The experimental discovery of the fractional quantum Hall effect (FQHE)
at the end of 1981 by Tsui, Stormer and Gossard was absolutely
unexpected since, at this time, no theoretical work existed that could
predict new struc- tures in the magnetotransport coefficients under
conditions representing the extreme quantum limit. It is more than
thirty years since investigations of bulk semiconductors in very strong
magnetic fields were begun. Under these conditions, only the lowest
Landau level is occupied and the theory predicted a monotonic variation
of the resistivity with increasing magnetic field, depending sensitively
on the scattering mechanism. However, the ex- perimental data could not
be analyzed accurately since magnetic freeze-out effects and the
transitions from a degenerate to a nondegenerate system complicated the
interpretation of the data. For a two-dimensional electron the positive
background charge is well separated from the two- gas, where dimensional
system, magnetic freeze-out effects are barely visible and an analysis
of the data in the extreme quantum limit seems to be easier. First
measurements in this magnetic field region on silicon field-effect
transistors were not successful because the disorder in these devices
was so large that all electrons in the lowest Landau level were
localized. Consequently, models of a spin glass and finally of a Wigner
solid were developed and much effort was put into developing the
technology for improving the quality of semi- conductor materials and
devices, especially in the field of two-dimensional electron systems.
