Crystallization and quantum melting of few electron system in a spherical quantum dot: quantum Monte Carlo simulation

Spherical quantum dots with a few charged Fermi particles (electrons or holes) are studied for different total spins. Simulation by quantum path integral Monte Carlo method is performed. The dependence of the electron correlations in the quantum dot is studied at different mean interelectron separation controlled by number of electrons in the quantum dot and by steepness of electron confinement (the latter parameter can be changed by the gate voltage). The ‘cold’ melting—quantum transition from Wigner crystal-like state (i.e. from regime of strongly correlated electrons) to a Fermi liquid-like state—driven by the steepness of electron confinement is studied. The pair correlation function and radial function characterizing electron quantum delocalization are analyzed.     

The Green's function of confined electrons in an external magnetic field: Analytical formulation

We derive the analytical form of the Green's function of 2-dimensional electrons with lateral confinement in a perpendicular magnetic field. The confinement potentials considered are infinite barriers at radius R (quantum dot) and at r and R (quantum ring).     

Interference of polariton waves in structures with wide GaAs/AlGaAs quantum wells

The optical reflection spectra of semiconductor GaAs/AlGaAs structures with wide quantum wells are studied experimentally. A theoretical analysis of the spectra is performed in terms of the exciton-polariton model in the approximation of quantum confinement of the exciton center of mass with regard to the contributions of both heavy and light excitons to the crystal polarization. The applicability range of the theory of the center-of-mass confinement for GaAs/AlGaAs heterostructures is estimated. It is established that, for quantum wells more than 180 nm wide, the interference effects observed in the reflection spectra of polariton waves are reproduced, to a good accuracy, by theoretical calculations based on the quantum confinement of the exciton center of mass. For quantum-well widths less than 150 nm, the experimental results are described better by the model of quantum confinement of electrons and holes.     

Induced quantum dots and wires: electron storage and delivery

We show that quantum dots and quantum wires are formed underneath metal electrodes deposited on a planar semiconductor heterostructure containing a quantum well. The confinement is due to the self-focusing mechanism of an electron wave packet interacting with the charge induced on the metal surface. Induced quantum wires guide the transfer of electrons along metal paths and induced quantum dots store the electrons in specific locations of the nanostructure. Induced dots and wires can be useful for devices operating on the electron spin. An application for a spin readout device is proposed.     

Operation of a planar Penning trap

We demonstrate experimentally the confinement of electrons in a novel planar Penning trap. Measurement of the eigenfrequencies of the trapped electron cloud exhibits similar behaviour as in conventional 3-dimensional penning traps. The trap may be of future use in quantum computing schemes using single cold electrons.     

Quantum rheology and the confinement of electrons in condensed-state nanostructures

Euler's equations for quantum rheology and the confinement of electrons in a system of active centers of nanometric scale of a condensed state are obtained using the formalism of kinematic electron-density waves. The conditions for the stability of the electron quantum walls of confinement in the form of the balance between the forces of electric and quantum nature are analyzed.E. A. Buketov Karagandinsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 60–67, August, 1994.     

Control of electron correlations in a spherical quantum dot

Spherical quantum dots containing several electrons are considered for different values of the total spin. Numerical calculations are carried out using the quantum path-integral Monte Carlo method. The dependence of the electron correlations on the dimensionless control quantum parameter q associated with the steepness of the confinement potential is studied. The quantum transition from a Wigner crystal-like state (i.e., from the regime of strongly correlated electrons) to a Fermi-liquid state (“cold” melting) driven by the parameter q is studied in detail. The behavior of the radial and pair correlation functions, which characterize quantum delocalization of the electrons, is considered.     

Hartree-Fock approximation of bipolaron state in quantum dots and wires

The bipolaronic ground state of two electrons in a spherical quantum dot or a quantum wire with parabolic boundaries is studied in the strong electron-phonon coupling regime. We introduce a variational wave function that can conveniently conform to represent alternative ground state configurations of the two electrons, namely, the bipolaronic bound state, the state of two individual polarons, and two nearby interacting polarons confined by the external potential. In the bipolaron state the electrons are found to be separated by a finite distance about a polaron size. We present the formation and stability criteria of bipolaronic phase in confined media. It is shown that the quantum dot confinement extends the domain of stability of the bipolaronic bound state of two electrons as compared to the bulk geometry, whereas the quantum wire geometry aggravates the formation of stable bipolarons.     

