Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar

Details Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar

2003-08-05

arxiv.org/abs/cond-mat/0308079v1

Phys. Rev. B 69, 035339 (2004)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

12 pages, 7 figures

Scientific paper

10.1103/PhysRevB.69.035339

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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