The structure of the most extended states of the two-dimensional non-interacting electron gas in a normal magnetic field

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Abstract
The inverse participation ratio and fractal dimension are calculated for states of a tight binding model of a two-dimensional non-interacting electron gas in a normal magnetic field with a random potential. Interest is concentrated on the most extended states. The results are compared with the literature on the fractal nature of the extended states of the continuum version of the model. Substantial differences are found between the behaviour of the fractal dimension of the models. The relevance of the findings to the quantum Hall effect is discussed. It is concluded that arguments linking the behaviour of the fractal dimensions of the most extended state to its supposed capacity to carry all current for the subband in the continuum model are not essential for understanding the quantum Hall effect.