Describing a T with Shengs Formula

The nature of the mechanism that leads to the low-temperature deviations of the experimental curve from the Sheng fit is yet unknown. One possible explanation is based on the idea that the areas of metallic conductivity are of finite size /23/. As polyacetylene with oriented chains can be regarded as a quasi-onedimensional system, the consequences of this fact on the conductivity are discussed in this and the following chapter for the one-dimensional and the three-dimensional case. 

If due to the finite size of the metallic system, only a finite number of states contribute to an energy band, we get a finite level spacing between neighbouring energy levels within a band. If this energy difference AE of 

For strictly onedimensional systems, this effect of localization due to level spacing would therefore be too large to explain the experimentally observed low-temperature conductivities with reasonable values of the conjugation lengths. We conclude that the approach of treating polyacetylene as a strictly one-dimensional system is not allowed and that three-dimensional coupling is important. For the three-dimensional case we obtain  

To get samples with a significantly higher conductivity, it is necessary to reduce the resistivity of the regions between the barriers. This should be possible, as a comparison with less conducting samples indicates that phonon scattering does not have a strong influence on or(300 K).  

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