Rayleigh-Schrödinger perturbation theory for electron-phonon interaction in two dimensional quantum dots with asymmetric parabolic potential

Within the framework of the second-order Rayleigh-Schr?dinger perturbation theory, we investigate the effects of the interaction of the electron and longitudinal-optical phonons in two-dimensional semiconductive quantum dots with respect to a general potential. We propose a simple expression for the ground state energy, and compare it with those obtained by Landau-Pekar strong coupling theory. It is shown both analytically and numerically that the results obtained from the second-order Rayleigh-Schr?dinger perturbation theory could be better than those from Landau-Pekar strong coupling theory when the coupling constant is sufficiently small. Moreover, some interesting problems, such as polarons in quasi-one-dimensional quantum wires, and quasi-zero-dimensional asymmetric or symmetric quantum dots can be easily discussed only by taking different limits. After the numerical calculations, we find that there exists a simple dimensional scaling and symmetry relation for the ground state polaron energy. Furthermore, we apply our results to some weak-coupling polar semiconductors such as GaAs, CdS. It is shown that the polaronic effects are found to be quiet appreciable if the confinement lengths and smaller than a few nanometers. Received: 3 December 1997 / Revised: 6 July 1998 / Accepted: 17 September 1998     

VARIATIONAL CALCULATION ON GROUND-STATE ENERGY OF BOUND POLARONS IN PARABOLIC QUANTUM WIRES

Within the framework of Feynman path-integral variational theory, we calculate the ground-state energy of a polaron in parabolic quantum wires in the presence of a Coulomb potential. It is shown that the polaronic correction to the ground-state energy is more sensitive to the electron－phonon coupling constant than the Coulomb binding parameter, and it increases monotonically with decreasing effective wire radius. Moreover, compared to the results obtained by Feynman Haken variational path-integral theory, we obtain better results within the Feynman path-integral variational approach (FV approach). Applying our calculation to several polar semiconductor quantum wires, we find that the polaronic correction can be considerably large.     

Ground state description of bound polarons in parabolic quantum wires

The Feynman-Haken variational path integral theory is, for the first time, generalized to calculate the ground-state energy of an electron coupled simultaneously to a Coulomb potential and to a longitudinal-optical (LO) phonon field in parabolic quantum wires. It is shown that the polaronic correction to the ground-state energy is more sensitive to the electron-phonon coupling constant than the Coulomb binding parameter and monotonically stronger as the effective wire radius decreases. We apply our calculations to several semiconductor quantum wires and find that the polaronic correction can be considerably large. Received 16 November 1998     

抛物量子点中强耦合磁极化子的性质

采用Pekar类型的变分方法研究了抛物量子点中强耦合磁极化子的基态和激发态的性质。计算了基态和激发态磁极化子的束缚能以及磁极化子的共振频率。讨论了这些量对回旋频率和有效限制强度的依赖关系,以及磁极化子光学声子平均数的性质,结果表明:由于Zeeman劈裂,抛物量子点中磁极化子的回旋共振频率劈裂为两支。基态和激发态磁极化子的束缚能以及磁极化子的共振频率都随回旋频率的增加而增大,随量子点的有效束缚强度的增大而减小。     

The ground- and first-excited states of magnetopolarons in two-dimensional quantum dots for all coupling strengths

The ground- and first-excited state energies of a magnetopolaron in a two dimensional parabolic quantum dot are studied within a variational calculation for all coupling strength. The Lee-Low-Pines-Huybrecht variational technique that is developed previously for all coupling strength has been extented for polarons in a magnetic field. The dependence of the polaronic correction on the magnetic field and the confinement length is investigated. The polarization potential and the renormalized cyclotron masses as a function of electron-phonon coupling strength and the strength of both confinement potential and magnetic field are also studied within the same approach. Received 16 December 2002 / Received in final form 14 April 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: kandemir@science.ankara.edu.tr     

