Self-trapping Transition Of Acoustic Polarons In Crystal Slab

Self-trapping transition of acoustic polaron in crystal slab andthe relative problems are investigated in this paper.The Hamiltonian described the electron-acoustic phononinteraction in crystal slab is derived by Huybrechts-like variationalmethod and Gaussian wave function. The numerical results for theground-state energies and their derivatives of the acoustic polaronin crystal slabs are obtained and to be used to investigate therelative questions of self-trapping transition for acoustic polaron.It can be found that the energies are reducing with theincreasing e-p interaction constant. There appears a knee in theground-state energy or derivative with respect to the e-p interactionconstant when the e-p coupling constant increase to a critical value.The critical value is called“phase transition”point where thepolaron state transforms from the quasi-free to the self-trapped. Theproducts ofαcby k0of the acoustic polaron in slabs are alsochecked. It is obviously that theαck0for different values of cutoffwave-vectors almost tend to a given value, which had been used asa criterion for the self-trapping transition qualitatively. Theself-trapping transition tends to be difficult to be realized with theincreasing thickness of the slab.The criterion of the self-trapping transition in slab is between in that for 2D and 3D cases. So that the self-trapping transition in slab isdifficult to be realized than that in 2D case, but easier than 3D case.The results indicate that the self-trapping of the electron in AlN isexpected to be observed in crystal slab systems. For GaN slab, theself-trapping of electron is impossible to be realized.