Non-linear response and electron-electron interactions in mesoscopic metal rings

TL;DR

This paper investigates how a time-dependent electric field induces a non-equilibrium current in mesoscopic metal rings, revealing connections to electron interactions, weak localization, and providing a basis for experimental testing.

Contribution

It establishes a theoretical link between non-linear response, electron-electron interactions, and weak localization effects in mesoscopic rings, with explicit calculations and experimental proposals.

Findings

Non-linear current proportional to electric field intensity

Connection between non-linear conductivity and weak localization correction

Explicit disorder-averaged current calculations as function of frequency and flux

Abstract

A time-dependent electric field gives rise to a stationary non-equilibrium current I^{(2)} around a mesoscopic metal ring threaded by a magnetic flux. We show that this current, which is proportional to the intensity of the field, is closely related to the exchange part of the interaction contribution to the equilibrium persistent current, and that the corresponding non-linear conductivity directly measures the weak localization correction to the polarization. We explicitly calculate the disorder average of I^{(2)} in the diffusive regime as function of the frequency of the electric field and the static flux piercing the ring, and suggest an experiment to test our theory.