The Quantum Hall Effect: Novel Excitations and Broken Symmetries

Authors:

S. M. Girvin

Name of the Journal:

Les Houches Lecture Notes, in: Topological Aspects of Low Dimensional Systems

Year of Publication:

2000

Volume:

Pages:

53-175

Editor Info:

Comtet A., Jolicœur T., Ouvry S., David F.

Publisher Name, Address and Year:

Springer-Verlag, Berlin and Les Editions de Physique, Les Ulis

Abstract:

The Quantum Hall Effect (QHE) is one of the most remarkable condensed-matter phenomena discovered in the second half of the 20^th century. It rivals superconductivity in its fundamental significance as a manifestation of quantum mechanics on macroscopic scales. The basic experimental observation is the nearly vanishing dissipation σ_xx → 0 (1.1) and the quantization of the Hall conductance

σ_xy=v e²/h

h

(1.2)

of a real (as opposed to some theorist’s fantasy) transistor-like device (similar in some cases to the transistors in computer chips) containing a two-dimensional electron gas subjected to a strong magnetic field. This quantization is universal and independent of all microscopic details such as the type of semiconductor material, the purity of the sample, the precise value of the magneticfield, and so forth. As a result, the effect is now used to mantain the standard of electrical resistance by metrology laboratories around the world. In addition, since the speed of light is now defined, a measurement of e²/h equivalent to a measurement of the fine structure constant of fundamental importance in quantum electrodynamics.

ISBN: 3-540-66909-4), (eprint: cond-mat/9907002).

DOI Link:

10.1007/3-540-46637-1_2

arXiv.org Number:

cond-mat/9907002