Strong-coupled electron—acoustic-phonon system in one dimension

A systematic strong-coupling perturbation theory is applied to the one-dimensional model of an electron interacting with acoustic phonons through the deformation potential. The Hamiltonian is diagonalized to the next order in the inverse coupling constant beyond the strong-coupling limit. The energy to this order involves a shift in the density of phonon modes due to the electron-phonon interaction. This shift is analyzed in terms of a phonon Green's function and is found to contain a resonance at phonon frequencies ~s/R where s is the speed of sound and R is the size of the polaron. There is also a depletion in the density of phonon modes due to the polaron, which iteself appears as a translational mode in the theory. This depletion is related to a form of Levinson's theorem.