Interaction effects and phase relaxation in disordered systems

TL;DR

This paper clarifies the effects of electron-electron interactions on weak localization in disordered conductors, demonstrating that the dephasing rate remains zero at zero temperature and correcting previous theoretical misunderstandings.

Contribution

It provides a rigorous perturbative analysis showing that virtual processes do not cause dephasing, and introduces the first calculation of second-order conductance corrections in disordered metals.

Findings

Virtual processes do not contribute to dephasing.

The dephasing rate remains zero at zero temperature.

First calculation of second-order conductance correction.

Abstract

This paper is intended to demonstrate that there is no need to revise the existing theory of the transport properties of disordered conductors in the so-called weak localization regime. In particular, we demonstrate explicitly that recent attempts to justify theoretically that the dephasing rate (extracted from the magnetoresistance) remains finite at zero temperature are based on the profoundly incorrect calculation. This demonstration is based on a straightforward evaluation of the effect of the electron-electron interaction on the weak localization correction to the conductivity of disordered metals. Using well-controlled perturbation theory with the inverse conductance $g$ as the small parameter, we show that this effect consists of two contributions. First contribution comes from the processes with energy transfer smaller than the temperature. This contribution is responsible for setting the energy scale for the magnetoresistance. The second contribution originates from the virtual processes with energy transfer larger than the temperature. It is shown that the latter processes have nothing to do with the dephasing, but rather manifest the second order (in $1/g$) correction to the conductance. This correction is calculated for the first time. The paper also contains a brief review of the existing experiments on the dephasing of electrons in disordered conductors and an extended qualitative discussion of the quantum corrections to the conductivity and to the density of electronic states in the weak localization regime.