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Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar

S. Kettemann
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Abstract

The 2-- to 1--dimensional crossover of the localisation length of electrons confined to a disordered quantum wire of finite width $L_y$ 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 $L_y$, 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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S. Kettemann. 2003-08-05. Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar. https://doi.org/10.1103/physrevb.69.035339

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