Dephasing due to electron-electron interaction in a diffusive ring

TL;DR

This paper analyzes how electron-electron interactions affect phase coherence and magnetoconductivity in diffusive rings, revealing different relaxation behaviors depending on harmonic number and system size.

Contribution

It provides an exact path integral calculation of magnetoconductivity in a ring, characterizing phase relaxation and predicting new behaviors based on the Nyquist length.

Findings

Phase coherence relaxation is non exponential for the zero harmonic.

Relaxation is exponential for non-zero harmonics.

New behaviors predicted when Nyquist length exceeds the ring perimeter.

Abstract

We study the effect of the electron-electron interaction on the weak localization correction of a ring pierced by a magnetic flux. We compute exactly the path integral giving the magnetoconductivity for an isolated ring. The results are interpreted in a time representation. This allows to characterize the nature of the phase coherence relaxation in the ring. The nature of the relaxation depends on the time regime (diffusive or ergodic) but also on the harmonics $n$ of the magnetoconductivity. Whereas phase coherence relaxation is non exponential for the harmonic $n=0$, it is always exponential for harmonics $n\neq0$. Then we consider the case of a ring connected to reservoirs and discuss the effect of connecting wires. We recover the behaviour of the harmonics predicted recently by Ludwig & Mirlin for a large perimeter (compared to the Nyquist length). We also predict a new behaviour when the Nyquist length exceeds the perimeter.