Decoherence of interacting electrons in disordered conductors: on the relation between influence functional and diagrammatic approaches

TL;DR

This paper connects the influence functional method with diagrammatic perturbation theory to clarify the role of different terms in electron decoherence in disordered conductors, showing that certain terms are only negligible at high temperatures.

Contribution

It demonstrates how the influence functional approach can reproduce standard diagrammatic results and clarifies the conditions under which certain terms can be neglected.

Findings

The influence functional approach recovers standard Cooperon self energy diagrams.

The term $S_R$ is as important as $S_I$ for decoherence.

Neglecting $S_R$ is valid only at high temperatures ($T > rac{ ext{ extbar} ext{ extbar} rac{ ext{ extbar} ext{ extbar} au_{el}$).

Abstract

We establish a connection between the influence functional approach of Golubev and Zaikin (GZ) and Keldysh diagrammatic perturbation theory for calculating the decoherence time of interacting electrons in disordered metals; we show how the standard diagrams for the Cooperon self energy can be recovered from GZ's influence functional $e^{- (i S_R + S_I)}$. This allows us to shed light on GZ's claim that $S_R$ is irrelevant for decoherence: $S_R$ generates as many important self energy diagrams as $S_I$; GZ's neglect of $S_R$ is permissible only at high temperatures ($T > \hbar / \tau_{el}$).