Coulomb Exchange Interaction Research Articles

Exchange effects in Coulomb quantum plasmas: Dispersion of waves in 2D and 3D quantum plasmas

We describe quantum hydrodynamic equations with the Coulomb exchange interaction for three and two dimensional plasmas. Explicit form of the force densities are derived. We present non-linear Schrödinger equations (NLSEs) for the Coulomb quantum plasmas with the exchange interaction. We show contribution of the exchange interaction in the dispersion of the Langmuir, and ion-acoustic waves. We consider influence of the spin polarization ratio on strength of the Coulomb exchange interaction. This is important since exchange interaction between particles with same spin direction and particles with opposite spin directions are different. At small particle concentrations n0≪1025cm−3 and small polarization the exchange interaction gives small decrease of the Fermi pressure. With increase of polarization role the exchange interaction becomes more important, so that it can overcome the Fermi pressure. The exchange interaction also decreases contribution of the Langmuir frequency. Ion-acoustic waves do not exist in limit of large polarization since the exchange interaction changes the sign of pressure. At large particle concentrations n0≫1025cm−3 the Fermi pressure prevails over the exchange interaction for all polarizations. We obtain a similar picture for two dimensional quantum plasmas.

Ab initio calculations on magnetism induced by composite defects in magnesium oxide

The local magnetic state induced by the composite defects, composed of an oxygen vacancy and a nitrogen substituting oxygen, in magnesium oxide has been studied by using ab initio calculation based on density functional theory. The calculated results show that local magnetic moment can be induced by the composite defects around the oxygen vacancy, when the exchange split of the oxygen vacancy is enhanced either by the hybridization between the N-p and nearest neighbor O-p orbitals or by applying on-site Coulomb repulsion (U) and exchange interaction (J). We show that the magnetic state induced by the composite defect is energetically more stable than the non-magnetic state. In addition, we show that the U and J applied on the p-orbitals of N and O atoms may significantly impact the calculated magnetic state of the composite defect, resulting in magnetic state for a configuration that is non-magnetic by generalized gradient approximation.

Two-qubit geometric phase gate for quantum dot spins using cavity polariton resonance

We describe a design to implement a two-qubit geometric phase gate, by which a pair of electrons confined in adjacent quantum dots are entangled. The entanglement is a result of the Coulomb exchange interaction between the optically excited exciton-polaritons and the localized spins. This optical coupling, resembling the electron-electron Ruderman-Kittel-Kasuya-Yosida (RKKY) inter- actions, offers high speed, high fidelity two-qubit gate operation with moderate cavity quality factor Q. The errors due to the finite lifetime of the polaritons can be minimized by optimizing the optical pulse parameters (duration and energy). The proposed design, using electrostatic quantum dots, maximizes entanglement and ensures scalability.

Theory of fine structure of correlated exciton states in self-assembled semiconductor quantum dots in a magnetic field

A theory of the fine structure of correlated exciton states in self-assembled parabolic semiconductor quantum dots in a magnetic field perpendicular to the quantum dot plane is presented. The correlated exciton wave function is expanded in configurations consisting of products of electron and heavy-hole 2D harmonic oscillator states (HO) in a magnetic field and the electron spin ${S}_{z}=\ifmmode\pm\else\textpm\fi{}1/2$ and a heavy-hole spin ${\ensuremath{\tau}}_{z}=\ifmmode\pm\else\textpm\fi{}3/2$ states. Analytical expressions for the short- and long-range electron-hole exchange Coulomb interaction matrix elements are derived in the HO and spin basis for arbitrary magnetic field. This allows the incorporation of short- and long-range electron-hole exchange, direct electron-hole interaction, and quantum dot anisotropy in the exact diagonalization of the exciton Hamiltonian. The fine structure of ground and excited correlated exciton states as a function of a number of confined shells, quantum dot anisotropy, and magnetic field is obtained using exact diagonalization of the many-body Hamiltonian. The effects of correlations are shown to significantly affect the energy splitting of the two bright exciton states.

