Interacting Electrons in Disordered Wires: Anderson Localization and Low-$T$ Transport

We study the conductivity $\sigma (T)$ 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 $\sigma (T)$, inducing a transition at $T=T_c$, so that $\sigma (T<T_c)=0$. The critical behavior of $\sigma (T)$ above $T_c$ is $\ln \sigma (T)\propto -(T-T_c{)}^{-1/2}$. The mechanism of transport in the critical regime is many-particle transitions between distant states in Fock space.

Figure 1

Diagrams for the golden rule (a) and higher-order decay amplitude (b).

Figure 2

Scheme of a high-order ballistic process: the string of particle-hole pairs (black and white circles). The initial state and intermediate virtual states (${\gamma }_i$) are shown in gray.

Figure 3

Schematic behavior of $\sigma (T)$ on the log-log scale: the weak-localization (WL), power-law hopping (PLH), and Anderson-Fock glass (AFG) regimes, with a localization transition at $T_c$. Dashed line: PLH and VRH contribution to $\sigma (T)$ in the case of a weak coupling to phonons.