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Two-Dimensional Electrons in a Strong Magnetic Field with Disorder: Divergence of the Localization Length

K. Ziegler
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Abstract

Electrons on a square lattice with half a flux quantum per plaquette are considered. An effective description for the current loops is given by a two-dimensional Dirac theory with random mass. It is shown that the conductivity and the localization length can be calculated from a product of Dirac Green's functions with the {\it same} frequency. This implies that the delocalization of electrons in a magnetic field is due to a critical point in a phase with a spontaneously broken discrete symmetry. The estimation of the localization length is performed for a generalized model with $N$ fermion levels using a $1/N$--expansion and the Schwarz inequality. An argument for the existence of two Hall transition points is given in terms of percolation theory.

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K. Ziegler. 1995-05-15. Two-Dimensional Electrons in a Strong Magnetic Field with Disorder: Divergence of the Localization Length. https://doi.org/10.1209/0295-5075%2F31%2F9%2F008

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