Implementation of Kohn's theorem for the ellipsoidal quantum dot in the presence of external magnetic field

An electron gas in a strongly oblated ellipsoidal quantum dot with impenetrable walls in the presence of external magnetic field is considered. Influence of the walls of the quantum dot is assumed to be so strong in the direction of the minor axis (the OZ axis) that the Coulomb interaction between electrons in this direction can be neglected and considered as two-dimensional. On the basis of geometric adiabaticity we show that in the case of a few-particle gas a powerful repulsive potential of the quantum dot walls has a parabolic form and localizes the gas in the geometric center of the structure. Due to this fact, conditions occur to implement the generalized Kohn theorem for this system. The parabolic confinement potential depends on the geometry of the ellipsoid, which allows, together with the magnetic field to control resonance frequencies of transitions by changing the geometric dimensions of the QD.     

Electron energy state spin-splitting in 3D cylindrical semiconductor quantum dots

In this article we study the impact of the spin-orbit interaction on the electron quantum confinement for narrow gap semiconductor quantum dots. The model formulation includes: (1) the effective one-band Hamiltonian approximation; (2) the position- and energy-dependent quasi-particle effective mass approximation; (3) the finite hard wall confinement potential; and (4) the spin-dependent Ben Daniel-Duke boundary conditions. The Hartree-Fock approximation is also utilized for evaluating the characteristics of a two-electron quantum dot system. In our calculation, we describe the spin-orbit interaction which comes from both the spin-dependent boundary conditions and the Rashba term (for two-electron quantum dot system). It can significantly modify the electron energy spectrum for InAs semiconductor quantum dots built in the GaAs matrix. The energy state spin-splitting is strongly dependent on the dot size and reaches an experimentally measurable magnitude for relatively small dots. In addition, we have found the Coulomb interaction and the spin-splitting are suppressed in quantum dots with small height. Received 15 May 2001 / Received in final form 14 May 2002 Published online 13 August 2002     

抛物量子点中弱耦合束缚极化子的相互作用能

研究了抛物量子点中弱耦合束缚极化子的性质,采用改进的线性组合算符和幺正变换方法导出了束缚极化子的振动频率、有效质量和相互作用能。讨论了量子点的有效受限长度、电子LO声子耦合强度和库仑场对抛物量子点中弱耦合极化子的振动频率、有效质量和相互作用能的影响。数值计算结果表明:弱耦合束缚极化子的振动频率和相互作用能随有效受限长度的减少而急剧增大,振动频率随库仑势以及电子LO声子耦合强度的增加而增加,而相互作用能随库仑势以及电子LO声子耦合强度的增加而减小。有效质量仅与电子LO声子耦合强度有关。     

Electron Raman scattering of a hydrogenic impurity in a disc-shaped quantum dot

We have carried out the theoretical calculation of the differential cross section for the electron Raman scattering process associated with a hydrogenic impurity in a disc-shaped quantum dot (QD). We consider the impurity states confined in a disc-shaped QD with parabolic potential in the presence of an external electric field. Effects of the electric field and the confinement strength on the differential cross section are investigated. We make a comparison about the Raman intensity between with and without the Coulomb interaction. We found that the differential cross section of the hydrogenic impurity in a disc-shaped QD dependent strongly on the confinement strength, the external electric field intensity and the Coulomb interaction.     

Quantum dot multiexcitons in a magnetic field

Multiexcitons confined in InGaAs/GaAs quantum dots (QDs) with a lateral size slightly exceeding the exciton Bohr radius are investigated by magnetophotoluminescence spectroscopy at 2 K. The Coulomb correlations in the two-exciton complex result in an additional confinement, which increases with decreasing dot size, while a magnetic field reduces this effect. A three-exciton complex is confined only by the geometric confinement potential of the QD. The exciton-exciton repulsion increases with decreasing dot size, while a magnetic field decreases the repulsion strongly when the magnetic length becomes smaller than the lateral size of the QD. A shell model for the QD multiexciton states is proposed. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 263–268 (25 August 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Bipolaron in a quasi-0D quantum dot

Bipolaron states in a quasi-0D quantum dot with a spherical parabolic confinement potential are investigated by applying the Feynman variational principle. The bipolaron coupling energy and self-action potential energy are found to increase with an increase in the Fröhlich electron–phonon-coupling constant. There is also a non-monotonic dependence of the bipolaron coupling energy on the quantum dot radius. With decreasing structure radius the bipolaron coupling energy increases. However, from a critical radius it starts decreasing as the radius decreases, due to the dominance of the coulomb-to-phonon mediated interaction. When electrons in the bipolaron are forcefully neighboured, the polarization of the structure is intensified and consequently there is Coulomb repulsion. The possibility of bipolaron formation depends on the strength of the direct Coulomb repulsion which, in turn, depends on the quantum dot radius. The main contribution to the bipolaron coupling energy comes from the self-action potential. This self-action potential energy influences the energy state of the bipolaron considerably. The ratio of optical-to-static dielectric constants significantly affects the bipolaron coupling energy.     

