, both in the Born approximation. The former favours disparate momenta of the two electrons, the latter equal momenta. Second, the analogue of the intensity-dependent resonances in above-threshold ionization spectra is investigated in the case of NSDI. For the Coulomb electron-electron interaction, a distinct signature is observed in the momentum distributions of the final two electrons.

A closer look at electron-electron correlation in laser-induced non-sequential double ionization

Abstract The S-matrix formalism for non-sequential double ionization (NSDI) in a rescattering scenario is further explored with two objectives in mind. First, two different forms of the electron-electron correlation are compared: the Coulomb repulsion and a three-body contact interaction including the ion, both in the Born approximation. The former favours disparate momenta of the two electrons, the latter equal momenta. Second, the analogue of the intensity-dependent resonances in above-threshold ionization spectra is investigated in the case of NSDI. For the Coulomb electron-electron interaction, a distinct signature is observed in the momentum distributions of the final two electrons.

Ising quantum Hall ferromagnet in magnetically doped quantum wells.

We report on the observation of the Ising quantum Hall ferromagnet with Curie temperature T(C) as high as 2 K in a modulation-doped (Cd,Mn)Te heterostructure. In this system field-induced crossing of Landau levels occurs due to the giant spin-splitting effect. Magnetoresistance data, collected over a wide range of temperatures, magnetic fields, tilt angles, and electron densities, are discussed taking into account both Coulomb electron-electron interactions and s-d coupling to Mn spin fluctuations. The critical behavior of the resistance "spikes" at T-->T(C) corroborates theoretical suggestions that the ferromagnet is destroyed by domain excitations.

A tunnelling spectroscopy study on thesingle-particle energy levels and electron-electroninteractions in CdSe quantum dots

We performed scanning tunnelling spectroscopy oninsulating colloidal CdSe quantum dots attached to gold with arigid self-assembled monolayer. By varying the tip-dot distancewe change the relative rate of tunnelling into versus tunnellingout of the dot over a wide range. If the tip is retracted relatively farfrom the dot, tunnelling in is much slower than tunnellingout of the dot; electrons tunnel one at a time through thedot. The resonances in the conductance spectrum correspond tothe single-particle energy levels of the CdSe quantum dot. Whenthe tip is brought closer to the dot, tunnelling in can becomeas fast as tunnelling out of the dot. Up to three electrons can be present in the particle; the electron-electron Coulombinteractions lead to a more complex conductance spectrum.

Dynamic correlations of the spinless Coulomb Luttinger liquid

The dynamic density response function, form-factor, and spectral function of a Luttinger liquid with Coulomb electron-electron interaction are studied with the emphasis on the short-range electron correlations. The Coulomb interaction changes dramatically the density response function as compared to the case of the short-ranged interaction. The form of the density response function is smoothing with time, and the oscillatory structure appears. However, the spectral functions remain qualitatively the same. The dynamic form-factor contains the $\delta$-peak in the long-wave region, corresponding to one-boson excitations. Besides, the multi-boson-excitations band exists in the wave-number region near to $2k_F$. The dynamic form-factor diverges at the edges of this band, while the dielectric function goes to zero there, which indicates the appearance of a soft mode. We develop a method to analyze the asymptotics of the spectral functions near to the edges of the multi-boson-excitations band.

Impact of electron–electron cusp on configuration interaction energies

The effect of the electron–electron cusp on the convergence of configuration interaction (CI) wave functions is examined. By analogy with the pseudopotential approach for electron–ion interactions, an effective electron–electron interaction is developed which closely reproduces the scattering of the Coulomb interaction but is smooth and finite at zero electron–electron separation. The exact many-electron wave function for this smooth effective interaction has no cusp at zero electron–electron separation. We perform CI and quantum Monte Carlo calculations for He and Be atoms, both with the Coulomb electron–electron interaction and with the smooth effective electron–electron interaction. We find that convergence of the CI expansion of the wave function for the smooth electron–electron interaction is not significantly improved compared with that for the divergent Coulomb interaction for energy differences on the order of 1 mHartree. This shows that, contrary to popular belief, description of the electron–electron cusp is not a limiting factor, to within chemical accuracy, for CI calculations.

