Quantum entanglement transition in vertically coupled two single-electron quantum dots with charged impurity

Effects of a charged impurity on the ground state of two vertically coupled identical single-electron quantum dots with and without applied magnetic field are investigated. In the absence of the magnetic field, the investigations of the charged impurity effect on the quantum entanglement (QE) in some low-lying states are carried out. It is found that, both the positive charged impurity (PCI) and the negative charged impurity (NCI)reduce the QE in the low-lying states under consideration except that the QE in the ground state is enhanced by the NCI. Additionally, in the domain of B from 0 Tesla to 15 Tesla, the ground state energy E, the ground state angular momentum L and the ground state QE entropy S are worked out. As far as the ground state are concerned, the PCI (NCI) blocks (induces) the angular momentum phase transition and the QE phase transition besides the known fact (i. e., the PCI/NCI decreases/increases the energy) in the magnetic field.     

Four-Electron Systems in a Coupled Double-Layer Quantum Dots

Making use of the method of few-body physics, the energy spectrum of a four-electron system consisting in a vertically coupled double-layer quantum dot as a function of the strength ofa magnetic field is investigated. Discontinuous ground-state transitions induced by an external magnetic field are shown. We find that, in the strong coupling case, the ground-state transitions depend not only on the external magnetic field B but also on the distance d between double-layer quantum dots. However, in the case of weak coupling, the ground-state transitions occur in the new sequence of the values of the magic angular momentum. Hence, the interlayer separation d and electron-electron interaction strongly affect the ground state of the coupled quantum dots.     

Vortex formation in quantum dots in high magnetic fields

We study electronic structures of two-dimensional quantum dots in high magnetic fields using the density-functional theory (DFT) and the exact diagonalization (ED). With increasing magnetic field, beyond the formation of the totally spin-polarized maximum density droplet (MDD) state, the DFT gives the ground-state total angular momentum as a continuous function with well-defined plateaus. The plateaus agree well with the magic angular momenta of the ED calculation. By constructing a conditional wave function from the Kohn–Sham states we show that vortices enter the quantum dot one-by-one at the transition to the state with the adjacent magic angular momentum. Vortices are also observed outside the high-density region of the quantum dot. These findings are compared to the ED results and we report a significant agreement. We also study interpretations and limitations of the density functional approach in these calculations.     

Multiband calculation of exciton diamagnetic shift in InP/InGaP self-assembled quantum dots

Exciton states in self-assembled InP/In_0.49Ga_0.51P quantum dots subject to magnetic fields up to 50 T are calculated. Strain and band mixing are explicitly taken into account in the single-particle models of the electronic structure, while an exact diagonalization approach is adopted to compute the exciton states. Reasonably good agreement with magneto-photoluminescence measurements on InP self-assembled quantum dots is found. As a result of the polarization and angular momentum sensitive selection rules, the exciton ground state is dark. For in-plane polarized light, the magnetic field barely affects the exciton spatial localization, and consequently the exciton oscillator strength for recombination increases only slightly with increasing field. For z polarized light, a sharp increase of the oscillator strength beyond 30 T is found which is attributed to the enhanced s character of the relevant portion of the exciton wave function.     

Quantum dot version of topological phase: Half-integer orbital angular momenta

We show that there exists a topological phase equal to π for circular quantum dots with an odd number of electrons. The non-zero value of the topological phase is explained by axial symmetry and two-dimensionality of the system. Its particular value (π) is fixed by the Pauli exclusion principle and leads to half-integer values for the eigenvalues of the orbital angular momentum. Our conclusions agree with the experimental results of T. Schmidt et al., Phys. Rev. B 51, 5570 (1995), which can be considered as the first experimental evidence for the existence of the new topological phase and half-integer quantization of the orbital angular momentum in a system of an odd number of electrons in circular quantum dots. The article is published in the original.     

