Aharonov-Bohm interference and Statistical phase-jumps in fractional quantum Hall Fabry-Perot interferometers based on bi-layer graphene

Quasi-particles in fractional quantum Hall (FQH) states are collective excitations that carry a fractional charge and anyonic statistics ¹. The fractional charge affects semi-classical properties like shot noise and charging energies, while the exchange statistics are primarily studied through quantum interference phenomena¹. One such tool, the Fabry-Pérot interferometer (FPI), is particularly useful for investigating the exchange statistics of anyonic excitations ^2–5.

In this talk, I will present a bilayer graphene-based FPI, allowing us to explore a wide range of operating regimes, from Coulomb-dominated to Aharonov-Bohm, across both integer and fractional quantum Hall states. We employ low-temperature electronic transport measurements in high magnetic fields. We use an analysis method to extract phase evolution from 2D resistance oscillation patterns, providing critical insights into anyonic excitations within the FPI. Moreover, we analyze the trajectory of constant phase lines in the resistance oscillations using the 1D-FFT method to assess the linear dependence of phase on the number of electrons in the interference loop for . The observation of pristine AB oscillations, along with their tunability, phase slips, and altered phase evolution, points to the nature of anyonic exchange statistics.

References



1. Stern, A. Anyons and the quantum Hall effect—A pedagogical review. Ann. Phys. 323, 204–249 (2008).

2. Kim, J. et al. Aharonov–Bohm interference and statistical phase-jump evolution in fractional quantum Hall states in bilayer graphene. Nat. Nanotechnol. 1–8 (2024) doi:10.1038/s41565-024-01751-w.

3. Samuelson, N. L. et al. Anyonic statistics and slow quasiparticle dynamics in a graphene fractional quantum Hall interferometer. arXiv (2024) doi:10.48550/arxiv.2403.19628.

4. Werkmeister, T. et al. Anyon braiding and telegraph noise in a graphene interferometer. arXiv (2024) doi:10.48550/arxiv.2403.18983.

5. Nakamura, J., Liang, S., Gardner, G. C. & Manfra, M. J. Direct observation of anyonic braiding statistics. Nat. Phys. 16, 931–936 (2020).