Aharanov-Bohm interference and fractional statistics in a quantum Hall interferometer

TL;DR

This paper models resistance oscillations in a quantum Hall interferometer to explore fractional quasiparticle statistics, predicting experimental signatures consistent with observed Aharonov-Bohm oscillations and proposing tests to confirm fractional statistics.

Contribution

It provides a theoretical framework linking Aharonov-Bohm oscillations to fractional statistics in quantum Hall systems, matching recent experimental results and suggesting new verifiable predictions.

Findings

Periodic oscillations with flux periods larger than the fundamental quantum observed

Theoretical results align well with recent experimental data

Predictions for further experiments to confirm fractional statistics

Abstract

We compute the temperature, voltage, and magnetic field dependences of the resistance oscillations of a model interferometer designed to measure the fractional statistics of the quasiparticles in the fractional quantum Hall (FQH) effect. The geometry is the same as that used in recent experiments reported in Refs. \cite{camino-prl,camino-T,zhou}. With appropriate assumptions concerning the relative areas of the inner and outer rings of the interferometer, we find theoretical results, including the existence of periodic Aharonov-Bohm oscillations with periods {\it larger} than the fundamental quantum of flux, which are in remarkably good agreement with experiment. It is then possible to make additional experimental predictions with no adjustable parameters which, if verified, would confirm the proposed interpretation of the experiment as a measurement of fractional statistics.