The Fractional Quantum Hall Effect

1. Front Matter

   Pages I-XII

   PDF

2. Introduction

   • Tapash Chakraborty, Pekka Pietiläinen

   Pages 1-9

3. Ground State

   • Tapash Chakraborty, Pekka Pietiläinen

   Pages 10-38

4. Elementary Excitations

   • Tapash Chakraborty, Pekka Pietiläinen

   Pages 39-82

5. Collective Modes: Intra-Landau Level

   • Tapash Chakraborty, Pekka Pietiläinen

   Pages 83-108

6. Collective Modes: Inter-Landau Level

   • Tapash Chakraborty, Pekka Pietiläinen

   Pages 109-120

7. Further Topics

   • Tapash Chakraborty, Pekka Pietiläinen

   Pages 121-140

8. Open Problems and New Directions

   • Tapash Chakraborty, Pekka Pietiläinen

   Pages 141-142

9. Back Matter

   Pages 143-175

   PDF

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 gas, where the positive background charge is well separated from the two­ 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.

• Hall effect
• Pet
• Quantum Hall effect
• development
• energy
• experiment
• experimental investigations
• geometry
• mechanics
• physics
• quantum mechanics
• spin
• statistical physics
• translation
• wave

• Max-Planck-Institut für Festkörperforschung, Stuttgart 80, Fed. Rep. of Germany

  Tapash Chakraborty

• Department of Theoretical Physics, University of Oulu, Oulu 57, Finland

  Pekka Pietiläinen

Policies and ethics