Electronic States and Transport Phenomena in Quantum Dot Systems

Electronic states and transport phenomena in semiconductor quantum dots are studied theoretically. Taking account of the electron-electron Coulomb interaction by the exact diagonalization method, the ground state and low-lying excited states are calculated as functions of magnetic field. Using the obtained many-body states, we discuss the temperature dependence of the conductance peaks in the Coulomb oscillation. In the Coulomb blockade region, elastic and inelastic cotunneling currents are evaluated under finite bias voltages. The cotunneling conductance is markedly enhanced by the Kondo effect. In coupled quantum dots, molecular orbitals and electronic correlation influence the transport properties.

Optical conductivity in normal-state fullerene superconductors

We calculate the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ in the normal-state fullerene superconductors by self-consistently including the impurity scatterings, the electron-phonon, and electron-electron Coulomb interactions. The finite bandwidth of the fullerenes and the vertex corrections are explicitly considered in calculating the renormalized Green's function. $\ensuremath{\sigma}(\ensuremath{\omega})$ is obtained by calculating the current-current correlation function with the renormalized Green's function in the Matsubara frequency and then performing analytic continuation to the real frequency at finite temperature. The Drude weight in $\ensuremath{\sigma}(\ensuremath{\omega})$ is strongly suppressed due to the interactions and transfered to the mid-infrared region around and above $0.06\mathrm{eV},$ which is somewhat less pronounced and much broader compared with the experimental observation by DeGiorgi et al.

Nonequilibrium electron dynamics in noble metals

Electron-electron and electron-lattice interactions in noble metals are discussed in the light of two-color femtosecond pump-probe measurements in silver films. The internal thermalization of a nonequilibrium electron distribution created by intraband absorption of a pump pulse is followed by probing the induced optical property changes in the vicinity of the frequency threshold for the d band to Fermi surface transitions. This is shown to take place with a characteristic time constant of 350 fs, significantly shorter than previously reported in gold. This difference is ascribed to a weaker screening of the electron-electron interaction by the d-band electrons in silver than in gold. These results are in quantitative agreement with numerical simulations of the electron relaxation dynamics using a reduced static screening of the electron-electron Coulomb interaction, and including bound electron screening. Electron-lattice thermalization has been studied using a probe frequency out of resonance with the interband transitions. In both materials, the transient nonthermal nature of the electron distribution leads to the observation of a short-time delay reduction of the energy-loss rate of the electron gas to the lattice, in very good agreement with our theoretical model.

Hysteresis effect due to the exchange Coulomb interaction in short-period superlattices in tilted magnetic fields

We calculate the ground-state of a two-dimensional electron gas in a short-period lateral potential in magnetic field, with the Coulomb electron-electron interaction included in the Hartree-Fock approximation. For a sufficiently short period the dominant Coulomb effects are determined by the exchange interaction. We find numerical solutions of the self-consistent equations that have hysteresis properties when the magnetic field is tilted and increased, such that the perpendicular component is always constant. This behavior is a result of the interplay of the exchange interaction with the energy dispersion and the spin splitting. We suggest that hysteresis effects of this type could be observable in magneto-transport and magnetization experiments on quantum-wire and quantum-dot superlattices.

Collective optical excitation of interacting localized electrons

We investigate theoretically the role of dynamic screening in the intersubband absorption process of a quasi-two-dimensional (quasi-2D) electron gas with in-plane localization caused by a strong disorder potential. Due to a correlation effect in the single-particle spectrum this system is equivalent to an array of randomly distributed, localized oscillators, which are mutually coupled by the electron-electron Coulomb interaction. In the limit of low-electron density, a broad absorption spectrum reflects the disorder-induced distribution of the individual transition energies. For increasing electron filling factor we find a depolarization-type blueshift similar to the case of quasi-2D systems without disorder. Simultaneously a dramatic line narrowing is observed, indicating a collective response of the interacting localized electrons. In this collective mode large clusters of mutually phase-adapted oscillators are formed in the layer plane. Our results are relevant for the interpretation of intraband absorption experiments in all kinds of disordered quasi-2D systems and in dense arrays of artificial quantum dots. A similar effect is expected for inter-Landau-level transitions in magnetically quantized 2D systems.