Elastic electron scattering and localization in a chain with isotopic disorder

We study elastic electron scattering and localization by ubiquitous isotopic disorder in one-dimensional systems appearing due to an interaction with phonon modes localized at the isotope impurities. By using a tight-binding model with an intersite hopping matrix element dependent on the interatomic distance, we find a 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 a 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.