Self-trapping Transition Of Acoustic Polarons In Free-standing Quantum Wells

With the speed development of nanotechnology,low-dimensional system has been studied by more and more people. According to the current technical level, materials of low-dimensional semiconductor quantum structure, such as quantum wires, quantum wells and quantum dots of good performance has been made today. In this structure, the electron is confined and the phonons subsystem will undergo modification. This special structure make it different with bulk materials in some performance, for example photoelectrical properties and transport properties of energy etc. For this reason, materials about low-dimensional semiconductor quantum structure has caused more people’s interests.The electron-longitudinal phonon(e-lp) interaction is one of the influences on physical properties of materials about low-dimensional semiconductor quantum structure. In this paper, we study on the self-trapping transition of acoustic polarons(formed by electron-phonon interaction) in free-standing quantum wells. We using Huybrechts-like variational method, by means of electron-phonon interaction Hamiltonian in free-standing quantum wells, applying two unitary transformations, and introducing linear operator about coordinate and momentum. The numerical results for the ground-state energies and their derivatives of the acoustic polaron in free-standing quantum wells are obtained and to be used to investigate the relative questions of self-trapping transition for acoustic polaron.The research results show that the energies are reducing with the increasing e-lp interaction constant. There appears a knee in the ground-state energy or derivative with respect to the e-lp interaction constant when the e-p coupling constant increase to a critical value. It is found that the critical coupling constant for the discontinuous transition from a quasi-free state to a trapped state of the acoustic polaron in free-standing quantum wells tends to shift toward the weaker electron-phonon coupling with the increasing cutoff wave-vector. The products of ac by q0 of the acoustic polaron in free-standing quantum wells, are also checked. It is obviously that the acq0 for different values of cutoff wave-vectors almost tend to a given value, which had been used as a criterion for the self-trapping transition qualitatively. The degree of difficulty of self-trapping transition of the acoustic polarons in free-standing quantum wells is between those in two-dimensional and three-dimensional systems. The self-trapping transition of the acoustic polarons occurs more difficult with increasing the width of the free-standing quantum wells. It is found that the self-trapping of acoustic polarons is related to the material itself (Lame constants).We use the criterion for the self-trapping transition in free-standing quantum wells to judge the self-trapping transition of acoustic polarons in actual materials theoretically. The results indicate that the self-trapping of acoustic polarons of AIN in free-standing quantum wells is expected to be observed. But the self-trapping of acoustic polarons of GaN and alkali-halide in free-standing quantum wells is difficult to be realized.