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Quantum Hall Conductivity in a Landau Type Model with a Realistic Geometry II

F. Chandelier·Y. Georgelin·T. Masson·J. -C. Wallet
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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 fractionnal 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 irrationnal, we show that monovalued wave functions can be constructed only on the graph of a free group with two generators. When $NB/2π$ is rationnal, the relevant space becomes a puncturated Riemann surface. We finally discuss our results from a phenomenological viewpoint.

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F. Chandelier, Y. Georgelin, T. Masson, J. -C. Wallet. 2004-05-19. Quantum Hall Conductivity in a Landau Type Model with a Realistic Geometry II. https://doi.org/10.1016/j.aop.2004.07.008

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