磁场中量子点四电子系统的基态性质

利用少体物理的方法，研究了磁场中二维量子点四电子系统基态能量与角动量间的变化关系，以及磁场强度和约束势的大小对四电子系统基态的影响.数值计算表明，量子力学对称性是幻数角动量出现的重要因素. 关键词：     

Half-polarized quantum hall states

We report a theoretical analysis of the half-polarized quantum Hall states observed in a recent experiment. Our numerical results indicate that the ground state energy of the quantum Hall nu = 2 / 3 and nu = 2 / 5 states versus spin polarization has a downward cusp at half the maximal spin polarization. We map the two-component fermion system onto a system of excitons and describe the ground state as a liquid state of excitons with nonzero values of exciton angular momentum.     

Mapping of the hole wave functions of self-assembled InAs-quantum dots by magneto-capacitance–voltage spectroscopy

We have performed magneto-capacitance–voltage spectroscopy for the valence band states of InAs quantum dots embedded in a p-type Schottky diode. By choosing the right measurement frequency and applying an in-plane magnetic field, we were able to map the k-space wave functions corresponding to the individual charging peaks. The wave functions belonging to the first two charging peaks show no nodes as expected for an s-like ground state. In contrast, nodes are observed for the next four charging peaks supporting the identification as excited states with finite orbital angular momentum. Peaks 3 and 4 show different wave functions compared to peaks 5 and 6, which points to different angular momenta for this two pairs of charging peaks.     

Barrier Li Quantum Dots in Magnetic Fields

The methods for the few-body system are introduced to investigate the states of the barrier Li quantum dots (QDs) in an arbitrary strength of magnetic field. The configuration, which consists of a positive ion located on the z-axis at a distaneed from the two-dimensional QD plane (the x-y plane) and three electrons in the dot plane bound by the positive ion, is called a barrier Li center. The system, which consists of three electrons in the dot plane bound by the ion,is called a barrier Li QD. The dependence of energy of the state of the barrier Li QD on an external magnetic field B and the distance d is obtained. The angular momentum L of the ground states is found to jump not only with the variation orB but also with d.     

Magnetic quantum ring in two-dimensional topological insulators

The quantum properties of topological insulator magnetic quantum rings formed by inhomogeneous magnetic fields are investigated using a series expansion method for the modified Dirac equation. Cycloid-like and snake-like magnetic edge states are respectively found in the bulk gap for the normal and inverted magnetic field profiles. The energy spectra, current densities and classical trajectories of the magnetic edge states are discussed in detail. The bulk band inversion is found to manifest itself through the angular momentum transition in the ground state for the cycloid-like states and the resonance tunneling effect for the snake-like states.     

Zeeman effect and magnetic anomalies in narrow-gap semiconductor quantum dots

We present a systematic theoretical study, based on the Kane–Weiler 8×8 k·p model, of the linear Zeeman splitting introduced by the interaction between the angular momentum and the magnetic field which can give a measure of the non-linear Zeeman effect associated with interband coupling and diamagnetic contributions. The conduction and valence bands g-factors are calculated for InSb spherical and semi-spherical quantum dots. The calculations of the g-factors showed an almost linear dependence, for the ground state, on the magnetic field. We have also found that the strong magnetic field dependence as well as the dependence on the dot size of the effective spin splitting can be unambiguously attributed to the strength of the inter-level mixing.     

量子盘三电子系统的基态性质

用少体物理的方法，研究了磁场中量子盘三电子系统极化态的基态能量和盘厚之间的关系.随着量子盘厚度的增加，三电子系统中的幻数角动量态即分数量子霍耳效应态将不再出现.结果还表明，幻数角动量消失的量子盘厚度随磁场强度的增加而减小. 关键词：     

Raising and Lowering Operators for Orbital Angular Momentum Quantum Numbers

Two vector operators aimed at shifting orbital angular momentum quantum number l successfully constructed based on the primary form proposed by Prof. X.L. Ka in 2001. The lowering operators can give the lowest angular momentum quantum numbers l for a given magnetic quantum number m in spherical harmonics |lm〉; and the state with minimum angular momentum quantum number in whole set of the spherical harmonics turns out to be |0,0〉. How to use the raising and lowering operators as acting on the state |0,0〉. to generate whole set of spherical harmonics is illustrated.     

