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Interacting electrons in disordered wires: Anderson localization and low-temperature transport

I. V. Gornyi·A. D. Mirlin·D. G. Polyakov
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Abstract

We study transport of interacting electrons in a low-dimensional disordered system at low temperature $T$. In view of localization by disorder, the conductivity $σ(T)$ may only be non-zero due to electron-electron scattering. 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 $σ(T)$, inducing a transition at $T=T_c$, so that $σ(T<T_c)=0$. The critical behavior of $σ(T)$ above $T_c$ is $\lnσ(T)\propto - (T-T_c)^{-1/2}$. The mechanism of transport in the critical regime is many-particle transitions between distant states in Fock space.

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I. V. Gornyi, A. D. Mirlin, D. G. Polyakov. 2005-06-16. Interacting electrons in disordered wires: Anderson localization and low-temperature transport. https://doi.org/10.1103/physrevlett.95.206603

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