On the possibility of implementation of Kohn’s theorem in the case of ellipsoidal quantum dots

An electron gas in a strongly oblated ellipsoidal quantum dot with impenetrable walls is considered. Influence of the walls of the quantum dot is assumed to be so strong in the direction of the minor axis (the OZ axis) that the Coulomb interaction between electrons in this direction can be neglected and considered as two-dimensional, coupled. On the basis of geometric adiabaticity we show that in the case of a few-particle gas a powerful repulsive potential of the quantum dot walls has a parabolic form and localizes the dot in the geometric center of the structure. Due to this fact, conditions occur to implement the generalized Kohn theorem for this system.     

Optical properties of two-electron quantum dots in low lying para- and ortho-states

Two low lying energy levels of 3D two-electron quantum dot with rigid confinement (the wave functions vanish at the surface of the quantum dot) are obtained by the variational and perturbation methods. There are two kind of quantum dots: para- and ortho-dots with antiparallel and parallel electron spins, respectively. An ensemble of the two-electron quantum dots contains para-dots in the ground state and ortho-dots in the lowest metastable state at low enough temperatures. The optical parameters of GaAs two-electron quantum dot are calculated with the help of obtained energy levels and compared with the optical parameters known for the one electron GaAs quantum dot. The Coulomb interaction between electrons is responsible for the blue shift of maxima of the absorption coefficient and refractive index of two-electron quantum dots.     

量子点中弱耦合束缚极化子的内部激发态性质

采用线性组合算符和幺正变换方法研究库仑束缚势对量子点中弱耦合束缚极化子激发态性质的影响。计算了束缚极化子的振动频率、第一内部激发态能量、激发能量和共振频率随量子点的有效受限长度,电子-声子耦合强度和库仑束缚势的变化关系。结果表明:量子点中弱耦合束缚极化子的振动频率、第一内部激发态能量、激发能量和共振频率随量子点的有效受限长度的减少而迅速增大,随库仑束缚势的增加而增大。     

Influence of the coulomb blockade effect on heat transfer in a one-dimensional system of spinless electrons

An analysis is made of some characteristics of the low-temperature thermal conductivity of a ballistic quantum dot, attributed to the influence of long-range Coulomb interaction in the geometric capacitance approximation. It is shown that at fairly low temperatures the thermal conductivity K exhibits Coulomb oscillations as a function of the electrostatic potential of the quantum dot. At the maximum of the Coulomb peak we find K ∝ T whereas at the minimum K ∝ T ³. The dependence K(T) is essentially nonmonotonic at temperatures corresponding to the characteristic spacing between the size-quantization levels in the quantum dot.     

The decoherence of the triangular and Coulomb bound potential quantum dot qubit

We study the eigenenergies and eigenfunctions of the ground and first-excited states of an electron which is strongly coupled to an LO-phonon in a quantum dot with a triangular bound potential and Coulomb bound potential by using the Pekar variational method. This system may be used as a two-level qubit. Phonon spontaneous emission causes the decoherence of the qubit. Numerical calculations are performed on the decoherence rate as a function of the polar angle, the Coulomb binding parameter, the coupling strength, the confinement length of the quantum dot and the dispersion coefficient.     

Excitation of radial collective modes in a quantum dot: Beyond linear response

The recent results on the linear breathing mode of the excitation spectrum of a quantum dot obtained by McDonald et. al [Phys. Rev. Lett. 111 , 256801 (2013)] are extended to the nonlinear regime. To accomplish this and analyze the results the response of five different models of two interacting electrons in a quantum dot to an external short lived radial excitation that is strong enough to excite the system well beyond the linear response regime is compared. The models considered describe the Coulomb interaction between the electrons in different ways ranging from mean‐field approaches to configuration interaction (CI) models, where the two‐electron Hamiltonian is diagonalized in a large truncated Fock space. The radially symmetric excitation is selected in order to severely put to test the different approaches to describe the interaction and correlations of an electron system in a nonequilibrium state. As can be expected for the case of only two electrons none of the mean‐field models can in full details reproduce the results obtained by the CI model. Nonetheless, some linear and nonlinear characteristics are reproduced reasonably well. All the models show activation of an increasing number of collective modes as the strength of the excitation is increased. By varying slightly the confinement potential of the dot it was observed how sensitive the properties of the excitation spectrum are to the Coulomb interaction and its correlation effects. In order to approach closer the question of nonlinearity one of the mean‐field models has been solved directly in a nonlinear fashion without resorting to iterations.     

