Aharonov-Bohm effect modeling in gate-defined ring in bilayer graphene

Quantum rings are one of the most basic realizations of the Aharonov-Bohm two-slit experiment in solids. The electron paths traversing the ring accumulate a phase difference which leads to conductance oscillation with the fundamental period $phi_0=h/e$, and higher harmonics corresponding to multiple rounds in the ring. The number of harmonics is limited by the phase coherence length of a sample, and thus has been used as an indicator of sample quality. In conventional, etched ring-shaped devices, the quality suffers from edge roughness, impurities, and defects, while electrostatic confinement appears as a way to longer coherence length. We develop an effective 4-band model based on the continuum approximation for Bernal-stacked bilayer graphene, and we demonstrate its performance by revisiting experiment on bilayer graphene-based ring [1]. The system is defined by gapping out the bulk, with a remaining conducting ring-shaped area. Our model reproduces the experimental results well, proving efficient for the modeling of bilayer graphene devices.

[1] S. Iwakiri et al., Nano Lett. 22, 6292 (2022).