Theory of the Integer Quantum Hall Effect — An Introductory Survey
The aim of these lectures is to give an introduction to the present state of the theory of the integer quantum Hall effect (IQHE). The elementary theory of the Hall effect and the quantum mechanics of free electrons in a strong magnetic field are recalled. The qualitative explanation of the IQHE due to the localization of electrons in a random potential is presented. The high field limit in which classical percolation theory can be applied is described in detail. The so-called gauge argument is described and critically commented upon. Further topics are: the topological, the scattering theoretical and the field theoretical approaches to the IQHE. The essential conclusion is that localization is a possible explanation of the IQHE but the theory is still far from being complete.
KeywordsFermi Energy High Magnetic Field Strong Magnetic Field Landau Level Quantum Hall Effect
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