Study Of Characteristics Of Squeezed Magnetopolarons And Electronic Band Structure

It is important to study characteristics of squeezed magnetopolarons and electronic band structure in solid state theory. There are five parts in this thesis.First, the Hamiltonian of two-dimensional magnetopolarons is dealt with squeezed states transformation, which is based on the Lee-Low-Pines and Huybrechts (LLP-H) canonical transformations. This method makes it possible to consider bilinear terms of the phonon operators as well as linear terms arising from the LLP-H transformations. The energies of the ground state and excited states are evaluated variationally. At the same time, the renormalized cyclotron masses for some possible transitions are discussed. Squeezed states transformation has the following advantages:Ⅰ. It can be used to calculate not only the ground state energy but also the excited states energies.Ⅱ. It can be applied to the entire range of the electron-phonon coupling constant. The ground state energies of magnetopolarons for different coupling constants and cyclotron frequencies have been calculated by single-mode squeezed states transformation, two-mode squeezed states transformation and LLP-H canonical transformations, respectively. It shows the magnetopolarons energy levels have been lowered. The squeezing effects are reduced as the strength of magnetic field increases. The squeezing corrections to the energy of magnetopolarons become quite large as the strength of the electron-phonon interaction increases. In addition, the two-mode squeezed states transformation gives more exact results. This method makes it possible to take account of the correlation between successively emitted virtual phonons as well as linear and bilinear forms of phonon operators.Second, some properties of magnetopolarons in two-dimensional parabolic QD (quantum dot) are investigated by two-mode squeezed states transformation. The ground state energy, the first excited states energies and the renormalized cyclotron masses for some possible transitions have been calculated. We have discussed the effects of the quantum dot and the magntic field on the characteristics of polarons, then compared the results of two-mode squeezed states transformation, single-mode squeezed states transformation and the LLP-H transformations. We find that the polaronic correction to the ground state of the electron becomes large as the electron-phonon coupling constantαincreases, and the results are qualitatively same for these three methods. Quantitatively, the polaronic enhancements are much larger for two-mode squeezed states transformation than the other two methods. It also shows that the polaronic correction to the ground state of the electron decreases deeply with the increase of the confinement length and tends asymptotically to a constant value at large value of the confinement length, which is similar for these three methods. The two-mode squeezed states transformation gives more stable state and this effect increases as the confinement length u 0 increases, and gives rise to a substantial shift in the polaronic correction for large values of the confinement length u 0.Third, the impurity magnetopolarons in two-dimensional parabolic QD have been studied using squeezed states transformation. We have considered the confinement effect of the quantum dot, the Coulomb bounding effect of the impurity and effect of the magnetic field. The polaronic corrections to the ground state have been calculated as functions of the coupling constant and the confinement strength of the quantum dot for different values of the Coulomb bounding potential. It shows the following characteristics:Ⅰ.The polaronic correction to the ground state becomes large as the electron-phonon coupling constantαincreases.Ⅱ.The polaronic correction to the ground state is much larger when the binding energy parameter takes larger values.Ⅲ.The polaronic correction to the ground state decreases deeply with the increase of the confinement length and tends asymptotically to a constant value at large value of the confinement length. In addition, we have calculated the ground state energy, the first excited states energies and the renormalized cyclotron masses versus the confinement strength and the cyclotron frequency.Fourth, we have investigated the properties of magnetobipolarons in two-dimensional parabolic QD using squeezed states transformation. The characteristics of magntobipolarons have been studied, such as the ground state energy, the first relaxed excited states energies and binding energy. We have calculated the binding energy of 2D magnetobipolarons versus certain parameters; for example, coupling constant, cyclotron frequency and the ratio of the dielectric constants. The effects of the parabolic QD and the magnetic field on the characteristics of bipolarons have been discussed. It shows that the magnetic field and the quantum dot can facilitate the stability of the bipolarons when the riatio of the dielectric constantsηis smaller than some value.Fifth, according to the effective mass theory, the magnetic Kronig-Penny potential is used to solve electronic band structure of GaAs/AlxGa1-xAs superlattice in a periodic magnetic field. Electrostatic modulation and periodic magnetostatic modulation along different directions are considered simultaneously to investigate the behavior of electrons in three dimensions. It shows that electrons not only can form some permitted bands along z direction, but also form some permitted bands along y direction. At the meantime, the characteristics of electronic band structure and its formative mechanism have been discussed in detail.