Abstract
Electronic Fabry-P{\'e}rot 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.