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.