Coherent “Metallic” Resistance and Medium Localization in a Disordered One-Dimensional Insulator

Abstract

It is believed that a disordered one-dimensional (1D) wire with coherent electronic conduction is an insulator with the mean resistance $⟨\ensuremath{\rho}⟩\ensuremath{\simeq}{e}^{2L/\ensuremath{\xi}}$ and resistance dispersion ${\ensuremath{\Delta}}_{\ensuremath{\rho}}\ensuremath{\simeq}{e}^{L/\ensuremath{\xi}}$, where $L$ is the wire length and $\ensuremath{\xi}$ is the electron localization length. Here we show that this 1D insulator undergoes at full coherence the crossover to a 1D ``metal,'' caused by thermal smearing and resonant tunneling. As a result, ${\ensuremath{\Delta}}_{\ensuremath{\rho}}$ is smaller than unity and tends to be $L/\ensuremath{\xi}$ independent, while $⟨\ensuremath{\rho}⟩$ grows with $L/\ensuremath{\xi}$ first nearly linearly and then polynomially, manifesting the so-called medium localization.