David F. Mross

Even-denominator quantum Hall states can host several types of anyons with distinct exchange statistics. Depending on the anyon type, exchanging two quasiparticles can impart a phase to the manybody wave function or even transform it into a different state. Here, we realize a gate-tunable FabryPérot interferometer with an embedded antidot that provides local control over the number of anyons within the interference loop. By independently tuning the magnetic field, carrier densities acrossthe device, and the antidot potential, we access regimes in which localized anyons form reproducibly and measure the associated statistical phases e^iθbraid . We resolve braiding phases of θ_braid = π and θ_braid =π2, which we attribute to e/2 quasiparticles encircling either e/2 or e/4 quasiparticles, respectively. We further observe switching between different anyon occupancies of the antidot over time, directly resolving individual anyon tunnelling events into the interference loop. Similar behavior occurs at filling factor one third. Our work addresses one of the two key challenges in observingnon-Abelian braiding, which requires control of both localized and interfering anyon types.

Topological and crystalline orders of electrons both benefit from enhanced Coulomb interactions in partially filled Landau levels. In bilayer graphene (BLG), the competition between fractional quantum Hall liquids and electronic crystals can be tuned electrostatically. Applying a displacement field leads to Landau-level crossings, where the interaction potential is strongly modified due to changes in the orbital wave functions. Here, we leverage this control to investigate phase transitions between topological and crystalline orders at constant filling factors in the lowest Landau level of BLG. Using transport measurements in high-quality hBN-encapsulated devices, we study transitions as a function of displacement field near crossings of N = 0 and N = 1 orbitals. The enhanced Landau-level mixing near the crossing stabilizes electronic crystals at all fractional fillings, including a resistive state at ν = 1/3 and a reentrant integer quantum Hall state at ν = 7/3. On the N = 0 side, the activation energies of the crystal and fractional quantum Hall liquid vanish smoothly and symmetrically at the transition, while the N = 1 transitions out of the crystal appear discontinuous. Additionally, we observe quantized plateaus forming near the crystal transition at half filling of the N = 0 levels, suggesting a paired composite fermion state stabilized by Landau level mixing

Position exchange of non-Abelian anyons affects the quantum state of their system in a topologically protected way¹. Their expected manifestations in even-denominator fractional quantum Hall (FQH) systems offer the opportunity to directly study their unique statistical properties in interference experiments². Here we present the observation of coherent AharonovBohm interference at two even-denominator states in high-mobility bilayer-graphene-based van der Waals (vdW) heterostructures by using the FabryPérot interferometry technique. Operating the interferometer at a constant filling factor, we observe an oscillation period corresponding to two flux quanta inside the interference loop, ΔΦ = 2Φ₀, at which the interference does not carry signatures of non-Abelian statistics. The absence of the expected periodicity of ΔΦ = 4Φ₀ may indicate that the interfering quasiparticles carry the charge e*=12e or that interference of e*=14e quasiparticles is thermally smeared. Notably, at two hole-conjugate states, we also observe oscillation periods of half the expected value, indicating interference of e*=23e quasiparticles instead of e*=13e. To investigate statistical phase contributions, we operated the FabryPérot interferometer (FPI) with controlled deviations of the filling factor, thereby introducing fractional quasiparticles inside the interference loop. The resulting changes to the interference patterns at both half-filled states indicate that the extra bulk quasiparticles carry the fundamental charge e*=14e, as expected for non-Abelian anyons.