Rotating electrons in quantum dots: Classical limit

We solve the problem of a few electrons in a two-dimensional harmonic confinement using a quantum mechanical exact diagonalization technique, on the one hand, and classical mechanics, on the other. The quantitative agreement between the results of these two calculations suggests that, at low filling factors, all the low energy excitations of a quantum Hall liquid are classical vibrations of localized electrons. The Coriolis force plays a dominant role in determining the classical vibration frequencies.     

Magnetic field and symmetry effects in small quantum dots

Shell phenomena in small quantum dots with a few electrons under a perpendicular magnetic field are discussed within a simple model. It is shown that various kinds of shell structures, which occur at specific values for the magnetic field lead to a disappearance of the orbital magnetization for particular magic numbers for noninteracting electrons in small quantum dots. Including the Coulomb interaction between two electrons, we found that the magnetic field gives rise to dynamical symmetries of a three-dimensional axially symmetric two-electron quantum dot with a parabolic confinement. These symmetries manifest themselves as near-degeneracy in the quantum spectrum at specific values of the magnetic field and are robust at any strength of the electron-electron interaction. A remarkable agreement between experimental data and calculations exhibits the important role of the thickness for the two-electron quantum dot for analysis of ground state transitions in a perpendicular magnetic field. The text was submitted by the author in English.     

Curvature effects on surface electron states in ballistic nanostructures

The curvature effect on the electronic states of a deformed cylindrical conducting surface of variable diameter is theoretically investigated. The quantum confinement of electrons normal to the curved surface results in an effective potential energy that affects the electronic structures of the system at low-energies. This suggests the possibility that ballistic transport of electrons in low-dimensional nanostructures can be controlled by inducing a local geometric deformation.     

Asymmetric quantum dots in an applied electric field: discontinuous electron density

We consider non-interacting electrons in asymmetric quantum dots with either hard wall boundary conditions (rectangular quantum dots) or anharmonic confinement (elliptic quantum dots). In both cases, due to finite size effects, a homogeneous electric field applied along the long axis is shown to induce abrupt changes in the electron density, parallel and perpendicular to the field direction. Making use of this property, we propose a pure electrical mechanism to control the magnitude of the effective exchange interaction between two weakly-coupled quantum dots. This kind of system has been proposed recently as possible realization of quantum gates for quantum computation.     

Multi-mode transport through a quantum nanowire with two embedded dots

We investigate the conductance of a quantum wire with two embedded quantum dots using a T-matrix approach based on the Lippmann-Schwinger formalism. The quantum dots are represented by a quantum well with Gaussian shape and the wire is two-dimensional with parabolic confinement in the transverse direction. In a broad wire the transport can assume a strong nonadiabatic character and the conductance manifests effects caused by intertwined inter- and intra-dot processes that are identified by analysis of the “nearfield” probability distribution of the transported electrons.     

限域量子态调控研究

电子、激子和声子等量子态在固体中的行为早已被人们所熟知. 然而,当体系的尺寸只有纳米量级的时候,已有的固体理论常常不能适用,需要新的低维物理理论的建立. 我们系统研究了低维体系限域量子态（包括电子、激子和声子）的行为对环境、应力、压力及光的响应和性质的调控. 较早认识到低维体系之显著的表面-体积比对量子态性质调控之有效性,系统地揭示了低维体系的一系列由表面和应力决定的新颖性质,证明了低维体系的表面和应力效应同量子限域效应同等重要. 本文概况了如下五个方面的结果：（1）一种使用应力效应调控电子能带结构的方法和（2）一种使用表面效应调控电子能带结构的方法（这两个方法都可将低维体系能带从间接能隙调控至直接能隙能带结构）;（3）一种低维体系表面掺杂方法,该方法将在低维体系掺杂中取代传统方法;（4）量子点表面诱导的光致异构现象;（5）基于表面自催化半导体低维结构的形成机理. 希望我们的研究工作有助于促进低维体系在光电子、纳电子、环境、能源、生物和医学等领域的应用.     

The energy levels of a two-electron two-dimensional parabolic quantum dot

This paper studies the two-electron total energy and the energy of the electron--electron interaction by using a variational method of Pekar type on the condition of electric--LO-phonon strong coupling in a parabolic quantum dot. It considers the following three cases: 1) two electrons are in the ground state; 2) one electron is in the ground state, the other is in the first-excited state; 3) two electrons are in the first-excited state. The relations of the two-electron total energy and the energy of the electron--electron interaction on the Coulomb binding parameter, the electron-LO-phonon coupling constant and the confinement length of the quantum dot are derived in the three cases.     

