Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar
S. Kettemann
Abstract
The 2-- to 1--dimensional crossover of the localisation length of electrons confined to a disordered quantum wire of finite width Ly is studied in a model of electrons moving in the potential of uncorrelated impurities. An analytical formula for the localisation length is derived, describing the dimensional crossover as function of width Ly, conductance g and perpendicular magnetic field B . On the basis of these results, the scaling analysis of the quantum Hall effect in high Landau levels, and the delocalisation transition in a quantum Hall wire are reconsidered.
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