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: \sigma =
u \; rac{e^2}{h},

where ''e'' is the Elementary Charge and ''h'' is Planck's Constant . In the "ordinary" quantum Hall effect, known as the integer quantum Hall effect, ''ν'' takes on Integer values (''ν'' = 1, 2, 3, etc.). There is another type of quantum Hall effect, known as the fractional quantum Hall effect, in which ''ν'' can occur as a Vulgar Fraction with an odd denominator (''ν'' = 2/7, 1/3, 2/5, 3/5, etc.)

The , a quantity of fundamental importance in Quantum Electrodynamics .

The integer quantization of the Hall conductance was originally predicted by Ando, Matsumoto, and Uemura in 1975 , on the basis of an approximate calculation. Several workers subsequently observed the effect in experiments carried out on the Inversion Layer of MOSFET s. It was only in 1980 that Von Klitzing , working with samples developed by Michael Pepper and Gerhard Dorda, made the totally unexpected discovery that the Hall conductivity was ''exactly'' quantized. For this finding, von Klitzing was awarded the 1985 Nobel Prize In Physics . The link between exact quantization and gauge invariance was subsequently found by Robert Laughlin .

The fractional effect is due to completely different physics, and was experimentally discovered in 1982 by Daniel Tsui and Horst Störmer , in experiments performed on Gallium Arsenide Heterostructure s developed by Arthur Gossard. The effect was explained by Robert B. Laughlin in 1983 , using a novel quantum liquid Phase that accounts for the effects of interactions between electrons. Tsui, Störmer, and Laughlin were awarded the 1998 Nobel Prize for their work. Although it was generally assumed that the discrete resistivity jumps found in the Tsui experiment were due to the presence of fractional charges, it was not until 1997 that R. de-Picciotto, et. al., directly observed fractional charges through measurements of quantum Shot Noise . The fractional quantum hall effect continues to be influential in theories about Topological Order .


REFERENCES


  • T. Ando, Y. Matsumoto, and Y. Uemura, J. Phys. Soc. Jpn. 39, 279 (1975)

  • K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980)

  • R.B. Laughlin, Phys. Rev. B. 23, 5632 (1981).

  • D.C. Tsui, H.L. Stormer, and A.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982)

  • R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).

  • R. de-Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin and D. Mahalu, Nature 389, 162-164 (1997)