Quantum crystallites and nonlinear optics

This is a review and analysis of the optical properties of quantum crystallites, with principal emphasis on the electro-optic Stark effect and all optical third order nonlinearity. There are also introductory discussions on physical size regimes, crystallite synthesis, quantum confinement theory, and linear optical properties. The experiments describe CdSe crystallites, exhibiting strong confinement of electrons and holes, and CuCl crystallites, exhibiting weak confinement of the exciton center of mass. In the CdSe system, neither the Stark effect nor the third order nonlinearity is well understood. The Stark shifts appear to be smaller than calculated, and field inducted broadening also occurs. The third order nonlinearity is only modestly stronger than in bulk material, despite theoretical prediction. Unexpectedly large homogeneous widths, due to surface carrier trapping, in the nominally discrete crystallite excited states appear to be involved. The CuCl system shows far narrower spectroscopic homogeneous widths, and corresponds more closely to an ideal quantum dot in the weak confinement limit. CuCl also exhibits exciton superradiance at low temperature. Surface chemistry and crystallite encapsulation are critical in achieving the predicted large Stark and third order optical effects in II-VI and III-V crystallites.     

Effect of the Electron—Phonon Coupling on Barrier D^— Quantum Dots in Magnetic Fields

The influence of the electron-phonon coupling of the energy of low-lying states of the barrier D^- center,which consists of a positive ion located on the z-azis at a distance from the two-dimensional quantum dot plane and two electrons in the dot plane bound by the ion,is investigated at arbitrary strength of maguetic field by mading use of the method of few-body physics.Discontinuous ground-state energy transitions induced by the magnetic field are reported.The dependence of the binding energy of the D^- ground state on the quantum dot radius is obtained.A considerable enhancement of the binding is found for the D^- ground state,which results from the confinement of electrons and electron-phonon coupling.     

Effects of Thermal Lattice Vibration on the Effective Potential of Weak-Coupling Bipolaron in a Quantum Dot

Based on the Huybrechts' linear-combination operator,effects of thermal lattice vibration on the effective potential of weak-coupling bipolaron in semiconductor quantum dots are studied by using the LLP variational method and quantum statistical theory.The results show that the absolute value of the induced potential of the bipolaron increases with increasing the electron-phonon coupling strength,but decreases with increasing the temperature and the distance of electrons,respectively;the absolute value of the effective potential increases with increasing the radius of the quantum dot,electron-phonon coupling strength and the distance of electrons,respectively,but decreases with increasing the temperature;the temperature and electron-phonon interaction have the important influence on the formation and state properties of the bipolaron:the bipolarons in the bound state are closer and more stable when the electron-phonon coupling strength is larger or the temperature is lower;the confinement potential and coulomb repulsive potential between electrons are unfavorable to the formation of bipolarons in the bound state.     

Strain-induced quantum confinement of electron gases

Zero-dimensional electron gases have been fabricated by the strain-patterning of a GaAs/AlAs heterojunction using amorphous carbon stressors. We have used steady-state, time-resolved and temperature-dependent photoluminescence measurements to probe the occupied density of states of the electron gases. We observe a novel lateral confinement mechanism and efficient transfer of modulation-doped electrons from the regions between the stressors to the quantum dots. In finite magnetic fields we have mapped the evolution of the electron states from which we estimate the number of electrons per dot to be 15.     

On the confinement potential formation in a two-electron quantum dot

A model of a quantum dot for two interacting electrons is proposed and analyzed. The properties of the ambient determining the form of the confinement potential for electrons are simulated using the electrostatic field of the image charge. Analytic expressions for the eigenvalues of each subsystem are derived taking into account the external magnetic field and using the representation of the system Hamiltonian as the sum of the Hamiltonians of the center of mass and of relative motion on the basis of the method of oscillator representation [M. Dineykhan and G. V. Efimov, Element. Chast. At. Yadra 26, 651 (1995); M. Dineykhan, G. V. Efimov, G. Ganbold, and S. N. Nedelko, Oscillator Representation in Quantum Physics, Lecture Notes in Physics, Vol. 26, Springer, Berlin (1995)]. The relative motion of electrons is responsible for a confinement potential which differs from the parabolic confinement potential and is a function of the electron effective mass as well as the characteristics of the image charge.