Electronic states of the icosahedral quasiperiodic systems in magnetic fields

The electronic properties of the icosahedral quasiperiodic system in a tile-dependent or uniform magnetic field is studied by quasi-Bloch scheme and the general solutions are obtained for the electronic states. The behavior of the three-dimensional (3D) non-interacting electrons in an icosahedral quasiperiodic system may be treated as the projection of that of the non-interacting pseudo-electrons in 6D. In the presence of the tile-dependent magnetic field, the non-interacting electrons are quasi-Bloch electrons, while they are partial quasi-Bloch electrons when the magnetic field is uniform.     

Scattering from correlated systems

A difficulty usually encountered in formulating the problem of scattering of identical particles from correlated systems is that the customary choice of an unperturbed Hamiltonian as the target Hamiltonian plus the kinetic energy of the projectile is not symmetric under particle exchange. This choice of unperturbed Hamiltonian leads to wavefunctions which, if they are antisymmetrized, are not orthonormal. In this paper an orthonormal, antisymmetrized set of basis states is constructed. These states are then used to construct a symmetric unperturbed Hamiltonian, so that a formal scattering equation with appropriate boundary conditions can be written. An expression for a T matrix describing nucleon-nucleus scattering can then be obtained. The formalism leads to a two-potential form for the T matrix, the first term of which describes the effect of the orthogonality of the scattering state and the negative energy states.     

Stabilization energies of charged multiexciton complexes calculated at configuration interaction level

Recombination and stabilization energies of multiexcitons confined in positively and negatively charged semiconductor InGaAs/GaAs quantum dot (QD) samples have been studied by employing large-scale configuration interaction (CI) calculations. The CI calculations show that at most six electrons or two holes can be confined in the QD. Multiply charged multiexciton complexes with up to five excess electrons or two excess holes are also found to be stable, even when a few electron–hole pairs are present in the QD. The chemical potential functions for charged QD samples do not possess the pronounced stepped form as obtained for the corresponding neutral multiexciton complexes. The negatively and the positively charged excitons (negative and positive trions) lie lower in energy as compared to a neutral exciton and a single non-interacting charge carrier in the lowest single-particle state of another quantum dot. The other charged multiexciton complexes studied are not confined with respect to the corresponding neutral multiexciton and a non-interacting charge carrier. To include the contributions from the heavy-hole light-hole (HH–LH) coupling, a perturbative treatment of the band-mixing effects was implemented. The perturbation-theory calculations show that the HH–LH coupling does not shift the energies in the present InGaAs/GaAs QD sample.     

Tunneling and reflection of an exciton incident upon a quantum heterostructure barrier

We investigate, in one spatial dimension, the quantum mechanical tunneling of an exciton incident upon a heterostructure barrier. We model the relative motion eigenstates of the exciton using a form of the one-dimensional hydrogen atom which avoids difficulties previously associated with 1D hydrogenic states. We obtain probabilities of reflection and transmission using the method of variable transmission and reflection amplitudes. Our calculations may be broadly divided into two sets. In the first set, we consider general qualitative aspects of exciton tunneling, such as the effect of different effective masses for electrons and holes and a relative difference in electron and hole barrier strengths. The second set models the tunneling of an exciton in a GaAs/Al(x)Ga(1-x)As heterostructure. In these calculations we find that, for energies such that the two lowest exciton states are coupled, the probability spectrum for transition from the ground state to the first excited state is identical to that for transition from the first excited state to the ground state. In addition, narrow peaks in the probability spectrum for transition are observed across this energy range for low dopant concentration x. Other interesting phenomena correlated with these peaks in the transition probability are reported.     

碱卤晶体中的电荷转移型激子

本文讨论碱卤晶体中的低激发电子态——电荷转移型激子(charge transfer exciton简写为CTE)。采用简并态微扰论的标准方法,研究CTE的能谱,推出CTE系统的有效哈密顿量。数值计算得到的CTE能级位置与实验测定的光吸收峰位置符合得较好。本文还得出了CTE的能带宽度和有效平移质量等物理量。 关键词：     

VPT2+K spectroscopic constants and matrix elements of the transformed vibrational Hamiltonian of a polyatomic molecule with resonances using Van Vleck perturbation theory

Vibrational levels of polyatomic molecules are analysed with Van Vleck perturbation theory to connect experimental energy levels to computed molecular potential energy surfaces. Vibrational matrix elements are calculated from a quartic potential function via second-order Van Vleck perturbation theory, a procedure that treats both weak and strong interactions among vibrational states by approximately block-diagonalising the vibrational Hamiltonian. A clear and complete derivation of anharmonic and resonance constants as well as general expressions for both on- and off-diagonal matrix elements of the transformed Hamiltonian is presented. The equations are written in partial fraction form and as a constant multiplied by a harmonic oscillator matrix element to facilitate removing the effect of strongly interacting resonant states both in analytical formulae and in computer code. The derived equations are validated numerically, and results for the isotopomers of formaldehyde (H₂CO, HDCO, D₂CO) are included. The implications of the equations on zero-point energy calculations and experimental fits are discussed. The VPT2+K method is defined by these results for use in fitting and calculating vibrational energy levels.     

