Two-site two-electron generalized Hubbard-Holstein model: a perturbation study

The two-site two-electron generalized Hubbard-Holstein model is studied within a perturbation method based on a variational phonon basis obtained through the modified Lang-Firsov (MLF) transformation. The ground-state wave function and the energy are found including up to the seventh and eighth order of perturbation, respectively. The convergence of the perturbation corrections to the ground state energy, as well as to the correlation functions, are investigated. The kinetic energy and the correlation functions involving charge and lattice deformations are studied as a function of electron-phonon(e-ph) coupling and electron-electron interactions for different values of the adiabaticity parameter. The simultaneous effect of the e-ph coupling and Coulomb repulsion on the kinetic energy shows interesting features.     

Effect of different site energies on polaronic properties

A two-site single polaron Holstein model is studied in presence of a difference in bare site energies (epsilon_d=epsilon₂-epsilon₁) using the perturbation theory with the variational modified Lang-Firsov (MLF) phonon basis. The polaronic ground-state wave function is calculated up to the fifth order of perturbation. The effect of epsilon_d (acts as a strength of diagonal disorder) on the polaron crossover, polaronic kinetic energy, oscillator wavefuncion and polaron localization are studied. Considering a double-exchange Holstein model with finite epsilon_d, role of disorder on the properties of the double-exchange system is also discussed.     

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.     

Variational treatment for the dynamical pseudo Jahn-Teller system

We present a variational treatment for the E × e pseudo Jahn-Teller system. Through canonical transformation the electron and phonon states are decoupled. An analytical form is obtained for the ground state energy by scaling transformation. Including both the dynamical displacement of phonon modes and the softening of phonon frequency, this approach yields fairly accurate results for the ground state energy. The energy splitting and Ham's reduction factor are calculated, which also generates fairly good results compared with other perturbation results. We argue that our variational wave function is valid for the weak and intermediate coupling range.     

Influence of Electric and Magnetic Fields on the Polaron in a Quantum Well

A combinative method of variational wavefunction and harmonic oscillator operator algebra, the ground-state energy correction to an electron confined in the quantum well of GaAs/Ga_1-xAl_x, As in the electric and magnetic fields along the growth axis has been studied by taking into account the interaction of different optical phonon modes with the electron. The ground-state energy is obtained as a function of the well width and the strength of electric and magnetic fields. The results show that the magnetic field greatly enhances the in terface-phonon part of the polaronic correction to electron ground-state energy in the well width d ≤ 300 Å. The electric field also enhances the polaron effect of interface mode, but decreases the part of bulk longitudinal mode.     

Binding energy of a polaron in asymmetric polar semiconductor heterostructures

By using a modified Lee-Low-Pines variational method, we have investigated the ground-state binding energy of a polaron confined in asymmetric single and step quantum wells (QWs) due to interface phonons, confined bulk-like LO phonons, and half-space LO phonons. The relative importance of the different phonon modes is analysed in detail. Our results show that the asymmetry and the well width of the QWs have a significant influence on the polaron energy. The polaron binding energy has an intimate relation to the potential parameters of QWs. The subband nonparabolicity has a little influence to the polaron binding energy. Comparing with the results calculated with perturbation theory, a good agreement is found.     

Polaronic effect on the binding energy of an impurity with varying position in parabolic quantum dots

The Feynman-Haken variational path integral theory is generalized to calculate the binding energy E_b of an electron coupled simultaneously to an impurity with varing position and to a longitudinal-optical (LO) phonon field in parabolic quantum dots. Our calculations are applied to some semiconductor materials and the results for the binding energy are obtained for different confinement length R of the dot and arbitrary position of the impurity. It is shown that the polaronic correction to E_b decreases with the displacement of the impurity and increases with the confinement length of the dot. More interestingly, it is not so strong as the polaronic correction to the ground-state energy of the system, and the behaviours of their variation with R are totally different.     

Polaronic effects due to surface optical vibration modes in a freestanding cylindrical wurtzite nanowire

The ground-state polaron self-trapped energy and effective mass due to the surface optical (SO) phonon modes in a freestanding wurtzite GaN nanowire (NW) were studied by means of the Lee–Low–Pines variational approach. Based on the dielectric continuum and Loudon’s uniaxial crystal models, the polar optical phonon modes in the one-dimensional (1D) systems are analyzed, and the vibrating spectra of SO modes and electron–SO phonon coupling functions are discussed and analyzed. The calculations on the ground-state polaron self-trapped energy and correction of effective mass due to the SO phonon modes in the 1D GaN NWs reveal that the polaron self-trapped energy and correction of effective mass are far larger than those in 1D GaAs NW systems. The reasons resulting in this obvious difference in the two 1D structures are mainly due to the different electron–phonon coupling constants and electron effective masses of bulk materials constituting the two types of 1D confined system. Finally, the polaronic properties of the wurtzite 1D GaN NWs have been compared with those of the wurtzite GaN-based two-dimensional quantum wells. The physical origination of these characteristics and their distinction in the different-dimensionality systems has been analyzed in depth.     