抛物量子点中强耦合束缚极化子的性质

采用Pekar类型的变分方法研究了抛物量子点中强耦合束缚极化子的基态和激发态的性质。计算了束缚极化子的基态和激发态的能量、光学声子平均数。讨论了量子点的有效束缚强度和库仑束缚势对基态能量、激发态能量以及光学声子平均数的影响。数值计算结果表明:量子点中强耦合束缚极化子的基态和激发态能量及光学声子平均数均随量子点的有效束缚强度的增加而减小,基态、激发态能量随库仑束缚势的增加而减小,光学声子平均数随库仑束缚势的增加而增大。     

库仑场对量子点中强耦合束缚极化子激发态性质的影响

采用线性组合算符和幺正变换方法研究量子点中强耦合束缚极化子的振动频率、第一内部激发态能量、激发能量和共振频率的性质。讨论了这些量随量子点的有效受限长度、电子-声子耦合强度和库仑束缚势的变化关系。通过数值计算结果表明:量子点中强耦合束缚极化子的振动频率、第一内部激发态能量、激发能量和共振频率随量子点的有效受限长度的减小而迅速增大,随库仑束缚势和电子-声子的耦合强度的增加而增大。     

The effects of intense laser on nonlinear properties of shallow donor impurities in quantum dots with the Woods-Saxon potential

A theoretical study of the effects of intense laser fields on the nonlinear properties of donor impurities in a quantum dot with Woods-Saxon potential is performed within the matrix diagonalization method with the use of the effective mass approximation. The great advantage of our methodology is that it enables confinement regimes by varying two parameters in the model potential. The intense laser effects are included through the Floquet method, by modifying the confining potential associated to the heterostructure. Based on the computed energies and wave functions, the optical absorption coefficients and the refractive index between the ground state (L=0) and the first excited state (L=1) have been examined. Several configurations of the barrier height, the dot radius, the barrier slope of the confinement potential and the incident intense laser radiation have been considered. The outcome of the calculation suggests that all the factors mentioned above can influence the nonlinear optical properties strongly.     

库仑场对非对称量子点中强耦合极化子声子平均数的影响

采用线性组合算符和幺正变换方法研究库仑场对非对称量子点中强耦合极化子振动频率和声子平均数的影响。导出量子点中强耦合束缚极化子振动频率和声子平均数随量子点的横向和纵向有效受限长度,库仑束缚势和电子-声子耦合强度的变化关系。数值计算结果表明:非对称量子点中强耦合束缚极化子的振动频率和声子平均数随量子点的横向和纵向有效受限长度的减小而迅速增大。随库仑束缚势和电子-声子耦合强度的增加而增大。     

Exciton related optical absorption in a spherical quantum dot

An exciton in a spherical quantum dot is studied analytically within the effective mass approximation. A parabolic confinement under an electric field is considered. The linear and nonlinear optical absorption coefficients are calculated within the density matrix formalism. No assumptions are made about the strength of the confinement. It is shown how the competing mechanisms of the Coulomb interaction, the confinement and the applied static electric field affect the optical absorption.     

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.     

声子色散和库仑势对量子点中极化子基态能量的影响

本文在声子色散和库仑束缚势的影响下利用压缩态变分法计算了抛物量子点中弱耦合极化子的基态能量。采用的变分方法是基于逐次正则并且利用单模压缩态变换处理通常被我们所忽略的在第一次幺正变换中产生的声子产生湮灭算符的双线性项。计算得出了在考虑声子色散和库仑束缚势的情况下抛物量子点中弱耦合极化子的基态能量的数学表达式。讨论了在弱耦合情况下,受限长度,电子-声子耦合常数,色散系数,库仑结合参数与基态能量之间的依赖关系。     

Bound polaron in a two- and three-dimensional quantum dot for arbitrary electron–phonon coupling strength

A variational approach is presented for calculating the ground-state (GS) binding energies of an electron bound to a Coulomb impurity in a polar semiconductor quantum dot (QD) with parabolic confinement in both two and three dimensions. We perform calculations for the entire range of the electron-phonon coupling constant and the Coulomb binding parameter and for arbitrary confinement length. It is found that the polaronic effect is stronger in a two dimensions (2D) dot than in a three dimensions (3D) dot and this trend is more pronounced with the increase of the coupling constant. Furthermore, the GS binding energy increases with increasing the Coulomb binding parameter in both 2D and 3D QDs for the same electron–phonon coupling constant. The results also indicate that this effect becomes much more pronounced with decreasing dimensionality.