Solitons, polarons, and excitons in polyacetylene: Step-potential model for electron-phonon coupling in π-electron systems

Christoph Kuhn
Phys. Rev. B 40, 7776 – Published 15 October 1989
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Abstract

The bond lengths in π-electron systems, determined by electron-phonon coupling, are calculated by using a simple step-potential model. The geometry of a system is obtained by finding the self-consistency between bond length and π-electron density in the middle of each bond. The model has no free parameter and leads to a satisfactory description of unsaturated hydrocarbon chains and rings and of defect states in trans-polyacetylene (kinks, polarons, bipolarons, and excitons). For defect-free trans-polyacetylene, the calculated bond-length alternation of 0.08 Å is in close agreement with x-ray data and gives a band gap of 1.34 eV. Kinks in odd-numbered systems show hyperbolic-tangent defect geometry and have an extent of 1218 sites, depending on the charge. Proceeding from negatively charged to neutral to positively charged kinks, the intergap state shifts towards the conduction band. Polarons created from the ground state by adding or subtracting one electron are bound and have an extent of 2024 sites, depending on the charge. Bipolarons created from the ground state by adding or subtracting two electrons are not bound and convert, by electron-phonon coupling, to a kink (K±) and an antikink (K¯±) pair with equal charge. Excitons created by excitation of the ground state are not bound and convert to a neutral K0K¯0 pair.

  • Received 3 February 1989

DOI:https://doi.org/10.1103/PhysRevB.40.7776

©1989 American Physical Society

Authors & Affiliations

Christoph Kuhn

  • Institut für Theoretische Physik, Eidgenössische Technische Hochschule–Zürich, CH-8093 Zürich, Switzerland

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Issue

Vol. 40, Iss. 11 — 15 October 1989

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