A Discrete Density Matrix Theory for Atoms¶in Strong Magnetic Fields

This paper concerns the asymptotic ground state properties of heavy atoms in strong, homogeneous magnetic fields. In the limit when the nuclear charge Z tends to ∞ with the magnetic field B satisfying B>> Z ^4/3 all the electrons are confined to the lowest Landau band. We consider here an energy functional, whose variable is a sequence of one-dimensional density matrices corresponding to different angular momentum functions in the lowest Landau band. We study this functional in detail and derive various interesting properties, which are compared with the density matrix (DM) theory introduced by Lieb, Solovej and Yngvason. In contrast to the DM theory the variable perpendicular to the field is replaced by the discrete angular momentum quantum numbers. Hence we call the new functional a discrete density matrix (DDM) functional. We relate this DDM theory to the lowest Landau band quantum mechanics and show that it reproduces correctly the ground state energy apart from errors due to the indirect part of the Coulomb interaction energy. Received: 20 October 2000 / Accepted: 3 November 2000     

On a relation of the angular frequency to the Aharonov–Casher geometric phase in a quantum dot

By analysing the behaviour of a neutral particle with permanent magnetic dipole moment confined to a quantum dot in the presence of a radial electric field, Coulomb-type and linear confining potentials, then, an Aharonov–Bohm-type effect for bound states and a dependence of the angular frequency of the system on the Aharonov–Casher geometric phase and the quantum numbers associated with the radial modes, the angular momentum and the spin are obtained. In particular, the possible values of the angular frequency and the persistent spin currents associated with the ground state are investigated in two different cases.     

Spectroscopy of nanoscopic semiconductor rings

Making use of self-assembly techniques, we realize nanoscopic semiconductor quantum rings in which the electronic states are in the true quantum limit. We employ two complementary spectroscopic techniques to investigate both the ground states and the excitations of these rings. Applying a magnetic field perpendicular to the plane of the rings, we find that, when approximately one flux quantum threads the interior of each ring, a change in the ground state from angular momentum l = 0 to l = -1 takes place. This ground state transition is revealed both by a drastic modification of the excitation spectrum and by a change in the magnetic-field dispersion of the single-electron charging energy.     

CORRELATION EFFECTS ON THE GROUNDSTATES OF THREE-ELECTRON QUANTUM DOTS IN A STRONG MAGNETIC FIELD

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Two Interacting Electrons in a Vertically Coupled Quantum Dot

We study a two-electron system in a double-layer quantum dot under a magnetic field by means of the exact diagonalization of the Hamiltonian matrix.We find that discontinuous ground-state energy transitions are induced by an external magnetic field in the case of strong coupling.However,in the case of weak coupling,the angular momentum L of the true ground state does not change in accordance with the change of the magnetic field B and remains L=0.     

Planar Dirac electrons in magnetic quantum dots

In this paper, we explore the size- and mass-dependent energy spectra and the electronic correlation of two- and three-electron graphene magnetic quantum dots. It is found that only the magnetic dots with large size can well confine the electrons. For large graphene magnetic dots with massless (ultra-relativity) electrons, the energy level structures of two Dirac electrons and even the ground state spin and angular momentum of three electrons are quite different from those of the usual semiconductor quantum dots. Also we reveal that such differences are not due to the magnetic confinement but originate from the character of the Coulomb interaction of two-component electronic wavefunctions in graphene. We reveal that the increase of the mass leads to both the crossover of the energy spectrum structures from the ultra-relativity to non-relativity ones and the increasing of the crystallization. The results are helpful for the understanding of the mass and size effects and may be useful in controlling the few-electron states in graphene-based nanodevices.