Low temperature decoherence by electron-electron interactions: Role of quantum fluctuations

TL;DR

This paper derives a comprehensive expression for conductivity in disordered conductors with electron-electron interactions, emphasizing quantum fluctuations' role in low-temperature decoherence and clarifying previous conflicting results.

Contribution

It extends prior work by explicitly including quantum fluctuations around classical paths, confirming zero-temperature decoherence, and refuting earlier perturbative critiques.

Findings

Quantum fluctuations are relevant only at short times in the perturbative regime.

Interaction-induced decoherence persists at zero temperature.

Previous perturbative approaches are shown to be irrelevant for long-time dynamics.

Abstract

We derive a general expression for the conductivity of a disordered conductor with electron-electron interactions (treated within the standard model) and evaluate the weak localization correction delta sigma_{wl} employing no approximations beyond the accuracy of the definition of delta sigma_{wl}. Our analysis applies to all orders in the interaction and extends our previous calculation by explicitly taking into account quantum fluctuations around the classical paths for interacting electrons (pre-exponent). We specifically address the most interesting low temperature limit and demonstrate that such fluctuations can only be important in the perturbative regime of short times while they are practically irrelevant for the Cooperon dynamics at longer times. We fully confirm our conclusion about the existence of interaction-induced decoherence of electrons at zero temperature for the problem in question. We also demonstrate irrelevance of a perturbative calculation by Aleiner et al. (AAV) [J. Low Temp. Phys. 126, 1377 (2002) and cond-mat/0110545] and discard AAV's critique of our earlier analysis.