量子点中强耦合极化子的性质

采用Pekar类型的变分方法研究了抛物量子点中强耦合极化子的基态和激发态的性质。计算了基态和激发态极化子的结合能、光学声子平均数和极化子的共振频率。讨论了这些量对有效限制强度和电子 体纵光学声子耦合强度的依赖关系。结果表明:抛物量子点中极化子的共振频率、基态和激发态极化子的结合能以及光学声子平均数都随量子点的有效束缚强度的增大而减小。光学声子平均数随电子 体纵光学声子耦合强度的增加而增大。     

Polaronic correction to the first excited electronic energy level in an anisotropic semiconductor quantum dot

Within the framework of second-order Rayleigh-Schrödinger perturbation theory, the polaronic correction to the first excited state energy of an electron in an quantum dot with anisotropic parabolic confinements is presented. Compared with isotropic confinements, anisotropic confinements will make the degeneracy of the excited states to be totally or partly lifted. On the basis of a three-dimensional Fröhlichs Hamiltonian with anisotropic confinements, the first excited state properties in two-dimensional quantum dots as well as quantum wells and wires can also be easily obtained by taking special limits. Calculations show that the first excited polaronic effect can be considerable in small quantum dots.     

稳恒电、磁场中量子阱内极化子的基态能量

采用Ｌａｒｓｅｎ谐振子算符代数运算与变分波函数相结合的方法，研究处于与生长轴方向平行的稳恒电、磁场中量子阱内的电子——体纵光学声子相互作用系统。得到系统包括二级微扰修正的、作为量子阶宽度、电子－声子耦合常数以及电、磁场强度函数的基态能量表达式。结果表明：对电子基态能量的极化影响，随阱宽及电场强度的增大而减弱，而随磁场强度的增大而增强。 关键词：     

双量子点结构中Majorana费米子的噪声特性

Majorana费米子是其自身的反粒子, 在拓扑量子计算中有着重要的应用. 利用粒子数表象下的量子主方程方法, 研究双量子点与Majorana费米子混合结构的电子输运特性, 特别是散粒噪声. 有无Majorana费米子耦合的电流与散粒噪声存在明显差别: 有Majorana费米子耦合时稳态电流差呈反对称, 噪声谱呈现相干振荡并且低频噪声显著增强. 量子点与Majorana费米子对称弱耦合时, 零频噪声由"峰"变为"谷", 并且"边谷"展宽逐渐减小; 当对称强耦合时, 零频噪声的谷深增加, "边谷"向高频端移动. 改变系统与电极的耦合强度时, 零频噪声由谷变成峰. 因此, 稳态电流结合散粒噪声可以探测双量子点结构中Majorana费米子是否存在.     

The Properties of the Polarons’ Ground State in Coupling Spherical Quantum Dots

International Journal of Theoretical Physics - Investigations on the properties of polarons in coupling quantum dots (QDs) are useful for the designs of quantum devices and applications of QDs....     

束缚磁极化子的性质

采用线性组合算符和幺正变换方法分别导出弱、强耦合情形下束缚磁极化子的振动频率和基态能量.结果表明库仑场的存在使得磁极化子的基态能量的绝对值变小.     

Polaronic effects in asymmetric quantum wire: An all-coupling variational approach

An all-coupling variational calculation based on Lee-Low-Pines-Huybrechts (LLPH) theory is performed to study the ground state and the first excited state in an asymmetric polar semiconductor quantum wire that is valid for the entire range of the electron-phonon coupling constant and arbitrary confinement length. It is shown that the polaronic effects are very important and size dependent, if the effective width of the wire is reduced below a certain length scale. It is also shown that asymmetry in a quantum wire can be used as an extra parameter to increase the stability of the polaron. Finally the theory is applied to a realistic CdS quantum wire.     

Intersublevel transitions in self-assembled quantum dots

Intersublevel transitions in semiconductor quantum dots are transitions of a charge carrier between quantum dot confined states. In InAs/GaAs self-assembled quantum dots, optically active intersublevel transitions occur in the mid-infrared spectral range. These transitions can provide a new insight on the physics of semiconductor quantum dots and offer new opportunities to develop mid-infrared devices. A key feature characterizing intersublevel transitions is the coupling of the confined carriers to phonons. We show that the effect of the strong coupling regime for the electron–optical phonon interaction and the formation of mixed electron–phonon quasi-particles called polarons drastically affect and control the dynamical properties of quantum dots. The engineering of quantum dot relaxation rates through phonon coupling opens the route to the realization of new devices like mid-infrared polaron lasers. We finally show that the measurement of intersublevel absorption is not limited to quantum dot ensembles and that the intersublevel ultrasmall absorption of a single quantum dot can be measured with a nanometer scale resolution by using phonon emission as a signature of the absorption. To cite this article: P. Boucaud et al., C. R. Physique 9 (2008).     

