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Symmetry, Universality and Critical Transitions in the Network Models

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Abstract:

We discuss various applications of the network models, starting with the original Chalker-Coddington (CC) network model, proposed to describe inter-plateaux transition in the integer quantum Hall effect (IQHE). We present a semi-classical picture which serves as a basis for the CC model. We then discuss various generalizations of the CC model: a two-channel per link, allowing to include spin or consider two lowest Landau levels; different symmetries of the transfer matrices corresponding to novel symmetry classes of the spin and thermal quantum Hall effects; quantum spin Hall effect with very nontrivial phase diagram. We proceed by presenting two recent network models: a weakly chiral network model constructed on the square lattices to describe levitation of extended states at low magnetic fields, and a triangular network model analogous to the original CC model, and its generalization, also supporting the levitation scenario. We discuss how the critical exponent of the transition depends on the existence of two critical energies. We conclude our review by discussing the generalization of the CC model, describing the effect of nuclear spin on the tunneling of electron, which allows spin-flip scattering.

Keywords: CRITICAL EXPONENT; LOCALIZATION LENGTH; NETWORK MODEL; QUANTUM HALL EFFECT

Document Type: Review Article

DOI: http://dx.doi.org/10.1166/jctn.2011.1698

Publication date: March 1, 2011

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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