HAIT Journal of Science and Engineering
Volume 1, Issue 3, pp. 436-469
© 2004 Holon Academic Institute of Technology


Quantum Hall electrodynamics:
classical and relativistic aspects

Israel D. Vagner

Research Center for Quantum Communication Engineering
at Department of Communication Engineering,
Holon Academic Institute of Technology, 52 Golomb Str., Holon 58102, Israel,

Department of Physics and Center for Quantum Device Technology,
Department of Electrical and Computer Engineering,
Clarkson University Potsdam, New-York 13699-5721,

Grenoble High Magnetic Fields Laboratory,
Max-Planck-Institute für Festkörperforschung and CNRS,
25 Avenue des Martyrs, BP166, F-38042, Grenoble, Cedex 9, France

e-mail: vagner_i@hait.ac.il

Received 26 June 2004, accepted 23 December 2004


Physics of any system is governed by a set of conservation laws which depends on the system dimensionality. A typical case are electrons in external magnetic filed. The central players here are the adiabatic invariance of the orbital magnetic moment of an electron in a magnetic field in classical physics and its quantum counterpart -- the Landau levels.

These general principles have recently attracted growing interest due to the puzzling discovery by R. Mani and A. Zudov's groups of nondissipative structures in two-dimensional electron systems under the classically strong magnetic fields wct>>1.

It may well be that this quantum-classical controversy is rather in terminnology, and the origin of physical mysteries of a magnetized two-dimensional electron gas is of more general, probably, topological origin, and follows from the internal symmetries of a two-dimensional electron system under magnetic fields.

While the experimental observation of the wave frequency dependent "windows" of vanishing magnetoresistivity are by now widely discussed in the literature, the aim of this review is to collect some already known information on the hidden symmetries of these systems, like relaivistic and scaling invariance, and to apply to them the Chern-Simons electrodynamics.

The relativisticaly invariant electrodynamics of quantum Hall media is discused and some new solutions are presented, generic to the two-dimensional electron system under magnetic field in nondissipative regime.

We review here also some previous works related to the classical-quantum finite frequency responce of the two-dimensional electron systems under a wide range of magnetic fields. The phenomenon of zero resistivity in these systems is instructive also as a rich enough toy model to study the basic laws of statistical physics, leading to fundamental understanding of Irreversibility. This is discussed in details in terms of the Basic Irreversible Cycle for Electrons in Magnetic Fields (BIC EMF). The helicon mode is chosen as a good example of an electromagnetic wave propagating due to the self-consistency of the electromagnetically induced Hall currents in the sample. The notion of the quantum-Hall-helicon mode is introduced.

Design and feasibility of relevant experiments are discussed.

PACS: 73.21.-b,73.40.-c,73.43.-f

Presented at International Workshop Correlated Electrons at High Magnetic Fields. Ein-Gedi/Holon, Israel, 19-23 December 2004

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