Interacting Electrons in Disordered Wires: Anderson Localization and Low-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi></mml:math>Transport

Abstract

We study the conductivity $\ensuremath{\sigma}(T)$ of interacting electrons in a low-dimensional disordered system at low temperature $T$. For weak interactions, the weak-localization regime crosses over with lowering $T$ into a dephasing-induced ``power-law hopping.'' As $T$ is further decreased, the Anderson localization in Fock space crucially affects $\ensuremath{\sigma}(T)$, inducing a transition at $T={T}_{c}$, so that $\ensuremath{\sigma}(T&lt;{T}_{c})=0$. The critical behavior of $\ensuremath{\sigma}(T)$ above ${T}_{c}$ is $\mathrm{ln}\ensuremath{\sigma}(T)\ensuremath{\propto}\ensuremath{-}(T\ensuremath{-}{T}_{c}{)}^{\ensuremath{-}1/2}$. The mechanism of transport in the critical regime is many-particle transitions between distant states in Fock space.