Intersubband optical absorptions of a two-electron quantum ring

In this Letter, the optical properties of a quantum ring with two electrons are studied. Its effective-mass Hamiltonian matrix was diagonalized with numerical methods, followed by the calculations of a number of optical quantities. We have found that the intersubband optical absorptions strongly depends on the ring radius, electron-electron interaction, and the incident optical intensity. We also found that the spin-singlet states are more sensitive to ring radius than the spin-triplet states.     

Interaction between localized moments in dilute alloys: Correlation effects

The effect of including dynamical correlations between electrons of opposite spins in determining the ground state energy of a pair of magnetically interacting impurity atoms in an otherwise normal metal is discussed. It is found that in the ground state of such a system the spins of the magnetic impurity atoms are aligned antiparallel. In other words, the interaction between the localized states is of antiferromagnetic exchange type. This result differs sharply from that predicted by the Hartree-Fock (H-F) theory, in which the ground state of the system can be either ferro- or antiferromagnetic, depending on the energies of the spin up and spin down electrons relative to the Fermi energy. The calculations are performed using many-body Green's function techniques in thet-matrix approximation.     

Electron energy distribution function and dense-gas ionization in the presence of a strong field

The mechanism for dense-gas ionization is analyzed in the case when the deceleration of electrons by gas can be neglected in the equation of motion of a single electron. An expression for the electron energy distribution function in the presence of a strong field is derived. The characteristic width of the distribution corresponds to the energy acquired by the electron at a length determined by the inverse Townsend coefficient. The electron energy distributions are calculated for various distances form the cathode. It is demonstrated that the distribution becomes independent of the coordinate at a distance from the cathode that is significantly greater than the inverse Townsend coefficient. In this case, the distribution coincides with the distribution obtained with analytical calculations. The absence of the coordinate dependence is realized even in the presence of an extremely strong field when, in accordance with the commonly accepted point of view, the majority of electrons are runaway electrons.     

Mesoscopic effects in the quantum Hall regime

We report results of a study of (integer) quantum Hall transitions in a single or multiple Landau levels for non-interacting electrons in disordered two-dimensional systems, obtained by projecting a tight-binding Hamiltonian to the corresponding magnetic subbands. In finite-size systems, we find that mesoscopic effects often dominate, leading to apparent non-universal scaling behavior in higher Landau levels. This is because localization length, which grows exponentially with Landau level index, exceeds the system sizes amenable to the numerical study at present. When band mixing between multiple Landau levels is present, mesoscopic effects cause a crossover from a sequence of quantum Hall transitions for weak disorder to classical behavior for strong disorder. This behavior may be of relevance to experimentally observed transitions between quantum Hall states and the insulating phase at low magnetic fields.     

Solving a two-electron quantum dot model in terms of polynomial solutions of a Biconfluent Heun equation

The effects on the non-relativistic dynamics of a system compound by two electrons interacting by a Coulomb potential and with an external harmonic oscillator potential, confined to move in a two dimensional Euclidean space, are investigated. In particular, it is shown that it is possible to determine exactly and in a closed form a finite portion of the energy spectrum and the associated eigenfunctions for the Schrödinger equation describing the relative motion of the electrons, by putting it into the form of a biconfluent Heun equation. In the same framework, another set of solutions of this type can be straightforwardly obtained for the case when the two electrons are submitted also to an external constant magnetic field.     

A Note on Normal Forms of Quantum States and Separability

We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the entanglement witness is further constructed in terms of local orthogonal observables for both bipartite and multipartite systems.     

Magnetic properties of quantum dots and rings

Exact many-body methods as well as current-spin-density functional theory are used to study the magnetism and electron localization in two-dimensional quantum dots and quasi-one-dimensional quantum rings. Predictions of broken-symmetry solutions within the density functional model are confirmed by exact configuration interaction (CI) calculations: In a quantum ring the electrons localize to form an antiferromagnetic chain which can be described with a simple model Hamiltonian. In a quantum dot the magnetic field localizes the electrons as predicted with the density functional approach. Received 5 December 2000     

Flip motion of heterogeneous buckled dimers on Ge(0 0 1) by electron injection from STM tip

Surface motion of a topological defect between p(2×2) and c(4×2) structures, a “kink”, across buckled Sn-Ge and Si-Ge dimers on Ge(0 0 1) surfaces was investigated using scanning tunneling microscopy. Energy thresholds of π^∗ electrons for flipping these dimers in the kink are obtained by analyzing the kink surface motion. Electronic states of these systems and energy barriers for flipping the dimers are examined by first-principles calculations for considering elementary processes of the electronically-excited flip motion of the dimers. We propose that the flip motion is caused by a resonant scattering of the π^∗ electrons with localized electronic states at the kink.     

