Filling-dependent geometric aspect ratio in semicircle analysis

Explain why the geometric aspect ratio required to align the measured semicircle trajectories with theoretical predictions depends on the fractional filling in the modified Hall-bar device.

Background

The measured resistance must be converted into resistivity using a geometric scaling factor associated with the modified Hall-bar geometry. COMSOL simulations yielded an aspect ratio of 1.32 and generally supported the experimental scaling, but the analysis required somewhat different aspect ratios at different fractional fillings. The simulations did not account for this filling dependence, leaving unresolved whether it reflects geometric, transport, or other experimental effects.

References

This aspect ratio of 1.32 is close to those used to scale the semicircles to their theoretical predictions; however, the simulations were unable to explain the need for an aspect ratio which depends on the filling.

— Quantum Phase Transitions and Fractional Quantized Anomalous Hall Insulators in Rhombohedral Graphene  (2609.09422 - Hadjri et al., 8 Sep 2026) in Methods, “Determination of the geometric aspect ratio of the device”