Self-Trapping Transition Of Acoustic Polarons In Lower Dimensional Systems

Self-trapping transition of acoustic polarons in lower dimensional systems and the relative problems are studied in this thesis.Farias et al pointed out that the critical electron-longitudinal acoustic-phonon (e-LA-p) coupling constant of the self-trapping transition of acoustic polarons in two dimensional(2D) systems is a certain value and independent of the cut-off wave vector.This conclusion is doubtful in Physics.The ground-state energy and effective mass of acoustic polarons in 2D systems are recalculated by using Huybrechts-like approach.The new self-trapping transition point is determined by a modified method. It is found that the critical point of the transition shifts toward the weaker e-LA-p coupling with increasing the cut-off wave vector.The results are qualitatively consistent with the previous works of the 3D acoustic polarons and more intelligible physically than that given by Farias et al.A new 2D e-LA-p interaction Hamiltonian is derived.The numerical results for the ground-state energy and effective mass of the acoustic polarons in 2D system and their derivatives with respect to the e-LA-p coupling constant are obtained and used to investigate the criterion of the self-trapping transition.For ease of comparison,the ground-state energies of the acoustic polarons in 3D and their derivatives are also calculated here.The 3D results agree with those obtained by using the Feynman path-integral approach.It is found that the critical coupling constant of the transition from the quasi-free state to the self-trapped state in the 2D case is much smaller than that in 3D for the given cut-off wave vector.The theory has been used to judge the possibility of the self-trapping transition for several real materials.The results indicate that the self-trappings of the electrons and light holes in A1N and the holes in GaN are expected to be observed in 2D systems.Considering the localization of the self-trapped states of acoustic polarons,the ground-state energy of the 2D acoustic poalron as a function of the e-LA-p coupling constant is investigated by using the localized Gaussian wave function.The results indicated that the Huybrechts-like approach is equivalent to the variational approach by using the Gaussian wave function.It is confirmed that the Huybrechts approach is an effective method to calculate the ground-state energies of acoustic polarons in the whole coupling range and investigate the self-trapping.The ground-state energy and effective mass of the 1D acoustic polarons are calculated by using an e-LA-p interaction Hamiltonian derived here.The first and second derivatives of the ground-state energy are calculated.The self-trapping of the acoustic polarons is discussed.It is found that the products of the critical coupling constant by the cut-off wave vector tend to a certain value.The critical coupling constant of the transition from quasi-free state to the self-trapped state in 1D case is much smaller than that in 3D and 2D systems for a given cut-off wave vector.The self-trapping transition of acoustic polarons is expected to be observed in the one dimensional systems of alkali halides and wide-band-gap semiconductors.The ground-state energies and their derivatives of the acoustic polarons in cylindrical quantum wire with different radius are variationally calculated by using the e-LA-p coupling Hamiltonian given by Yu et al.The possibility of self-trapping transition of the acoustic polarons is investigated.It is indicated that the critical coupling constant shifts toward the weaker e-LA-p coupling with increasing the cut-off wave vector.The critical value of self-trapping transition of the acoustic polarons in the quantum wire is between those in ID and 3D systems.The self-trapping transition of acoustic polarons occurs easier with decreasing the radius of the quantum wire.