A 2D electron-longitudinal-acoustic-phonon interaction Hamiltonian is derived and used to calculate the groundstate energy of the acoustic polarons in two dimensions. The numerical results for the ground-state energy of the acoustic polarons in two and three dimensions are obtained. 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 quasifree state to the self-trapped state in the 2D case is much smaller than in the 3D case for a given cutoff wave-vector. The theory has been used to judge the possibility of the self-trapping for several real materials. The results indicate that the self-trappings of the electrons in AlN and the holes in AlN and GaN are expected to be observed in 2D systems.
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