Coulomb and Exchange Interaction Effect on Magnetic Properties of MnO

This calculation focus on the effect of Coulomb interaction U and exchange interaction J on spin magnetic moment Ms of MnO by using the local spin density approximation plus the Coulomb interaction (LSDA+U) method within full potential linear muffin-tin orbital (FP-LMTO). Our calculated results indicated that the spin magnetic moments correlated to U and J. The relevant results exhibited the increasing spin magnetic moments with increasing Coulomb interaction and exchange interaction. Furthermore, equation of spin magnetic moments, which good correspondence to the experimental data, were obtained and the relation of U and J parameter was defined.

Two-photon photoluminescence excitation spectroscopy of single quantum dots

We present an experimental and theoretical study of single semiconductor quantum dots excited by two nondegenerate, resonantly tuned, variably polarized lasers. The first laser is tuned to excitonic resonances. Depending on its polarization it photogenerates a coherent single-exciton state. The second laser is tuned to biexciton resonances. By scanning the energy of the second laser for various polarizations of the two lasers, while monitoring the emission from the biexciton and exciton spectral lines, we map the biexciton photoluminescence excitation spectra. The resonance-rich spectra of the second photon absorption are analyzed and fully understood in terms of a many-carrier theoretical model which takes into account the direct and exchange Coulomb interactions between the quantum confined carriers.

Nonmonotonic inelastic tunneling spectra due to surface spin excitations in ferromagnetic junctions

The paper addresses inelastic spin-flip tunneling accompanied by surface spin excitations (magnons) in ferromagnetic junctions. The inelastic tunneling current is proportional to the magnon density of states which is energy-independent for the surface waves and, for this reason, cannot account for the bias-voltage dependence of the observed inelastic tunneling spectra. This paper shows that the bias-voltage dependence of the tunneling spectra can arise from the tunneling matrix elements of the electron-magnon interaction. These matrix elements are derived from the Coulomb exchange interaction using the itinerant-electron model of magnon-assisted tunneling. The results for the inelastic tunneling spectra, based on the nonequilibrium Green's function calculations, are presented for both parallel and antiparallel magnetizations in the ferromagnetic leads.

Observation of exchange Coulomb interactions in the quantum Hall state atν=3

Coulomb exchange interactions of electrons in the nu=3 quantum Hall state are determined from two inter-Landau level spin-flip excitations measured by resonant inelastic light scattering. The two coupled collective excitations are linked to inter-Landau level spin-flip transitions arising from the N=0 and N=1 Landau levels. The strong repulsion between the two spin-flip modes in the long-wave limit is clearly manifested in spectra displaying Coulomb exchange contributions that are comparable to the exchange energy for the quantum Hall state at nu=1. Theoretical calculations within the Hartree-Fock approximation are in a good agreement with measured energies of spin-flip collective excitations.

Formation of a narrow group of intense lines in the photoexcitation and emission spectra corresponding to 3s23pN–(3s3pN+1 + 3s23pN−13d) transitions

The strong mixing of the 3s3pN+1 and 3s23pN−13d configurations and its influence on the electric dipole transitions from/to the ground configuration 3s23pN have been considered in the isoelectronic sequences at the ionization degrees 5 ⩽ q ⩽ 35 and various numbers of electrons in the 3pN shell. It is shown that the redistribution of intensity from 3s–3p to 3p–3d transitions and its concentration in a narrow interval of wavelengths manifests itself in the photoexcitation and emission spectra for all isoelectronic sequences, but is more expressed for a half-filled and an almost-filled 3pN shell. It takes place at the condition that in the single-configuration approximation the energy levels of the 3s3pN+1 configuration, mainly populated by the photoexcitation from the ground level, are situated below such levels of the 3s23pN−13d configuration. This condition is fulfilled for the isoelectronic sequences up to q = 30; at larger ionization degrees such levels of both configurations begin to overlap and it causes the widening of the spectrum. For 3s23pN–3s23pN−13d transitions at N = 4 and 5 another reason for the narrowing of the spectrum is the existence of term groups formed by the Coulomb exchange interaction.

