Current density distribution for the quantum Hall effect

Abstract Our microscopic understanding of the integer quantum Hall effect is still incomplete. For decades, there has been a controversial discussion about ‘where the current flows’ if the Hall resistance is quantized. Here, we analyze the current density distribution in a Hall bar based on the screening properties of a two-dimensional electron system in the quantum Hall regime. Compared to previous publications, we consider the non-local nature of the quantum Hall effect and include a related persistent current that exists inside a Hall bar if the Hall resistance is quantized. We find, that the persistent current density decreases with increasing Hall voltage. Accounting for this dependence, we find, that the current flows in the opposite directions along opposite edges of the Hall bar, while the share of the current imposed through the contacts flows along the edge of the Hall bar with the higher chemical potential.