Self-trapping transition of acoustic polaron in free-standing square quantum dots

The interaction of the electron and acoustic phonon in free-standing square quantum dot systems is investigated theoretically. The electron-acoustic phonon interaction Hamiltonian is derived by taking the displacement vector's divergence of the acoustic phonon. The variational ground-state energies and their derivatives of the acoustic polaron in square quantum dot structures are numerically computed for different cutoff wave-vectors. The discriminating standards for the self-trapping transition of the acoustic polaron in square quantum dots are confirmed quantitatively. The results indicate that the self-trapping transition of the electron in wide-band-gap semiconductors and alkali halides square quantum dot structures might be occured.