Absence of bound states in extremely asymmetric positive diatomic molecules

It is shown that the Hamiltonian for a diatomic molecule consisting ofN electrons and two dynamic nuclei with chargesZ ₁ andZ ₂ has no bound states if one of the charges is sufficiently large. The nuclear motion is completely unrestricted, and the kinetic energy of both nuclei can be included in the Hamiltonian. One of the nuclear charges can be arbitrarily small, provided that the other is sufficiently large.Research supported in part by NSF grant DMS-8908125     

Computational modeling of quantum-confined impact ionization in Si nanocrystals embedded in SiO2

Injected carriers from the contacts to delocalized bulk states of the oxide matrix via Fowler–Nordheim tunneling can give rise to quantum-confined impact ionization (QCII) of the nanocrystal (NC) valence electrons. This process is responsible for the creation of confined excitons in NCs, which is a key luminescence mechanism. For a realistic modeling of QCII in Si NCs, a number of tools are combined: ensemble Monte Carlo (EMC) charge transport, ab initio modeling for oxide matrix, pseudopotential NC electronic states together with the closed-form analytical expression for the Coulomb matrix element of the QCII. To characterize the transport properties of the embedding amorphous SiO₂, ab initio band structure and density of states of the α-quartz phase of SiO₂ are employed. The confined states of the Si NC are obtained by solving the atomistic pseudopotential Hamiltonian. With these ingredients, realistic modeling of the QCII process involving a SiO₂ bulk state hot carrier and the NC valence electrons is provided.     

Local density approximation in site-occupation embedding theory

ABSTRACT

Site-occupation embedding theory (SOET) is a density functional theory (DFT)-based method which aims at modelling strongly correlated electrons. It is in principle exact and applicable to model and quantum chemical Hamiltonians. The theory is presented here for the Hubbard Hamiltonian. In contrast to conventional DFT approaches, the site (or orbital) occupations are deduced in SOET from a partially interacting system consisting of one (or more) impurity site(s) and non-interacting bath sites. The correlation energy of the bath is then treated implicitly by means of a site-occupation functional. In this work, we propose a simple impurity-occupation functional approximation based on the two-level (2L) Hubbard model which is referred to as two-level impurity local density approximation (2L-ILDA). Results obtained on a prototypical uniform eight-site Hubbard ring are promising. The extension of the method to larger systems and more sophisticated model Hamiltonians is currently in progress.     

Coupled magnetoplasma and phonon systems

A long-wavelength Hamiltonian approach for coupled plasmons and polar phonons in a degenerate semiconductor with and without a uniform d.c. magnetic field is presented. Neglecting ionic motion, and with a uniform magnetic field present, a Hamiltonian is formulated for the magnetoplasma oscillations and a Hamiltonian is presented which includes the coupling between longitudinal optical phonons and collective hybrid-cyclotron plasma resonances. Canonical transformations, which put the latter Hamiltonian into second quantized diagonal form, are given. The normal modes, obtained by diagonalizing the appropriate Hamiltonian, correspond to the zeros and the infinities of the appropriate dielectric function. In analogy with the electron-phonon case, the resonances for a compensated system of coupled electrons and holes, in the presence of a uniform magnetic field, are treated by means of a Hamiltonian. The coupling in the above problems is represented by a product of two sets of plasma frequencies, the electron and ion or the electron and hole in the latter case. In all cases the coupling is independent of the magnetic field.     

Scars of periodic orbits in the stadium action billiard

Compact billiards in phase space, or action billiards, are constructed by truncating the classical Hamiltonian in the action variables. The corresponding quantum mechanical system has a finite Hamiltonian matrix. In previous papers we defined the compact analog of common billiards, i.e., straight motion in phase space followed by specular reflections at the boundaries. Computation of their quantum energy spectra establishes that their properties are exactly those of common billiards: the short-range statistics follow the known universality classes depending on the regular or chaotic nature of the motion, while the long-range fluctuations are determined by the periodic orbits. In this work we show that the eigenfunctions also follow qualitatively the general characteristics of common billiards. In particular, we show that the low-lying levels can be classified according to their nodal lines as usual and that the high excited states present scars of several short periodic orbits. Moreover, since all the eigenstates of action billiards can be computed with great accuracy, Bogomolny's semiclassical formula for the scars can also be tested successfully.     

Exact ground states of the extended Hubbard model on the Kagomé lattice

We discuss the exact plaquette-ordered ground states of the generalized Hubbard model on the Kagomé lattice for several fillings, by constructing the Hamiltonian as a sum of products of projection operators for up and down spin sectors. The obtained exact ground states are interpreted as Néel ordered states on the bond-located electrons. We determine several parameter regions of the exact ground states, and calculate the entanglement entropy. We examine the above results by numerical calculations based on exact diagonalization and density-matrix renormalization group methods.