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Chalker-Coddington network model and its applications to various quantum Hall systems

Kagalovsky, V (Sami Shamoon College of Engineering)
Tuesday 04 November 2008, 09:50-10:40


We start by detailed description of the original Cahlker Coddington network model and briefly discuss its various generalizations. We then study a physical system consisting of noninteracting quasiparticles in disordered superconductors that have neither time-reversal nor spin-rotation invariance. This system belongs to class D within the recent classification scheme of random matrix ensembles, and its phase diagram contains three different phases: metallic and two distinct localized phases with different quantized thermal Hall conductances. We find that critical exponents describing different transitions (insulator-to-insulator and insulator-to-metal) are identical within the error of numerical calculations. Finally, we discuss localization-delocalization transition in quantum Hall systems with a random field of nuclear spins acting on two-dimensional electron spins via hyperfine contact Fermi interaction. 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 percolations.


[ppt ]

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