Interaction effects in a multi-channel Fabry-P\'erot interferometer in the Aharonov-Bohm regime

TL;DR

This paper models the effects of strong short-range electron-electron interactions in a multi-channel Fabry-Pérot interferometer within the integer quantum Hall regime, explaining experimental observations through an edge-magnetoplasmon scattering matrix approach.

Contribution

It introduces a theoretical framework using edge-magnetoplasmon scattering matrices to analyze interaction effects in multi-channel interferometers, including energy dissipation scenarios.

Findings

Backscattering current and differential conductance depend on the number of trapped channels.

The formalism captures experimental features observed in the integer Hall regime.

Model accommodates channels absorbed into Ohmic contacts, accounting for energy dissipation.

Abstract

We investigate a Fabry-P\'erot interferometer in the integer Hall regime in which only one edge channel is transmitted and n channels are trapped into the interferometer loop. Addressing recent experimental observations, we assume that Coulomb blockade effects are completely suppressed due to screening, while keeping track of a residual strong short range electron-electron interaction between the co-propagating edge channels trapped into the interferometer loop. This kind of interaction can be completely described in the framework of the edge-magnetoplasmon scattering matrix theory allowing us to evaluate the backscattering current and the associated differential conductance as a function of the bias voltage. The remarkable features of these quantities are discussed as a function of the number of trapped channels. The developed formalism reveals very general and provides also a simple way to model the experimentally relevant geometry in which some of the trapped channels are absorbed into an Ohmic contact, leading to energy dissipation.