Theory of the Integer and Fractional Quantum Hall Effects

Shosuke Sasaki
Center for Advanced High Magnetic Field Science, Graduate School of Science, Osaka University, Machikaneyama, Toyonaka, Osaka, Japan

Series: Classical and Quantum Mechanics, Physics Research and Technology
BISAC: SCI057000

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This book aims to describe the physics of the integer and fractional quantum Hall effects (QHE) from a theoretical side.

In the classical Hall effect, the Hall resistance is proportional to the applied magnetic field strength and varies continuously. So, the discovery of a stepwise change of the Hall resistance by von Klitzing in an ultra-thin layer of a MOSFET was a big surprise.

The QHE is a macroscopic phenomenon and shows the exact quantum structure, which is one of the most fundamental phenomena in physics.

The fractional quantum Hall effect has been explained assuming quasi-particles with fractional charges or Jain’s composite fermions, the existence of which has not been verified experimentally. The author has been developing a theory based on a standard treatment of an interacting electron system without assuming any quasi-particle.

This book will be easily understood by undergraduate students. Knowledge of quantum field theory is needed to study Chapter 9. (Imprint: Nova)

Preface

Chapter 1. Formulation of the Problem

Chapter 2. Integer Quantum Hall Effect

Chapter 3. Coulomb Energy in the FQH States

Chapter 4. Binding Energy of Electron Pair

Chapter 5. Valle, Flat and Peak Structures in the Energy Spectrum

Chapter 6. Effect of Higher Order Perturbation and Contribution from Upper Landau Levels

Chapter 7. Plateaus of Quantum Hall Resistance

Chapter 8. Accuracy of Hall Resistance Confinement

Chapter 9. Spin Polarization in the Fractional Quantum Hall States

Chapter 10. FQHE under a Tilted Magnetic Field

Chapter 11. Further Experiments

Chapter 12. Discussions on Traditional Theories

Chapter 13. Summary

References

Appendix

Index

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