The optical conductivity of the quasi one-dimensional conductors: the role of forward scattering by impurities

TL;DR

This paper analyzes how forward scattering by impurities affects the optical conductivity in quasi-one-dimensional conductors, revealing that weak disorder causes a finite conductivity at zero frequency, contrasting with traditional linearized models.

Contribution

It introduces a method to account for energy dispersion curvature in conductivity calculations, showing that weak forward scattering disorder leads to a finite zero-frequency conductivity.

Findings

Transport scattering rate vanishes as omega^2 at low frequencies

Real part of conductivity remains finite as omega approaches zero

Imaginary part of conductivity diverges at low frequencies

Abstract

We calculate the average conductivity sigma (omega) of interacting electrons in one dimension in the presence of a long-range random potential (forward scattering disorder). Taking the curvature of the energy dispersion into account, we show that weak disorder leads to a transport scattering rate that vanishes as omega^2 for small frequency omega. This implies that the real part of the conductivity remains finite for omega -> 0, while the imaginary part diverges. These effects are lost within the usual bosonization approach, which relies on the linearization of the energy dispersion. We discuss our result in the light of a recent experiment.