Fractional Charge Spectroscopy in a Bilayer Graphene Quantum Hall Antidot

Electrons in the fractional quantum Hall effect collectively give rise to quasiparticles known as anyons. These excitations carry a fractional charge and obey neither fermionic nor bosonic exchange statistics. Among them, non-Abelian anyons are predicted to encode information non-locally in their braiding history, making them attractive candidates for fault-tolerant topological quantum computation. However, to fully identify these quasiparticles, both their exchange statistics and their fractional charge must be measured. While recent advances in anyonic interference have revealed braiding and phase jumps consistent with fractional exchange statistics, a direct measurement of the fractional charges remains essential to establish their fundamental properties. In GaAs, the historical platform for these studies, fractional charges have been measured through shot noise techniques, but newer platforms remain comparatively unexplored. Bilayer graphene is particularly promising because its electrically tunable band structure and exceptional cleanliness host fractional states inaccessible in GaAs, including even-denominator states that are candidates to host non-Abelian anyons. Nonetheless, poor-quality ohmic contacts have largely limited charge detection in bilayer graphene so far. Quantum Hall antidots, tunable hills in the electrostatic potential landscape, address this gap: they act as controlled impurities around which single quasiparticles localize, and their charge can be extracted from the periodic tunneling events.

In this thesis, we study gate-defined quantum Hall antidots in bilayer graphene. By tuning the antidot into the Coulomb-dominated regime, we extract the charge of the tunneling quasiparticles through conductance oscillations. In the integer quantum Hall regime, we find the expected electron charge and further show that the oscillation regime can be tuned, shifting from a Coulomb-dominated to an Aharonov-Bohm-dominated regime. In the odd-denominator electron-like fractional states, we observe oscillations consistent with the minimal fractional excitation charge, whereas in their hole-conjugate states, we observe a distinct tunneling charge, which we believe depends on the parity of the integer edge modes. Finally, in the even-denominator fractional states, we resolve both the minimal excitation e/4, and its double e/2, revealing a crossover between two regimes that is likely governed by the slope of the antidot potential. These results open the way toward the control and manipulation of individual anyons and establish gate-defined quantum Hall antidots as a simple, versatile, and broadly applicable route to probing fractional charge in van der Waals materials.