Electron drift orbits in crossed electromagnetic fields and the quantum Hall effect
Abstract
The classical drift motion of electrons in crossed electric and magnetic fields provides an interesting example of a system with an on average constant velocity -- despite the presence of an electric field. This drift-velocity depends solely on the ratio of the electric and magnetic fields and not on the initial momentum of the electron. The present work describes the quantum-mechanical version of this drift-motion, which differs drastically from the classical result: The drift becomes dependent on the energy and a quantization of the transport occurs. The results bear implications for the theory of the quantum Hall effect: Current theories neglect the electric Hall-field (which is perpendicular to a magnetic field) and thus do not include the quantization due to the crossed-field geometry. I will discuss why it is not possible to eliminate the electric field and how one can explain the quantization in crossed fields in a semiclassical picture. These results make it possible to construct an alternative theory of the quantum Hall effect.
Cite
@article{arxiv.cond-mat/0512690,
title = {Electron drift orbits in crossed electromagnetic fields and the quantum Hall effect},
author = {Tobias Kramer},
journal= {arXiv preprint arXiv:cond-mat/0512690},
year = {2007}
}
Comments
9 pages, 2 figures Slightly updated version, of the book version