The Quantum Hall Effect

After a foreword by Klaus von Klitzing, the first chapters of this book discuss the prehistory and the theoretical basis as well as the implications of the discovery of the Quantum Hall effect on superconductivity, superfluidity, and metrology, including experimentation. The second half of this volume is concerned with the theory of and experiments on the many body problem posed by fractional effect. Specific unsolved problems are mentioned throughout the book and a summary is made in the final chapter.

The quantum Hall effect was discovered on about the hundredth anniversary of Hall's original work, and the finding was announced in 1980 by von Klitzing, Dorda and Pepper. Klaus von KIitzing was awarded the 1985 Nobel prize in physics for this discovery.

Contenu

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.- 2.1. Basic Principles.- 2.2. The Devices.- 2.3. The Basic Experiment.- 2.4. Initial Experiments.- 2.5. Precision Measurement Techniques.- 2.6. Quantum Hall Resistors.- 2.7. An Absolute Resistance Standard.- 2.8. The Fine-Structure Constant.- 2.9. Temperature Dependence of ?xx.- 2.10. Temperature Dependence of ?xy.- 2.11. Current Distribution and Edge Effects.- 2.12. Current Dependence and Breakdown.- 2.13. Hall Step Widths and Shapes.- 2.14. Thermomagnetic Transport.- 2.15. Magnetic Moment.- 2.16. Magnetocapacitance.- 2.17. Magneto-Photoresponse.- 2.18. Conclusions.- 2.19. Acknowledgements.- 2.20. Notes.- 3 Effects of Imperfections and Disorder.- 3.1. Introduction.- 3.2. The Impurity Potential.- 3.3. Weak Potential.- 3.4. Scattering Potential.- 3.5. Smooth Potential.- 3.6. Continuum Percolation Model.- 3.7. General Potential.- 3.8. Numerical Studies.- 3.9. Acknowledgements.- 3.10. Notes.- 3.11. Problems.- 4 Topological Considerations.- 4.1. Topological Quantum Numbers.- 4.2. Quantum Hall Effect in a Periodic Potential.- 4.3. Generalization of the Topological Interpretation.- 4.4. Notes.- 5 Field Theory, Scaling and the Localization Problem.- 5.1. Introduction.- 5.2. Basic Notions.- 5.3. The Search for the Principle.- 5.4. Structure of the Effective Field Theory.- 5.5. Instantons and Scaling.- 5.6. Notes.- B: The Fractional Effect.- 6 Experimental Aspects.- 6.1. Introduction.- 6.2. Conditions for the Observation of the FQHE and the Choice of Semiconductor Systems.- 6.3. The Fractional Quantum Hall Effect.- 6.4. Magneto-Transport in Two Dimensions.- 6.5. Future Experiments.- 6.6. Acknowledgements.- 6.7. Notes.- 7 Elementary Theory: The Incompressible Quantum Fluid.- 7.1. Introduction.- 7.2. Quantized Motion of Small Numbers of Electrons.- 7.3. Variational Ground State.- 7.4. Computational Methods.- 7.5. Fractionally Charged Quasiparticles.- 7.6. Exactness of the Fractional Quantum Hall Effect.- 7.7. More Than One Quasiparticle.- 7.8. Conclusions.- 7.9. Acknowledgements.- 8 The Hierarchy of Fractional States and Numerical Studies.- 8.1. Introduction.- 8.2. Pseudopotential Description of Interacting Particles with the Same Landau Index.- 8.3. The Principle Incompressible States: A Non-Variational Derivation.- 8.4. Quasiparticle and Quasihole Excitations.- 8.5. The Hierarchy of Quasiparticle-Quasihole Fluids.- 8.6. Translationally Invariant Geometries for Numerical Studies.- 8.7. Ground-State Energy Studies.- 8.8. Pair Correlations and the Structure Factors.- 8.9. Quasiparticle Excitations.- 8.10. Collective Excitations.- 8.11. Acknowledgements.- 9 Collective Excitations.- 9.1. Introduction.- 9.2. Density Waves as Elementary Excitations.- 9.3. Collective Modes in the FQHE.- 9.4. Magnetophonons and Magnetorotons.- 9.5. Further Superfluid Analogies: Vortices.- 9.6. Quasi-Excitons.- 9.7. Magnetoplasmons and Cyclotron Resonance.- 9.8. Other Collective Modes.- 9.9. Role of Disorder.- 9.10. Acknowledgements.- 9.11. Notes.- 9.12. Problems.- C: The Quantum Hall Effect.- 10 Summary, Omissions and Unanswered Questions.- 10.1. Integer Effect at Zero Temperature.- 10.2. IQHE at Finite Temperatures.- 10.3. Metrology.- 10.4. Basic Picture of the Fractional Effect.- 10.5. Remarks on the Neglect of Landau Level Mixing.- 10.6. Wanted: More Experiments.- 10.7. Towards a Landau-Ginsburg Theory of the FQHE.- 10.8. Acknowledgements.- 10.9. Notes.- 10.10. Problems.- Appendix Recent Developments.- A.1. Introduction.- A.2. Off-Diagonal Long-Range Order.- A.3. Ring Exchange Theories.- A.5. Even-Denominator and Spin-Reversed States.- A.6. Spin-Reversed Hierarchy.- A.7. Summary and Conclusions.- References.