Melting of a Wigner crystal in an ionic dielectric

The melting of a Wigner Crystal of electrons placed into a host polar material is examined as a function of the density and the temperature. When the coupling to the longitudinal optical modes of the host medium is turned on, the WC is progressively transformed into a polaronic Wigner crystal. We estimate the critical density for crystal melting at zero temperature using the Lindeman criterion. We show that above a certain critical value of the Fr?hlich electron-phonon coupling, the melting towards a quantum liquid of polarons is not possible, and the insulator-to-metal transition is driven by the ionization of the polarons (polaron dissociation). The phase diagram at finite temperature is obtained by making use of the same Lindeman criterion. Results are also provided in the case of an anisotropic electron band mass, showing that the scenario of polaron dissociation can be relevant in anisotropic compounds such as the superconducting cuprates at rather moderate e-ph couplings. Received 13 August 1999     

针对电子极化子迁移的哈伯德U修正受限密度泛函理论方法：TiO2实例研究

极化子的形成和迁移对过渡金属氧化物的物理和化学性质有重要影响. 含哈伯德$U$修正的密度泛函理论和受限密度泛函理论方法经常被应用于小极化子迁移性质的理论研究. 本文在投影缀加波框架中实现了哈伯德$U$修正的受限密度泛函理论(cDFT+U),并将其应用于体相TiO₂中的极化子迁移性质的计算. 确认了哈伯德U的取值对极化子性质的理论预测有重要影响. 采用基于cDFT计算所获得的哈伯德U值,可对TiO₂金红石和锐钛矿相中的极化子性质获得与实验符合很好的描述. 本文表明,使用与理论上一致的方式计算获得的哈伯德U值,cDFT+U有望成为一种有效的不需经验输入而计算过渡金属氧化物极化子性质的第一性原理方法.     

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.     

非对称量子点中弱耦合极化子的相互作用能

采用改进的线性组合算符和幺正变换方法,研究非对称量子点中弱耦合极化子的性质.导出了非对称量子点中弱耦合极化子的振动频率和相互作用能随量子点的横向和纵向有效受限长度和电子-声子耦合强度的变化关系.数值计算结果表明:非对称量子点中弱耦合极化子的振动频率和相互作用能随量子点的横向和纵向有效受限长度的减小而迅速增大,表现出奇特的量子尺寸效应.     

Polaronic behavior of undoped high-T(c) cuprate superconductors from angle-resolved photoemission spectra

We present angle-resolved photoemission spectroscopy (ARPES) data on undoped La2CuO4, indicating polaronic coupling between bosons and charge carriers. Using a shell model, we calculate the electron-phonon coupling and find that it is strong enough to give self-trapped polarons. We develop an efficient method for calculating ARPES spectra in undoped systems. Using the calculated couplings, we find the width of the phonon sideband in good agreement with experiment. We analyze reasons for the observed dependence of the width on the binding energy.     

Feasibility study of the quantum XOR gate based on coupled asymmetric semiconductor quantum dots

We propose an implementation of the quantum XOR (controlled-NOT) gate on the basis of coupledasymmetricquantum dots. Results of our numerical simulations show that the coupling constant of the dipole–dipole interaction and the probability of spontaneous emission can be tuned over a wide range by a proper choice of the potential profile, material parameters, and distances between the dots. We argue that the use of the asymmetric potential profile provides better conditions for having the Ising-type interaction between the dots than earlier proposed schemes based on regular symmetric quantum dots biased with an electric field. Our system gives better resolution of different quantum states, avoids any undesirable time evolution of these states, and can be driven with a femtosecond laser. The qubit manipulation and time coherency requirements are also discussed.