Theory of solitons, polarons and multipolarons in one dimension: An alternative formulation

TL;DR

This paper introduces a new formulation for analyzing solitons, polarons, and multipolarons in one-dimensional conducting polymers, providing exact solutions for their energies and gap functions.

Contribution

It presents an alternative real-space Green function approach to derive exact excitation energies and gap functions in quasi-one-dimensional polymers.

Findings

Exact expressions for soliton, polaron, and multipolaron energies

Self-consistent gap functions for arbitrary electron-phonon coupling

Application to cis-polyacetylene

Abstract

We develop an alternative formulation of the theory of solitons, polarons and multipolarons in quasi-one-dimensional degenerate and non-degenerate conducting polymers, starting from the continuum Hamiltonian introduced by Brazovskii and Kirova. Based on a convenient real-space representation of the electron Green function in one dimension, we present a simple method of calculating the Green function and the density of states in the presence of a single soliton or polaron defect, using which we derive exact expressions for the soliton, polaron and multipolaron excitation energies and the self-consistent gap functions for an arbitrary value of the electron-phonon coupling constant. We apply our results to $cis$-polyacetylene.