Self-Trapping Transition Of Acoustic Polarons In Rectangular Quantum Wires

With the development of molecular-beam epitaxy and microfabrication techniques, it is possible to produce various low-dimensional materials:such as superlattices,quantum wells,quantum wires, and quantum dots, et.al. Low-dimensional systems have not only unique physical properties,but also wider application prospects.Thus, it is important to study those systems in modern physics, material physics and developing technique. The property of quantum wires is one of the most significant fields.The investigations of the elementary excitations in these systems are very important for understanding their optical and electric properties.In this paper we study the self-trapping problems of acoustical polarons in rectangular quantum wires.According to Yu et al,who gave this rectangular quantum wires electron-phonon interaction Hamiltonian, a Huybrechts-like-approach is applied along the quantum wire, and a bound wave function is adopted in the cross section of the quantum wire to describing the electron states of self-trapping.The energies and their derivatives of acoustic polarons in rectangular quantum wire with different shapes and cross-sectional dimensions are variationally calculated,we obtain the conditions of the self-trapping transition. The results show that the critical coupling constant shifts toward the weaker e-LA-p coupling with increasing the ratio of the length to the cross-section under certain conditions of cut-off wave vectors, at constant area of the cross-section. Changing area of the cross-section, the critical value of self-trapping transition of acoustic polarons is between those in 1D and 3D systems.The less the cross section dimension of the quantum wire is, the easier of self-trapping transition of acoustic polarons occurs.