Quantum Hall Effect: A Perspective

A. Overview.- B. The Basics.- C. The Integer Quantum Hall Effect.- D. The Quantum Hall Effect in a Periodic Potential.- E. The Fractional Quantum Hall Effect.- References:.- Reprinted Articles.- The Discovery of the Hall Effect: Ewdin Hall's Hiterto Unpublished Account, in "The Hall effect and its applications" (1980).- Diamagnetismus der Metalle, Zeitscrift fur Physik (1930).- Der Diamagnetismus von frein Elektronen, Zeitscrift fur Physik (1931).- The Dependence of the Susceptibility of Diamagnetic Metals upon the Field, Kon. Akad. van Wefenschappen (1930).- Magnetische Widerstandsvergroserung in Einkristallen von Wismut bei Tiefen Temperaturen, Kon. Akad. van Wefenschappen (1930).- Magnetoresistance, in "The Fermi Surface" (1960).- Magneto-oscillatory Conductance in Silicon Surfaces, Phys. Rev. Lett. (1966).- Theory of Hall Effect in a two-Dimensional Electron System, J. Phys. Soc. Jpn. (1975).- Quantum Galvanomagnetic Properties of n-Type Inversion Layers on Si(100) MOSFET, Surf. Sci. (1976).- The Discovery of Quantum Hall Effect, Metrologia (1986).- New method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance, Phys. Rev. Lett. (1980).- Quantized Hall Resistance and the Measurement of the Fine-Structure Constant, Phys. Rev. (1981).- Quantized Hall Conductivity in two Dimensions, Phys. Rev. (1981).- Quantized Hall Conductance, Current Carrying Edge States and the Existence of Extended States in a two Dimensional Disordered Potential, Phys. Rev. (1982).- Theory of Quantized Hall Conductivity in two Dimensions, J. Phys. C (1982).- Localization and Scaling in the Quantum Hall Regime, Phys. Rev. (1985).- Quantization of Coupled Orbits in Metals, Proc. Roy. Soc. (1962).- Energy Levels and Wave Functions of BlochElectrons in Rational and Irrational Magnetic Fields, Phys. Rev. (1976).- Quantized Hall Effect in Two Dimensional Periodic Potentials, Phys. Rep. (1984).- Quantised Hall Effect in a Two Dimensional Periodic Potential, J. Phys. C (1982).- Two Dimensional Magnetotransport in the Extreme Quantum Limit, Phys. Rev. Lett. (1982).- Odd and Even Fractionally Quantized States in GaAs-GaAlAs Heterojunctions, Surf. Sci. (1986).- Magnetic Field Dependence of Activation Energies in the Fractional Quantum Hall Effect, Phys. Rev. Lett. (1985).- Second activation Energy in the Fractional Quantum Hall Effect, J. Phys. Soc. Jpn. (1987).- Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations, Phys. Rev. Lett. (1983).- Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States, Phys. Rev. Lett. (1983).- Ground State of Two Dimensional Electrons in Strong Magnetic Fields and $$\frac{1}{3}$$ Quantized Hall Effect, Phys. Rev. Lett. (1983).- Statistics of Quasiparticles and the Hierarchy of Fractional Quantized Hall States, Phys. Rev. Lett. (1984).- Magneto-roton Theory of Collettive Excitations in the Fractional Quantum Hall Effect, Phys. Rev. (1986).- Off Diagonal Long-Range Order, Oblique Confinement, and the Fractional Quantum Hall Effect, Phys. Rev. Lett. (1987).