Self-Trapping of Acoustic Polaron in One Dimension

The ground-state energy and effective mass of an acoustic polaron in one
dimension are calculated by using an electron--longitudinal-acoustic-phonon interaction Hamiltonian derived here. The self-trapping of the acoustic polaron is discussed. It is found that the critical coupling constant shifts toward weaker electron--phonon interaction with the increasing cutoff wave vector and the products of the critical coupling constant by the cutoff wave vector
tend to a certain value. The self-trapping of acoustic polarons in one
dimension is easier to be realized than that in three- and two-dimensional systems. The self-trapping transition of acoustic polarons is expected to be observed in the one dimensional systems of alkali halides and wide-band-gap semiconductors.