Lattice Vibrations in trans-Polyacetylene

Abstract

We have used a selfconsistent scheme to calculate the complete phonon spectrum of the Su-Schrieffer-Heeger Hamiltonian for polyacetylene. The system may be undoped, or may contain a polaron, or a soliton-antisoliton pair, or a neutral soliton, or a charged soliton. The structure of the system may be a ring or an open-chair of finite number of atoms. In all systems which contain defect states, the optical-phonons around k = 0 get soft. Therefore, the formation of a discommensurate region upon doping can be viewed as a transition from a perfect Peierls region driven by phonon mode-softening. The vibration patterns of eigenmodes and the induced variation of electronic charge density are analyzed. The so-derived informations lead to a unified picture of the solitary electronic wavefunction and the solitary phonon wavefunction. Our results are compared with those derived by other authors, and with relevant experiments.