Linear Mode Analysis around a Soliton in Trans-Polyacetylene (CH)_x

Abstract

The eigenvalue problem for linear modes around a single soliton in the model of Takayama, Lin-Liu and Maki (a continuum version of the Su-Schrieffer-Heeger model for trans-(CH)_x) is numerically solved. Three localized modes are found. The phase shift analysis of extended phonons yields consistent results with the existence of the three localized modes and further shows that the effective potential for the extended phonons, arising due to the presence of the soliton, is reflection-less. The results obtained here can be used in the calculation of the diffusion constant of the solitons in trans-(CH)_x.