Two-impurity scattering in quasi-one-dimensional systems

TL;DR

This paper predicts a deep narrow gap in the resistivity of quasi-one-dimensional systems caused by non-Born scattering effects at defect pairs, which is significant for multi-channel systems but not for strictly 1D systems.

Contribution

It introduces the concept of non-Born scattering effects leading to a resistivity gap in quasi-1D systems with low defect concentration.

Findings

Resistivity peaks have a deep narrow gap at their center due to non-Born effects.

Resistivity at the gap bottom scales as the square of defect concentration.

The effect is specific to multi-channel systems and absent in strictly 1D systems.

Abstract

In a quasi-one-dimensional system (a tube) with low concentration of defects $n$ the resistivity $\rho$ has peaks (van-Hove singularities) as a function of Fermi-energy. We show that due to non-Born scattering effects a deep narrow gap should appear just in the center of each peak. The resistivity at the bottom of a gap ($\rho_{\min}\propto n^2$) is dominated by scattering at rare "twin" pairs of close defects, while scattering at solitary defects is suppressed. The predicted effect is characteristic for multi-channel systems, it can not be observed in strictly one-dimensional one.