Anomalous Transmission in a Hierarchical Lattice
Abstract
We present an analytical method of studying "extended" electronic eigenstates of a diamond hierarchical lattice, which may be taken as the simplest of the hierarchical models recently proposed for stretched polymers. We use intuitive arguments and a renormalization-group method to determine the distribution of amplitudes of the wave functions corresponding to some of these "extended" eigenstates. An exact analysis of the end-to-end transmission property of arbitrarily large finite lattices reveals an anomalous behavoiur. It is seen that while for a special value of the energy the lattice, however large, becomes completely transparent to an incoming electron, for the other energy eigenvalues the transmission decreases with system size. For one such energy eigenvalue we analytically obtain the precise scaling form of the transmission coefficient. The same method can easily be adopted for other energies.
Keywords
Cite
@article{arxiv.cond-mat/0001237,
title = {Anomalous Transmission in a Hierarchical Lattice},
author = {Anirban Chakraborti and Bibhas Bhattacharyya and Arunava Chakrabarti},
journal= {arXiv preprint arXiv:cond-mat/0001237},
year = {2009}
}
Comments
15 pages, 6 figures. To be published in Physical Review B