Anti-dot geometries for precise manipulation of the interference of fractional quasiparticles in Bernal bilayer quantum Hall graphene

In Fabry-Pérot interferometers, quasiparticle exchange statistics in the fractional quantum Hall regime have been observed in various 2-dimensional electronics systems. The double braiding phase of these anyonic particles has been measured by probing the phase shift of the intereference signal as the localized anyon occupation in the interferometer changes. However, thus far, the anyon occupation is determined by uncontrolled disorders in the device in most of these experiments. We aim to control the number of localized quasiparticles through gate controlled anti-dot structures in the interferometer that allow for precise manipulation of the number of quasiparticles encircled by the chiral edge channels. We discuss how these controllable anti-dot structures are useful tuning knobs for measuring states that may host quasiparticles with non-abelian exchange statistics in bilayer graphene.