Three-dimensional effects on extended states in disordered models of polymers

TL;DR

This paper investigates how three-dimensional effects influence extended electronic states in disordered polymer models, revealing conditions under which states become delocalized despite disorder, with implications for experimental verification.

Contribution

It introduces an exactly solvable model for disordered polymers showing the emergence of extended states at specific energies due to resonant effects.

Findings

Reflection coefficient vanishes at resonant energy for dimer defects

Transmission approaches unity near resonant energy in disordered systems

Multifractal analysis confirms true extended states in the thermodynamic limit

Abstract

We study electronic transport properties of disordered polymers in the presence of both uncorrelated and short-range correlated impurities. In our procedure, the actual physical potential acting upon the electrons is replaced by a set of nonlocal separable potentials, leading to a Schr\"odinger equation that is exactly solvable in the momentum representation. We then show that the reflection coefficient of a pair of impurities placed at neighboring sites (dimer defect) vanishes for a particular resonant energy. When there is a finite number of such defects randomly distributed over the whole lattice, we find that the transmission coefficient is almost unity for states close to the resonant energy, and that those states present a very large localization length. Multifractal analysis techniques applied to very long systems demonstrate that these states are truly extended in the thermodynamic limit. These results reinforce the possibility to verify experimentally theoretical predictions about absence of localization in quasi-one-dimensional disordered systems.