Abstract
Presently, the accuracy of the determination of the fine structure constant via the quantized Hall effect seems to be limited only by instrumental and not fundamental factors. For a first physical understanding of the effect, and to get insight into the fundamental limitation of the accuracy it is necessary to study the properties of electrons in two dimensional systems subject to a magnetic field, and to a random potential representing the disorder present in all real systems. I present a summary of some recent theoretical efforts concerning this problem. For a two dimensional gas of noninteracting electrons the magnetic field alone leads to well separated highly degenerate Landau levels associated with quantum states, which are Gaussian like. A random potential alone leads to exponential localisation of all electron wave functions. The effects of the interplay between the random potential and the magnetic field are presently not very well understood. For weak magnetic fields there are indications that the field delocalises the electron states. For strong fields numerical evidence has been provided for the existence of a mobility edge which energetically separates localised from extended states. The implications of this model for the quantized Hall effect are discussed.
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Kramer, B. (1983). Electrons in Two Dimensional Disordered Systems in an External Magnetic Field. In: Cutler, P.H., Lucas, A.A. (eds) Quantum Metrology and Fundamental Physical Constants. NATO Advanced Science Institutes Series, vol 98. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2145-1_28
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DOI: https://doi.org/10.1007/978-1-4899-2145-1_28
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