Soliton lattice in highly doped trans-polyacetylene.

Abstract

The geometrical and electronic properties of highly doped trans-polyacetylene are studied by use of a total Hamiltonian consisting of the Su-Schrieffer-Heeger Hamiltonian, describing the electron hopping along the polymer chain, an extended Hubbard term due to the intrachain electron-electron interaction, and an external Coulomb potential arising from interchain electrostatic interactions and interactions with counterions. The three-dimensional structure of the system including polymer chains and dopant ions is that obtained from x-ray crystallography studies of sodium-doped trans-polyacetylene. At all doping levels (y\ensuremath{\le}12 at. %), and for all chain lengths (100N224) included in this study, the ground-state configuration is a soliton lattice, commensurate with the periodicity of the external potential. A self-consistent treatment of the soliton charge distribution entering the external potential is essential in order to calculate the electronic properties of the system correctly. For a regular distribution of the counterions, the evolution of the single-particle gap in the electronic spectrum exhibits a sharp decrease in the gap at doping levels between y\ensuremath{\sim}8 and 10 at. %. Increasing the doping level further does not lower the gap significantly. This result indicates the possibility of having a purely electronic phase transition within the soliton-lattice configuration, in agreement with experimental data. The size of the energy gap at high doping levels is, however, in the nonmetallic regime. When disorder in the positions of the counterions is introduced, the electronic states at the soliton and conduction-band edges tail off and close the gap around the Fermi level above \ensuremath{\sim}10 at.% doping. This phenomenon occurs already at very weak (intrinsic) disorder for which the counterions are displaced by maximum one-half of a carbon-carbon bond length.