The Quantum Hall Effect

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.

1 Introduction -- 1.1. Introduction -- 1.2. Preview of Coming Attractions -- 1.3. The Ordinary Hall Effect -- 1.4. Measuring the Conductance -- 1.5. Introduction to the Quantum Case -- 1.6. Impurity Effects -- 1.7. Gauge Arguments -- 1.8. Inversion Layers -- 1.9. Acknowledgements -- 1.10. Notes -- 1.11. Problems -- A The Integer Effect -- 2 Experimental Aspects and Metrological Applications -- 3 Effects of Imperfections and Disorder -- 4 Topological Considerations -- 5 Field Theory, Scaling and the Localization Problem -- B: The Fractional Effect -- 6 Experimental Aspects -- 7 Elementary Theory: The Incompressible Quantum Fluid -- 8 The Hierarchy of Fractional States and Numerical Studies -- 9 Collective Excitations -- C: The Quantum Hall Effect -- 10 Summary, Omissions and Unanswered Questions -- References.