Quantum hall conductivity in a Landau type model with a realistic geometry II |
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Authors: | F. Chandelier T. Masson J.-C. Wallet |
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Affiliation: | a Groupe de Physique Théorique, Institut de Physique Nucléaire F-91406 Orsay Cedex, France b Laboratoire de Physique Théorique (UMR 8627) Bât 210, Université Paris-Sud Orsay F-91405 Orsay Cedex, France |
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Abstract: | We use a mathematical framework that we introduced in a previous paper to study geometrical and quantum mechanical aspects of a Hall system with finite size and general boundary conditions. Geometrical structures control possibly the integral or fractional quantization of the Hall conductivity depending on the value of NB/2π (N is the number of charge carriers and B is the magnetic field). When NB/2π is irrational, we show that monovaluated wave functions can be constructed only on the graph of a free group with two generators. When NB/2π is rational, the relevant space becomes a punctured Riemann surface. We finally discuss our results from a phenomenological viewpoint. |
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Keywords: | 71.10.&minus w 02.40.&minus k |
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