Aharonov-Bohm Interference in Even-Denominator Fractional Quantum Hall States

Position exchange of non-Abelian anyons affects the quantum state of their system in a topologically-protected way. Their expected manifestations in even-denominator fractional quantum Hall (FQH) systems offer the opportunity to directly study their unique statistical properties in interference experiments. In this work, we present the observation of coherent Aharonov-Bohm interference at two even-denominator states in high-mobility bilayer graphene-based van der Waals heterostructures by employing the Fabry-Pérot interferometry (FPI) technique. Operating the interferometer at a constant filling factor, we observe an oscillation period corresponding to two flux quanta inside the interference loop, $ΔΦ=2Φ_0$, at which the interference does not carry signatures of non-Abelian statistics. The absence of the expected periodicity of $ΔΦ=4Φ_0$ may indicate that the interfering quasiparticles carry the charge $e^* = \frac{1}{2}e$ or that interference of $e^* = \frac{1}{4}e$ quasiparticles is thermally smeared. Interestingly, at two hole-conjugate states, we also observe oscillation periods of half the expected value, indicating interference of $e^* = \frac{2}{3}e$ quasiparticles instead of $e^* = \frac{1}{3}e$. To probe statistical phase contributions, we operated the 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 additional bulk quasiparticles carry the fundamental charge $e^*=\frac{1}{4}e$, as expected for non-Abelian anyons.

💡 Research Summary

The authors investigate the elusive non‑Abelian anyons predicted to exist in even‑denominator fractional quantum Hall (FQH) states by performing Aharonov‑Bohm (AB) interferometry in high‑mobility bilayer‑graphene van‑der‑Waals heterostructures. A gate‑defined Fabry‑Pérot interferometer (FPI) is fabricated using a bilayer‑graphene channel encapsulated by hexagonal‑boron‑nitride, with graphite top and bottom gates split into eight independently biased regions. Two quantum point contacts (QPCs) are formed by split gates (LSG, RSG) and fine‑tuned by air‑bridge gates, allowing counter‑propagating edge modes to tunnel and generate interference.

Measurements are carried out in a three‑dimensional parameter space: magnetic field B, plunger‑gate voltage V_PG (which changes the interferometer area), and center‑gate voltage V_CG (which sets the bulk filling factor). By moving along trajectories of constant filling factor (α_c = ∂B/∂V_CG), the authors keep the electron density inside the interferometer fixed while varying B and V_CG together. In this regime the interference phase θ consists only of the AB contribution, θ_AB = 2π (e*/e) Φ/Φ₀, where e* is the charge of the tunneling quasiparticle.

At the half‑filled states ν = −½ (hole side) and ν = +3⁄2 (electron side) the Fourier analysis of the “pajama” patterns (R_D versus B and V_PG) reveals a flux periodicity ΔΦ ≈ 2 Φ₀. This is unexpected for the Pfaffian or anti‑Pfaffian states, which predict a 4 Φ₀ period for the interference of fundamental e* = ¼ e quasiparticles. The observed 2 Φ₀ period can be interpreted in two ways: (i) the interfering quasiparticle carries charge e* = ½ e, so a single winding gives ΔΦ = 2 Φ₀; or (ii) the fundamental non‑Abelian e* = ¼ e quasiparticles interfere but only even windings contribute because the presence of bulk non‑Abelian excitations leads to rapid switching among degenerate ground states, suppressing the 4 Φ₀ component.

The same 2 Φ₀ periodicity is reproduced for the electron‑doped ν = 3⁄2 plateau, confirming that the phenomenon is robust on both sides of charge neutrality. The interferometer area extracted from the integer ν = 1 and ν = 2 states matches the lithographic area (≈ 1 µm²) within experimental uncertainty, reinforcing the reliability of the extracted periods.

In contrast, for the hole‑conjugate states ν = −2⁄3 and ν = 5⁄3 the authors find a flux period of roughly ½ Φ₀, indicating that the interfering quasiparticle carries charge e* = 2⁄3 e rather than the minimal bulk charge e* = 1⁄3 e. Similar behavior is observed for the particle‑like states ν = −1⁄3 and ν = 4⁄3, where the period corresponds to e* = ν e. This systematic trend—interfering charge equal to ν e for all examined fractions—mirrors recent Mach‑Zehnder results in GaAs and suggests that the tunneling operator with the smallest scaling dimension may not always dominate the interference signal; interactions at the QPC can favor higher‑charge quasiparticles.

To probe the anyonic statistical contribution, the authors deliberately deviate from the constant‑filling trajectory, thereby introducing localized bulk quasiparticles (N_qp ≠ 0). In this regime the interference phase acquires an additional term θ_stat = N_qp θ_anyon. The measured R_D shows discrete phase slips consistent with the addition of quasiparticles of charge e* = ¼ e, exactly the charge expected for the fundamental non‑Abelian excitations of the Pfaffian/anti‑Pfaffian states. This observation provides direct evidence that the bulk quasiparticles carry the non‑Abelian anyonic charge, even though the dominant AB period remains 2 Φ₀.

Overall, the work demonstrates (1) robust AB interference at two even‑denominator plateaus in bilayer graphene, (2) an unexpected 2 Φ₀ periodicity implying either e* = ½ e tunneling or double‑winding of e* = ¼ e quasiparticles, and (3) a clear statistical phase shift when bulk quasiparticles are introduced, confirming the anyonic nature of the excitations. The use of bilayer graphene, with its high mobility, tunable displacement field, and multiple half‑filled states (alternating Pfaffian and anti‑Pfaffian candidates), establishes a versatile platform for future experiments aimed at braiding non‑Abelian anyons and implementing topological quantum computation.