Continuum models for solitons in one-dimensional systems with Peierls' gap and commensurability 3

Continuum solutions of the Su-Schrieffer-Heeger model [Phys. Rev. B 22, 2099 (1980)] of Peierls' chain with uniform and soliton kink structure are presented in the mean-field approximation neglecting electron-electron interactions and for classical ion-displacement fields. The trimerized case is presented in detail, and the general commensurability-M case is outlined. For $M=3$ the results agree in all essential features with Su and Schrieffer's studies [Phys. Rev. Lett. 46, 738 (1981)]. We find fractionally charged solitons. The soliton shape, and charge and spin distributions, depend significantly on its net charge state. We also find that some solitons are energetically unstable against breakup into pairs.