Amplitude and phase modes in trans-polyacetylene: Resonant Raman scattering and induced infrared activity.

The resonant Raman scattering (RRS) from the three ${A}_{g}$ modes of trans-polyacetylene and the charged-induced ir modes are analyzed with use of the amplitude- and phase-mode theories. It is shown that the observed phonon frequencies and the relative intensities of all modes obtained at various laser excitation energies \ensuremath{\Elzxh}${\ensuremath{\omega}}_{L}$ is accounted for by a single phonon propagator which also describes the charge-induced infrared-active modes. The dispersion of the RRS frequencies with \ensuremath{\Elzxh}${\ensuremath{\omega}}_{L}$ exhibits inhomogeneity of the sample which in turn provides the functional dependence of the \ensuremath{\pi}-electron gap ${E}_{g}$ on an effective coupling parameter \ensuremath{\lambda}\ifmmode \tilde{}\else \~{}\fi{}. We show that inhomogeneity in both the electron-phonon and the electron-electron interaction parameters yields inhomogeneity in \ensuremath{\lambda}\ifmmode \tilde{}\else \~{}\fi{}. The experimental gap-versus-\ensuremath{\lambda}\ifmmode \tilde{}\else \~{}\fi{} relation is consistent with the Peierls model but allows for weak electron-electron interactions which enhance the gap. We propose a method by which the distribution in \ensuremath{\lambda}\ifmmode \tilde{}\else \~{}\fi{}, P(\ensuremath{\lambda}\ifmmode \tilde{}\else \~{}\fi{}), is directly derived from the experimental spectra. It appears that different samples show different breadth for the distribution function; samples with sharper RRS features have narrower P(\ensuremath{\lambda}\ifmmode \tilde{}\else \~{}\fi{}). We give an experimental estimate of the \ensuremath{\sigma}-bond contribution to the force constant of the carbon-carbon stretching mode and the electron-phonon interaction parameter. The pinning parameter of the charged carriers and its distribution are derived directly from the infrared absorption spectra induced either by doping or by photogeneration. The pinning of the doping-induced carriers is stronger and its distribution is wider; giving thus rise to the broader lines in the doping-induced infrared spectra. The mass of the photogenerated solitons is estimated from the relative strength of the infrared spectra and is approximately equal to the band effective mass of the electrons.