二维极化子在磁场中的基态能量

谐振子算符的代数运算方法被用于研究磁场中同时与表面光学声子及表面声学声子相互作用的二维电子。得到二维极化子在强磁场中直至四级微扰的基态能量以及它在任意强经磁场中的二级微扰基态能量表达式。结果发现,对磁场中二维极化子基态能量的影响中,表面声学声子有着与表面光学声子同样的甚至更为突出的贡献,是不容忽视的。 关键词：     

声子色散对抛物量子点中极化子基态能量的影响

在声子色散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。讨论了抛物量子点中在电子-声子弱耦合情况下,受限长度,电子-声子耦合常数,色散系数与极化子基态能量之间的依赖关系。     

嵌入量子点的介观Aharonov-Bohm环的基态与持续电流

对嵌入量子点的介观金属环进行了研究.在二级微扰变分近似下得出了其基态能量表达式和基态持续电流表达式，并在库仑排斥势趋于无穷大的假设下，得到了系统Kondo温度及持续电流的数值计算结果.并且将它们与一级微扰变分近似所得结果进行了对比，指出了它们之间存在的差异，对于这一系统二级微扰变分近似将给出更好的数值计算结果. 关键词： Kondo效应 持续电流 变分法     

表面磁极化子的光学声子平均数

采用Tokuda改进的线性组合算符、Lagrange乘子和变分法,讨论了强、弱耦合表面磁极化子的性质。计算了极化子的基态能量和光学声子平均数。以AgCl和ZnS晶体为例进行了数值计算。讨论了表面磁极化子振 动频率、基态能量和光学声子平均数与磁场B和拉格朗日乘子u的关系。     

A new variational calculation for N-dimensional polarons in the strong-coupling limit

A novel variational approach is presented for the calculation of the ground-state energy of the polaron in arbitrary N dimensions in the strong-coupling limit. By using the phonon coherent state to represent the wavefunction of phonons, a self-consistent integro-differential equation for the electron wavefunction is derived. The calculated results of the ground-state energy for N = 1, 2 and 3 agree well with the best results in the literature. It is also found that, for arbitrary N, the present results are less than the Feynman path integral ones by small percentages. It is proposed that this approach should be universal for systems involving polarons in the strong-coupling regime.     

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     

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。     

Size dependence of ground-state energy of the excitons in spherical Y2O3

The exciton energies of rare earth oxides (Ln₂O₃) have rarely been calculated by the theory. Experimentally, the blue-shift of exciton energy in nanocrystals deviates from the traditional size confinement effect. Herein, the dependence of the ground-state energy of an exciton in Y₂O₃ spheres on particle radius was calculated by using a variational method. In the model, an exciton confined in a sphere surrounded by a dielectric continuum shell was considered. The ground-state energy of exciton comprises kinetic energy, coulomb energy, polarization energy and exciton–phonon interaction energy. The kinetic and coulomb energy were considered by the effective mass and the dielectric continuum and the exciton–phonon interaction energy was given by the intermediate coupling method. The numerical results demonstrate that the present model is roughly consistent with the experimental results. The confinement effect of the kinetic energy is dominant of the blue-shift of the exciton energy in the region of R < 5 nm, while confinement effect of the coulomb energy is dominant of the blue-shift of the exciton energy in the region of R > 5 nm. The polarization energy contributes largely to the exciton energy as the particle size is smaller than ~ 10 nm, while the exciton–phonon interaction energy takes only a little contribution in all the range.     

Comment on the piezopolaron bound states in semiconductors

Following the perturbation theory of Bajaj et al. the ground state energy of a bound piezopolaron is computed for ZnS, ZnSe, ZnTe and CdTe. Extending this theory to the excited states, the L.A. phonon contributions to the Lamb-shifts in these piezoelectric semiconductors are obtained. It is found that these contributions are smaller by seven to eight orders when compared to the L.O. phonon contributions.     

On improvable bounds for polaron systems in an external potential

A variational approach is proposed that allows one to obtain in a regular way a sequence of improvable upper bounds for the ground-state energy of various polaron models confined in an external electrostatic potential. The proposed approach can be used for an arbitrary electron–phonon interaction constant and allows generalization to the case of polaron-type systems in a constant external magnetic field.     

Energy and effective mass of a polaron in asymmetric semiconductor quantum well structures

In this paper, the correct electron extended states wave functions and the density of states in asymmetric single quantum wells (QWs) are given for the first time, we put right mistakes from some previous papers of some other authors. Within the framework of the secondorder perturbation theory, the ground-state polaron binding energy and effective mass correction in asymmetric single QWs are studied including the full energy specturm, i.e., the discrete energy levels in the well and the continuum energy spectrum above the barrier, and all possible optical-phonon modes. The effects of the finite electronic confinement potential and the subband nonparabolicity are considered. The relative importance of the different phonon modes is investigated. Our results show that the polaron energy and effective mass are sensitive to the asymmetry of the structure and have a close relation to the interface phonon dispersion. When well width and one side barrier height of asymmetric QWs are fixed and identical with those of symmetric QW, the polaron binding energy and effective mass in asymmetric QWs are always less than those in symmetric QW. It is necessary to include the continuum energy spectrum as intermediate states in the study of polaron effects in QWs in order to obtain the correct results. The subband non-parabolicity has little influence on the polaron effects. The polaron energies given in this paper are excellent agreement with our variational results.     

Magnetpolaron effect in two-dimensional anisotropic parabolic quantum dot in a perpendicular magnetic field

We study the two-dimensional weak-coupling Fr o¨hlich polaron in a completely anisotropic quantum dot in a perpendicular magnetic field. By performing a unitary transformation, we first transform the Hamiltonian into a new one which describes an anisotropic harmonic oscillator with new mass and trapping frequencies interacting with the same phonon bath but with different interaction form and strength. Then employing the second-order Rayleigh–Schr o¨dinger perturbation theory, we obtain the polaron correction to the ground-state energy. The magnetic field and anisotropic effects on the polaron correction to the ground-state energy are discussed.