Abstract
Starting from the extensional Su-Schrieffer-Heeger model Hamiltonian containing intrachain e-e interactions, a bond-bending term, and an external Coulomb potential arising from the interchain-charged solitons and counterions, all the two-dimensional vibrational modes around the soliton lattice are calculated for doping levels from y = 3.33 at. % to y = 16.67 at. %. Thirteen localized vibrational modes are found for dopant concentrations from 3.33 to 13.33 %, in which seven modes are infrared active and correspond with the infrared absorption peaks. No localized modes have been found for doping levels above y = 16.67 at. %. In addition, the frequencies of the modes are decreased and their localizations are weakened when the dopant concentrations increase.
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