Elastic electron scattering and localization in a chain with isotopic disorder

TL;DR

This paper investigates how isotopic disorder in one-dimensional systems causes elastic electron scattering and localization, revealing mass-dependent backscattering and the formation of localized electron states.

Contribution

It introduces a tight-binding model accounting for isotope-dependent intersite hopping, highlighting the roles of impurity pairs and distances in electron localization.

Findings

Mass-dependent backscattering probability identified.

Single isotopic impurities can create weakly bound localized states.

Disorder induces finite electron mean free path and Anderson localization.

Abstract

We study elastic electron scattering and localization by ubiquitous isotopic disorder in one-dimensional systems appearing due to interaction with phonon modes localized at isotope impurities. By using a tight-binding model with intersite hopping matrix element dependent on the interatomic distance, we find mass-dependent backscattering probability by single and pairs of isotopic impurities. For the pairs, in addition to the mass, the distance between the isotopes plays the critical role. Single impurities effectively attract electrons and can produce localized weakly bound electron states. In the presence of disorder, the electron free path at positive energies becomes finite and the corresponding Anderson localization at the spatial scale greatly exceeding the distance between the impurities becomes possible.