Optical absorption of a soliton lattice and applications totrans-polyacetylene

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Abstract
X-ray measurements and electrochemical data have established that doping of trans-polyacetylene with more than ∼0.5 at. % of an alkali metal results in ordered phases. On the evidence of very low spin susceptibility up to ∼6 at. %-Na doping, the ordered phase is a regular array of solitons, i.e., a soliton lattice. We have calculated the optical conductivity of such a soliton lattice employing the correct electronic band structure and wave functions. In contrast to earlier calculations we find that the matrix element vanishes for transitions to the conduction band from the valence band and the lower half of the soliton band; the vanishing is due to the order parameter changing sign after half a soliton-lattice period. The integrals for the optical absorption due to transitions from the upper half of the soliton band to the conduction band were evaluated numerically for the impurity concentration, corresponding to the ordered phase for Na doping, 6.67 at. %, or a soliton-lattice period of 15 trans-polyacetylene lattice constants. The resulting absorption consists of two sharp peaks, a singular one due to transitions between the edges of the soliton and conduction bands and a second due to transitions from the center of the soliton band to an almost parallel region in wave-vector space of the conduction band. We show that the sum rule is satisfied despite the suppression of the valence-band to conduction-band transitions. To compare with experimental data it is necessary to add the contributions of the highly doped ordered portion of the sample to the essentially undoped portion. The results account for the observation that the valence-band to conduction-band transition does not go to higher energy with doping, as predicted by earlier theories. Although we have not done detailed calculations taking into account the many effects that remove the singularities and smear out the absorption for an actual sample, it is clear that our theory can account for the very broad midgap absorption observed at even the lowest doping concentrations.