Isotope Effect on the Formation Energy of Soliton in t - Polyacetylene

The formation energy of a soliton was derived in the TLM model to be 2∆ 0 /π which is independent of the masses of the polymer atoms. We estimate effects of the electron-phonon coupling on the soliton formation energy, particularly, through modifications of the harmonic oscillations of (CH) groups. A model based on the amplitude mode formalism is used and the electron-phonon coupling is taken into account to make the effective potential of lattice vibration. Among dynamical degrees of freedom in the lattice vibration, a trans-lational mode of the soliton is separately examined, since it corresponds to a zero-energy mode. We get a difference in the formation energy between the two isotopes of about 0.03eV. Soliton trapping around defects or impurities changes the formation energy and enlarges the isotope difference. §1 Introduction The trans-polyacetylene is an ideal material which has excitations such as solitons, polaron, bipolaron, and so on. They can be described very well by the SSH model which was proposed by Su et al. 1) This model contains the electron phonon interaction in addition to electron hopping and lattice vibrations. Takayama et al. 2) made the TLM model which is a continuum version of the SSH model. It makes the analytical study of polyacetylene possible. A number of experimental studies have supported the presence of a kink excitation in t-polyacetylene (t-(CH) x). 3)−6) Suzuki et al. have reported an optical absorption measurement in lightly doped polyacetylene. 5) They have found that the absorption related to the electronic mid-gap state is enhanced by doping. This result has been interpreted as transitions between the mid-gap levels of solitons, induced by the doping, and the conduction band.