9 A pr 1 99 9 Transport properties of the hierarchical model for stretched polymers

We prove that the hierarchical fractal model recently proposed for describing the stretched polymers [A. N. Samukhin et al, Phys. Rev. Lett. 78, 326(1997)] is equivalent to a one-dimensional chain with hierarchical aperiodic structure. By use of the transfer matrix technique we calculate the electronic transmission and the dc conductance. We find that there exist sharp-edged transmission subbands and gaps, but the transmission subbands are rich in substructures which show self-similarity. The temperature dependence of conductance g(T ) is sensitive to the variation of the Fermi level and to the structure parameters m and n of the original fractal structure. The relationship of the obtained results to the experimental data and other theoretical works is discussed. PACS numbers: 73.61.Ph,05.60.+w,71.30.+h,72.90.+y ∗E-mail: [email protected] Typeset using REVTEX 1