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

We derive an effective low-energy theory of disordered interacting quantum wires. Our theory describes Anderson localization in the limit of vanishing dephasing and reduces to standard abelian bosonization in the limit of vanishing disorder. In a system with many transport channels, it exhibits the diffusive physics characteristic for multi-channel quantum wires.

The dc-conductivity of electrons on a square lattice interacting with a local repulsion in the presence of disorder is computed by means of quantum Monte Carlo simulations. We provide evidence for the existence of a transition from an Anderson insulator to a correlated disordered metal with a universal value of the critical dc-conductivity \sigma_{dc,crit} = (1.18 \pm 0.06) e^{2}/h at the transition.

We consider low-temperature behavior of weakly interacting electrons in disordered conductors in the regime when all single-particle eigenstates are localized by the quenched disorder. We prove that in the absence of coupling of the electrons to any external bath dc electrical conductivity exactly vanishes as long as the temperatute $T$ does not exceed some finite value $T_c$. At the same time, it can be also proven that at high enough $T$ the conductivity is finite. These tw...

We consider critical eigenstates in a two dimensional quasicrystal and their evolution as a function of disorder. By exact diagonalization of finite size systems we show that the evolution of properties of a typical wave-function is non-monotonic. That is, disorder leads to states delocalizing, until a certain crossover disorder strength is attained, after which they start to localize. Although this non-monotonic behavior is only present in finite-size systems and vanishes in...

At low temperature T, a significant difference between the behavior of crystals on the one hand and disordered solids on the other is seen: sufficiently strong disorder can give rise to a transition of the transport properties from conducting behavior with finite resistance R to insulating behavior with R=infinity as T -> 0. This well-studied phenomenon is called the disorder-driven metal-insulator transition and it is characteristic to non-crystalline solids. In this review ...

We consider the dynamics of an electron in an infinite disordered metallic wire. We derive exact expressions for the probability of diffusive return to the starting point in a given time. The result is valid for wires with or without time-reversal symmetry and allows for the possibility of topologically protected conducting channels. In the absence of protected channels, Anderson localization leads to a nonzero limiting value of the return probability at long times, which is ...

The Anderson localization transition is considered at finite temperatures. This includes the electrical conductivity as well as the electronic thermal conductivity and the thermoelectric coefficients. An interesting critical behavior of the latter is found. A method for characterizing the conductivity critical exponent, an important signature of the transition, using the conductivity and thermopower measurements, is outlined.

Based on a selfconsistent theory of localization we study the electron transport properties of a disordered system in the framework of the Anderson model on a Bethe lattice. In the calculation of the dc conductivity we separately discuss the two contributions to the current-current correlation function dominating its behaviour for small and large disorder. The resulting conductivity abruptly vanishes at a critical disorder strength marking the localization transition.

We review recent progress in the study of transport properties of interacting electrons subject to a disordered potential which is strong enough to localize all single-particle states. This review may also serve as a guide to the recent paper by the authors [Annals of Physics (2006), in press]. Here we skip most of the technical details and make an attempt to discuss the physical grounds of the final-temperature metal-insulator transition described in the above-mentioned pape...

Suppression of the critical temperature in homogeneously disordered superconducting films is a consequence of the disorder-induced enhancement of Coulomb repulsion. We demonstrate that for the majority of thin films studied now this effect cannot be completely explained in the assumption of two-dimensional diffusive nature of electrons motion. The main contribution to the $T_c$ suppression arises from the correction to the electron-electron interaction constant coming from sm...