We demonstrate theoretically how a two-dimensional electron gas can be used to probe local potential profiles using the Hall effect. For small magnetic fields, the Hall resistance is inversely proportional to the average potential profile in the Hall cross and is independent of the shape and the position of this profile in the junction. The bend resistance, on the other hand, is much more sensitive on the exact details of the local potential profile in the cross junction.
@article{arxiv.cond-mat/9901135,
title = {Hall potentiometer in the ballistic regime},
author = {B. J. Baelus and F. M. Peeters},
journal= {arXiv preprint arXiv:cond-mat/9901135},
year = {2009}
}