Fabry-Pérot Interferometry at the ν=2/5 Fractional Quantum Hall State

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).