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

Anderson localization1 in a random system is sensitive to a distance dependence of the excitation transfer amplitude V(r). If V(r) decreases with the distance r slower than 1/r^d in a d-dimensional system then all excitations are delocalized at arbitrarily strong disordering, due to the resonant interaction of far separated quantum states (Fig. 1). At finite temperature T>0 the density of excitations is finite and they can influence each other by means of their interaction. M...

Temperature dependent transport of disordered electronic systems is examined in the presence of strong correlations. In contrast to what is assumed in Fermi liquid approaches, finite temperature behavior in this regime proves largely dominated by inelastic electron-electron scattering. This conclusion is valid in the strong coupling limit, where the disorder, the correlations and the Fermi energy are all comparable, as in many materials near the metal-insulator transition.

The quantum coherence of electrons can be probed by studying weak localization corrections to the conductivity. Interaction effects lead to dephasing, with electron-electron interactions being the important intrinsic mechanism. A controversy exists whether or not the dephasing rate, as measured in a weak localization experiment, vanishes at low temperatures. We review the non-perturbative analysis of this question and some of the arguments which have been raised against it. T...

In one-dimensional electronic systems with strong repulsive interactions, charge excitations propagate much faster than spin excitations. Such systems therefore have an intermediate temperature range [termed the "spin-incoherent Luttinger liquid'" (SILL) regime] where charge excitations are "cold" (i.e., have low entropy) whereas spin excitations are "hot." We explore the effects of charge-sector disorder in the SILL regime in the absence of external sources of equilibration....

In disordered systems, our present understanding of the Anderson transition is hampered by the possible presence of interactions between particles. We demonstrate that in boson gases, even weak interactions deeply alter the very nature of the Anderson transition. While there still exists a critical point in the system, below that point a novel phase appears, displaying a new critical exponent, subdiffusive transport and a breakdown of the one-parameter scaling description of ...

We introduce a new method to analysis the many-body problem with disorder. The method is an extension of the real space renormalization group based on the operator product expansion. We consider the problem in the presence of interaction, large elastic mean free path, and finite temperatures. As a result scaling is stopped either by temperature or the length scale set by the diverging many-body length scale (superconductivity). Due to disorder a superconducting instability mi...

We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. Two alternative approaches to the problem are developed, both combining fermionic and bosonic treatment of the underlying physics. We calculate the relevant dephasing rate, which for spinless electrons is governed ...

The growing need for smaller electronic components has recently sparked the interest in the breakdown of the classical conductivity theory near the atomic scale, at which quantum effects should dominate. In 2012, experimental measurements of electric resistance of nanowires in Si doped with phosphorus atoms demonstrate that quantum effects on charge transport almost disappear for nanowires of lengths larger than a few nanometers, even at very low temperature (4.2K). We mathem...

Motivated by Weyl semimetals and weakly doped semiconductors, we study transport in a weakly disordered semiconductor with a power-law quasiparticle dispersion $\xi_{\bf k}\propto k^\alpha$. We show, that in $2\alpha$ dimensions short-correlated disorder experiences logarithmic renormalisation from all energies in the band. We study the case of a general dimension $d$ using a renormalisation group, controlled by an $\varepsilon=2\alpha-d$-expansion. Above the critical dimensi...

We study the temperature-dependent quantum correction to conductivity due to the interplay of spin density fluctuations and weak disorder for a two-dimensional metal near an antiferromagnetic (AFM) quantum critical point. AFM spin density fluctuations carry large momenta around the ordering vector $\mathbf{Q}$ and, at lowest order of the spin-fermion coupling, only scatter electrons between "hot spots" of the Fermi surface which are connected by $\mathbf{Q}$. Earlier, it was ...