Fabry-Pérot Interferometry at the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mo>/</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:mrow></mml:math> Fractional Quantum Hall State
James Nakamura, Shuang Liang, G. C. Gardner, Michael J. Manfra
Abstract
Electronic Fabry-Pérot interferometry is a powerful method to probe quasiparticle charge and anyonic braiding statistics in the fractional quantum Hall regime. We extend this technique to the hierarchy ν=2/5 fractional quantum Hall state, possessing two edge modes that in our device can be interfered independently. The outer edge mode exhibits interference similar to the behavior observed at the ν=1/3 state, indicating that the outer edge mode at ν=2/5 has properties similar to the single mode at ν=1/3. The inner mode shows an oscillation pattern with a series of discrete phase jumps indicative of distinct anyonic braiding statistics. After taking into account the impact of bulk-edge coupling, we extract an interfering quasiparticle charge e^{*}=0.17±0.02 and anyonic braiding phase θ_{a}=(-0.43±0.05)×2π, which serve as experimental verification of the theoretically predicted values of e^{*}=1/5 and θ_{a}=-(4π/5).