Localization and conductance fluctuations in the integer quantum Hall effect: Real--space renormalization group approach

Details Localization and conductance fluctuations in the integer quantum Hall effect: Real--space renormalization group approach Localization and conductance fluctuations in the integer quantum Hall effect: Real--space renormalization group approach

1997-01-02

arxiv.org/abs/cond-mat/9701010v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

17 pages, RevTex, 7 figures

Scientific paper

10.1103/PhysRevB.56.1422

We consider the network model of the integer quantum Hall effect transition. By generalizing the real--space renormalization group procedure for the classical percolation to the case of quantum percolation, we derive a closed renormalization group (RG) equation for the universal distribution of conductance of the quantum Hall sample at the transition. We find an approximate solution of the RG equation and use it to calculate the critical exponent of the localization length and the central moments of the conductance distribution. The results obtained are compared with the results of recent numerical simulations.

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