Radiative versus nonradiative optical processes in PbS nanocrystals

The Stokes shift detected in PbS nanocrystals is analyzed by optical absorption (OA), photoluminescence (PL) and atomic force microscopy (AFM). The samples were synthesized by fusion method over two different glass substrates, and identical size PbS dot structures with radius 4.1 nm grown showed PL and OA peaks separated by 0.15 and 0.10 eV. The origin of these large Stokes shifts are analyzed whether they are attributed to the nonradiative recombination associated to impurity states in prepared doped samples or to radiative transitions between exciton states induced by electron-hole (e-h) exchange Coulomb interaction.

Efficiency of spin injection in novel InAs quantum dot structures: exciton vs. free carrier injection

Unambiguous experimental evidence for a significant difference in efficiency of excitonic vs. free carrier spin injection is provided in novel laterally arranged self-assembled InAs/GaAs quantum dot structures, from optical orientation and tunable laser spectroscopy. A lower efficiency of exciton spin injection as compared to free carrier spin injection from wetting layers into QDs results in a distinct feature in luminescence polarization of the QDs as a function of excitation photon energy. It is shown that this difference is not related to carrier density and state-filling effects arising from the difference in optical absorption efficiency between the excitons and free carriers. Rather, it is a genuine property for exciton spin injection that suffers stronger spin relaxation due to Coulomb exchange interaction.

Chirality dependence of theK-momentum dark excitons in carbon nanotubes

Using a collection of twelve semiconducting carbon nanotube samples, each highly enriched in a single chirality, we study the chirality dependence of the $K$-momentum dark singlet exciton using phonon sideband optical spectroscopy. Measurements of bright absorptive and emissive sidebands of this finite momentum exciton identify its energy as 20 - 38 meV above the bright singlet exciton, a separation that exhibits systematic dependencies on tube diameter, $2n+m$ family, and semiconducting type. We present calculations that explain how chiral angle dependence in this energy separation relates to the Coulomb exchange interaction, and elaborate the dominance of the $K_{A_1'}$ phonon sidebands over the zone-center phonon sidebands over a wide range of chiralities. The Kataura plot arising from these data is qualitatively well described by theory, but the energy separation between the sidebands shows a larger chiral dependence than predicted. This latter observation may indicate a larger dispersion for the associated phonon near the $K$ point than expected from finite distance force modeling.

Hierarchy of spin and valley symmetry breaking in quantum Hall single-layer graphene

We explore several microscopic mechanisms for breaking the $n=0$ fourfold Landau level degeneracy in a single-layer graphene. Valley-scattering random potential, Zeeman interaction, and electron-phonon coupling are considered in the presence of SU(4)-symmetric Coulomb exchange interaction. Among all the mechanisms considered, it is the electron-phonon coupling combined with the Zeeman interaction which leads to the full splitting of the $n=0$ Landau levels. A recent controversy of "valley-first" or "spin-first" breaking of SU(4) symmetry of the $n=0$ graphene Landau level is examined in light of our results. Existence of midgap states between Landau levels of opposite valley polarity are demonstrated.

Rigorous solution of a Hubbard model extended by nearest-neighbour Coulomb and isotropic exchange interaction on a triangle and tetrahedron

In the preprint cond-mat/0701060 we detected a factor two error in the coding of the Heisenberg term of the Hamiltonian. In the result the exchange term used in the paper was that of an anisotropic Heisenberg model with $J_x=J_y=J$ and $J_z=J/2$. Thus all results given for which J=0 was chosen, remain unchanged, whereas all results containing the exchange parameter remain true for the extended Hubbard model with anisotropic exchange. That model is of some interest by itself, due to the relation to the XXZ model. The differing results for isotropic exchange are given here.

Rigorous solution of a Hubbard model extended by nearest‐neighbour Coulomb and isotropic exchange interaction on a triangle and tetrahedron

In connection with the study of the extended Hubbard model on an isosceles triangular cluster, we discovered a factor two error in the coding of the Ising part of the Heisenberg term in the Hamiltonian. In consequence the rigorous results remain valid, but not for the isotropic Heisenberg model, but for an anisotropic Heisenberg model.

