On a Self-Trapped Acoustic Polaron with the Site Diagonal and Site Off-Diagonal Electron-Phonon Interaction

By including the site off-diagonal electron-phonon interaction which is not taken into consideration in usual, self-trapped acoustic polaron is studied generally on the basis of the complete discrete model of the classical lattice. The self-consistent equations for the polaron are solved without any assumption except that the polaron in the ground state has the same symmetry as the original crystal lattice. The following facts are shown. The effect of the site off-diagonal interaction on one center trapped state makes the polaron radius large and the lattice deformation reduced and thus the polaron unstable in comparison with that of the site diagonal interaction. Moreover, the site off-diagonal interaction makes many center trapped state more favourable than one center trapped state. The stable polaron states for various cases of trapping and the stability condition for one center trapping are discussed. Brief comment for the magnetic polaron coupled with the lattice deformation is also given.