Numerical model with intersection inhomogeneity and validation of Drude behavior for multi-terminal devices

Develop a numerical transport model that incorporates spatial inhomogeneity of E_x and E_y near intersections in multi-terminal Hall bars (for example via a path-integral formulation), and determine whether this corrected model yields perfect agreement with measured multi-terminal current divisions and confirms that the Drude model correctly describes diffusive transport for devices with more than three terminals.

Background

The authors note that while a three-terminal configuration is captured well by the Drude model, discrepancies arise in four-terminal geometries between plateaus, which they attribute to inhomogeneous fields near intersections.

They propose constructing a more realistic numerical scheme that explicitly accounts for intersection inhomogeneity and conjecture that such a model would reconcile theory with experiment and uphold the Drude description for more than three terminals.

References

A more realistic model would require a suitable numerical calculation, e.g., based on a path integral formalism. We conjecture, that such a corrected model would yield perfect agreement with measurements, namely that the Drude model is still correct for more than three terminals, where it worked perfectly for three terminals.

— Chiral nature of current flow in the regime of the quantized Hall effect  (2407.01277 - Sirt et al., 2024) in Subsection "Limits of our model in the diffusive regime" (sec:limits)