Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2005-12-28
Group theoretical methods in physics. Institute of Physics Conference Series Number 185. Cocoyoc, Mexico, 2004, pp. 353-358, E
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
9 pages, 2 figures Slightly updated version, of the book version
Scientific paper
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.
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