Transport properties of the hierarchical model for stretched polymers

TL;DR

This paper models stretched polymers as a hierarchical aperiodic chain, analyzing their electronic transport properties, revealing self-similar transmission subbands and temperature-dependent conductance sensitive to structural parameters.

Contribution

It establishes the equivalence of a hierarchical fractal model for polymers to a one-dimensional chain and calculates its transport properties using transfer matrix techniques.

Findings

Existence of sharp-edged transmission subbands and gaps.

Self-similar substructures within transmission bands.

Conductance varies with temperature and Fermi level, influenced by fractal parameters.

Abstract

We prove that the hierarchical fractal model recently proposed for describing the stretched polymers [A. N. Samukhin et al, Phys. Rev. Lett.{\bf 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.