Localization in Strong Magnetic Fields and Quantum Hall Effect

概要

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Transport properties of the two-dimensional system in strong magnetic fields are reviewed mainly from a theoretical point of view. It is emphasized that the quantization of the Hall conductivity into the integer multiple of -e^2/h requires the presence of both localized and extended states in Landau levels. Brief reviews are given on Laughlin's and related arguments leading to the quantized Hall effect. The numerical study of the localization based on the Thouless-number method and the finite-size scaling method are reviewed in detail, while other theories like perturbations and nonlinear σ models are reviewed more briefly. States are shown to be localized exponentially except those just at a single energy where the inverse localization length vanishes. In the vicinity of extended states, the inverse localization length shows a power-law dependence on energy.
理論物理学刊行会の論文
1986-03-25