General argument supporting Bose–Einstein condensate of dark excitons in single and double quantum wells

We show through a novel general field theory argument that for the very same reason that excitons are bright, i.e. emitting photons, they have a higher energy than dark excitons, whatever the carrier spatial configurations is, i.e., even in stressed geometry or for electrons well separated from holes as in a double quantum well structure. Indeed, the same channel which produces the necessary finite electron–hole effective overlap to make them bright, allows for Coulomb interband exchange processes, which are nothing but a sequence of virtual recombination and creation of one electron–hole pair, a fact known in relativistic quantum field theory but never extended to semiconductor physics. The repulsive electron–hole Coulomb exchange interaction, which exists for bright excitons, but not for dark excitons, pushes the bright exciton energy up. If we now remember that dark excitons with spins ± 2 are formed in a natural way through carrier exchange between opposite spin bright excitons, we here predict that in a double quantum well sample with one parabolic trap–a configuration quite appropriate to get a high density–exciton Bose–Einstein condensation should appear, when cooling down the sample, as a dark spot made of ( ± 2 ) excitons at the center of the trap. In this paper, we also suggest a possible link between the observed ring structure in a double quantum well and the formation of dark exciton condensate.

Mechanisms of non-radiative energy transfer involving lanthanide ions revisited

In this work, the theoretical background of the Coulomb direct and exchange interactions in non-radiative energy transfer involving lanthanide ions is critically reviewed. Emphasis is given to the shielding effect produced by the filled 5s and 5p sub-shells of the lanthanide ion and the appropriate use of the so-called forced electric dipole intensity parameters of 4f–4f transitions, two aspects that have been often overlooked in the literature. An effective exchange hamiltonian, based on Mülliken-type approximations, and an expression for the resonant or quasi-resonant energy mismatch spectral overlap factor are proposed. Both cases of ion-to-ion and intramolecular energy transfer processes are discussed. Numerical estimates are compared with previous calculations, showing that order of magnitude differences appear. The analysis indicates that the donor–acceptor distance dependence of transfer rates by the exchange mechanism goes beyond the single exponential behavior adopted from Dexter’s approach.

Enhancement of paramagnetic effects during spin alignment in 2D semiconductors

Effects of magnetic ordering associated with the Coulomb exchange interaction of free electrons in a 2D Fermi system are considered. It is shown that the paramagnetic response is substantially enhanced by Fermi-liquid effects. The phase transition to a state with spontaneous polarization of spins can be observed when Heisenberg parameter J is not smaller than μF/3.06 (approximately one-third of the Fermi energy) and not larger than half the Fermi energy (J ≤ μF/2).

Spin characteristics of excitonic absorption in multiply charged quantum dots

The excitonic absorption spectra of negatively charged self-assembled quantum dots as a function of resident electron number $({N}_{e}=0--5)$ are theoretically studied using the configuration interaction method. Spin Pauli blockade, Coulomb (exchange and correlation) interactions, and symmetry of dot shape are identified as the three main underlying mechanisms, sensitively depending on ${N}_{e}$, in the spin characteristic spectra. In particular, we predict that polarized absorption in triply charged dots exhibits anomalous spin-dependent features, resulting from the intrinsic correlations in charged exciton ${X}^{\ensuremath{-}3}$.

Grid-based energy density analysis: Implementation and assessment

Grid-based energy density analysis (grid-EDA) that decomposes the total energy into atomic energies by a space-partitioning function is proposed. The kinetic energy, nuclear attraction, and exchange-correlation functional are evaluated on grid points and are split into atomic contributions. To reduce numerical errors in the conventional scheme of numerical integration, the electronic Coulomb and HF exchange interactions are evaluated by the pseudospectral method, which was first applied to an ab initio method by Friesner [Chem. Phys. Lett. 116, 39 (1985)], and are decomposed into atomic contributions. Grid-EDA using the pseudospectral method succeeds in ensuring less than 1 kcalmol error in total energies for small molecules and providing reliable atomic energy contributions for the problematic lithium cluster, which exhibits a strong basis-set dependence for Mulliken-type EDA. Also, site-dependent atomization energies are estimated by grid-EDA for cluster models such as Li(48), C(41)H(60), and Mg(32)O(32). Grid-EDA reveals that these models imitate crystal environments reasonably because atomization energies estimated from the inner atoms of the models are close to the experimental cohesive energies.