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HAIT Journal of Science and Engineering A Volume 5, Issues 1-2, pp. 29-40 © 2008 Holon Institute of Technology | |||
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Classical versus quantum percolation in quantum Hall systems in presence of nuclear polarization
Victor Kagalovsky1,*, Israel Vagner2,3,
and Alexander Chudnovskiy4
1Sami Shamoon College of Engineering, Beer-Sheva 84100, Israel | 2Research Center for Quantum Communication Engineering, Holon Institute of Technology, 52 Golomb St., Holon 58102, Israel 3Cavendish Laboratory, Cambridge University, Madingley Road, Cambridge CB3OHE, United Kingdom 4Institut für Theoretische Physik, Universität Hamburg, Jungiusstr. 9, 20355 Hamburg, Germany *Corresponding author: victork@sce.ac.il Received 25 April 2007
| We study localization-delocalization transition in quantum Hall systems with a random field of nuclear spins acting on two-dimensional (2d) electron spins via hyperfine contact (Fermi) interaction. We use Chalker-Coddington network model, which corresponds to the projection onto the lowest Landau level. The inhomogeneous nuclear polarization acts on the electrons as an additional confining potential, and, therefore, introduces additional parameter p (the probability to find a polarized nucleus in the vicinity of a saddle point of random potential) responsible for the change from quantum to classical behavior. In this manner we obtain two critical exponents corresponding to quantum and classical percolation. We also study how the 2d extended state develops into the one-dimensional (1d) critical state. PACS: 73.20.Fz, 73.20.Jc, 74.43.-f, 31.30.Gs, 76.60.Es |