Based on the variational method of Pekar type, we study the energies and the wave-functions of the ground and the first-excited states of magneto-bipolaron, which is strongly coupled to the LO phonon in a parabolic potential quantum dot under an applied magnetic field, thus built up a quantum dot magneto-bipolaron qubit. The results show that the oscillation period of the probability density of the two electrons in the qubit decreases with increasing electron-phonon coupling strength α, resonant frequency of the magnetic field ω c , confinement strength of the quantum dot ω 0 , and dielectric constant ratio of the medium η; the probability density of the two electrons in the qubit oscillates periodically with increasing time t, angular coordinate ϕ 2 , and dielectric constant ratio of the medium η; the probability of electron appearing near the center of the quantum dot is larger, and the probability of electron appearing away from the center of the quantum dot is much smaller.

The influence of polaron effects on the effective potential of weak-coupling exciton in semiconductor quantum dots (QDs) is studied based on the Lee-Low-Pines-Huybrechts variational method. The results show that the effective potential of the exciton consists of three parts: coulomb potential, induced potential and confining potential. Numerical calculations for the GaAs quantum dot, as an example, are performed. The result indicates that the effective potential of the exciton increases with the electron-hole distance. It is found that the polaron effects have remarkable influence on the states of the exciton: helpful to the stability of the light-hole exciton, but unfavorable to the stability of the heavy-hole exciton.The exciton effects have significant influence on the physical processes (such as optical absorption, luminescence, lasing, optical non-linear action and so on) in semiconductors and have an important application in the research and development of semiconductor optoelectronic devices. In the quantized low-dimensional electronic structure, especially in the quantum dot (QD) structure under three-dimensional (3D) confinement, it has been found experimentally that the binding energy of the exciton is much larger than that in 3D semiconductor materials, and the exciton effects become more strong and stable under higher temperature or electric field [1][2][3] . To theoretically explain the optical experimental results of the QD, the exciton theory of the QD was developed. Hui [4] studied the effect of dielectric constant on the exciton , s ground-state energy of CdSe quantum dots based on the effective mass approximation model. Zhang et al. [5] solved the ground state of excitons confined in spherical core-shell quantum-dot quantum-well nanoparticles using the stochastic variational method. Dong et al. [6] studied the exciton states in vertically stacked self-assembled quantum disks by the effective mass approximation. Xie [7] discussed an exciton trapped by a Gaussian confining potential QD by means of the method of numerical diagonalization of Hamiltonian in the effective-mass approximation. Dou et al. [8] studied the size dependence of biexciton binding energy in a single QD using an atomic force microscopy and micro-photoluminescence measurements. Furthermore, Liu et al. [9] investigated the influence of spin on the properties of strong coupling magnetopolarons in semiconductor quantum dots. In this paper, the influence of polaron effects on the ground state of weakcoupling exciton in semiconductor QDs is studied based on the Lee-Low-Pines-Huybrechts variational method for the first time. The results indicate that the polaron effects have remarkable influence on the states of the exciton. This work can provide some references to explain the photoelectric properties of QDs. We consider an exciton bound in a parabolic QD within the effective mass approximation, and the Frolich Hamiltonian of the interaction system among electrons, holes and longitudinal optical (LO) phonons can be written as where R a...

On the basis of Lee-Low-Pines unitary transformation, the properties of strong-coupling magnetopolarons in quantum disks (QDs) induced by the Rashba spin-orbit interaction are studied using the Tokuda improved linearly combined operator method. Results show that the state properties of magnetopolarons are closely linked with the sign of the interaction energy Eint, and the Eint of magnetopolarons changes with the transverse confinement strength 0, the cyclotron frequency of the external magnetic field c, the electron-LO phonon coupling strength , and the thickness L of QDs. The average number N of phonons increases with increasing c, 0 and , but the oscillation decreases with increasing thickness L of QDs. The effective mass m0* of magnetopolarons splits into two (m+*, m-*), induced by the Rashba spin-orbit interaction, and the values of them increase with increasing c, 0 and , but the oscillation decreases with increasing thickness L of QDs. For the ground state of magnetopolarons in QDs, the electron-LO phonon interaction plays a significant role, meanwhile, the Rashba spin-orbit coupling effect cannot be ignored. Only for the lower volocity of the electrons, can the polaron effect and the Rashba spin-orbit interaction effect on the magnetopolaron be obvious.

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.

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