Hopping Conductivity in One Dimension

Abstract

An asymptotic upper bound at low temperatures $\ensuremath{\sigma}\ensuremath{\propto}{e}^{\frac{\ensuremath{-}T}{{T}_{0}}}$ is established to the electrical conductivity of the Mott hopping model in one dimension. This removes the logical basis for arguing in favor of hopping conductivity in one dimension, $d=1$, using the asymptotic form $\ensuremath{\sigma}\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}{(\frac{{T}_{0}}{T})}^{\frac{1}{(1+d)}}]$ as recently proposed for certain highly inhomogeneous solids.