The Quantum Hall Effect

1. Front Matter

   Pages i-xvii

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2. Introduction

   1. Introduction

      • Richard E. Prange

      Pages 1-35

3. The Integer Effect

   1. Front Matter

      Pages N1-N1

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   2. Experimental Aspects and Metrological Applications

      • Marvin E. Cage

      Pages 37-68

   3. Effects of Imperfections and Disorder

      • Richard E. Prange

      Pages 69-99

   4. Topological Considerations

      • David J. Thouless

      Pages 101-116

   5. Field Theory, Scaling and the Localization Problem

      • Adrianus M. M. Pruisken

      Pages 117-173

4. The Fractional Effect

   1. Front Matter

      Pages N3-N3

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   2. Experimental Aspects

      • Albert M. Chang

      Pages 175-232

   3. Elementary Theory: the Incompressible Quantum Fluid

      • Robert B. Laughlin

      Pages 233-301

   4. The Hierarchy of Fractional States and Numerical Studies

      • F. Duncan, M. Haldane

      Pages 303-352

   5. Collective Excitations

      • Steven M. Girvin

      Pages 353-378

5. The Quantum Hall Effect

   1. Front Matter

      Pages N5-N5

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   2. Summary, Omissions and Unanswered Questions

      • Steven M. Girvin

      Pages 381-399

6. Back Matter

   Pages 401-419

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analyze the Hall effect in the plateau region relative to the fundamental value 2 h/e i expected in the simple one-electron picture for integer filling factors of Landau levels. Subsequent work in my laboratory in Wiirzburg using a super­ conducting solenoid confirmed the constancy of the Hall resistance both in Dorda's samples and in samples supplied by M. Pepper of the Cavendish Laboratory. With technical assistance from the Physikalisch-Technische Bundesanstalt in Braunschweig, an absolute measurement of the Hall resistance confirmed the 2 fundamental quantization relation RIJ = h/ei to an accuracy of about 1 part in ]05. Recalling the practical applications of the Josephson effect, my initial thinking was oriented toward the idea of a resistance standard, but various groups at national laboratories which are involved in high precision measurements of fun­ damental constants pointed out that, in addition, the quantized Hall resistance yields a new fundamental measure of the fine structure constant Ci. These then were the initial events which led to the remarkable surge of interest within both the metrology and condensed matter physics communities in quantum transport in inversion layer systems. Subsequent developments have been many and varied and are described in detail in this volume.

• Josephson effect
• Potential
• QHE
• Quantum Hall effect
• condensed matter
• condensed matter physics
• electron
• field theory
• geometry
• invariant
• quantization
• scattering
• semiconductor
• topological quantum number
• vortices

• Department of Physics and Astronomy, University of Maryland, College Park, USA

  Richard E. Prange

• Surface Science Division, National Bureau of Standards, Gaithersburg, USA

  Steven M. Girvin

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