Impact of bulk-edge coupling on observation of anyonic braiding statistics in quantum Hall interferometers

TL;DR

This study measures electrostatic coupling in quantum Hall interferometers to better understand and observe anyonic braiding statistics, confirming theoretical predictions and analyzing deviations in experimental data.

Contribution

It provides experimental methods to determine electrostatic coupling constants and compares results with theoretical models of anyonic statistics in quantum Hall systems.

Findings

Electrostatic parameters K_I and K_IL are experimentally determined.

Observed phase jumps are consistent with anyonic statistics predictions.

Electrostatic effects explain deviations from ideal anyonic phase values.

Abstract

Quantum Hall interferometers have been used to probe fractional charge, and more recently, fractional statistics of quasiparticles. Theoretical predictions have been made regarding the effect of electrostatic coupling on interferometer behavior and observation of anyonic phases. Here we present measurements of a small Fabry-Perot interferometer in which these electrostatic coupling constants can be determined experimentally, facilitating quantitative comparison with theory. At the $\nu = 1/3$ fractional quantum Hall state, this device exhibits Aharonov-Bohm interference near the center of the conductance plateau interrupted by a few discrete phase jumps, and $\Phi_0$ oscillations at higher and lower magnetic fields, consistent with theoretical predictions for detection of anyonic statistics. We estimate the electrostatic parameters $K_I$ and $K_{IL}$ by two methods: by the ratio of oscillation periods in compressible versus incompressible regions, and from finite-bias conductance measurements, and these two methods yield consistent results. We find that the extracted $K_I$ and $K_{IL}$ can account for the deviation of the values of the discrete phase jumps from the theoretically predicted anyonic phase $\theta _a = 2\pi /3$. In the integer quantum Hall regime, we find that the experimental values of $K_I$ and $K_{IL}$ can account for the the observed Aharonov-Bohm and Coulomb dominated behavior of different edge states.