Quantum Hall Effect: Current Distribution and the Role of Measurement

TL;DR

This paper demonstrates that in quantum Hall experiments with quantized Hall conductivity, the bulk states carry most of the current, highlighting the importance of contact-induced equilibration of edge channels.

Contribution

It reveals that bulk states dominate current transport in the quantum Hall regime regardless of geometry, emphasizing the role of contacts in equilibrating edge channels.

Findings

Bulk states carry most of the current in the quantum Hall regime.

Contacts play a crucial role in equilibrating edge channels.

Current distribution is geometry-independent in the quantized regime.

Abstract

Based on very general arguments we show that for any geometry of the experiment, in the regime when the measurement leads to a quantized Hall conductivity, almost the entire current injected into the sample is carried by the bulk states. The crucial role of the contacts equilibrating different edge channels is emphasized.