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

F. Chandelier; Y. Georgelin; T. Masson; J. -C. Wallet

doi:10.1016/j.aop.2004.07.008

paper

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

arXiv:cond-mat/0405441 · doi:10.1016/j.aop.2004.07.008

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 $N B /2 π$ ( $N$ is the number of charge carriers and $B$ is the magnetic field). When $N B /2 π$ is irrationnal, we show that monovalued wave functions can be constructed only on the graph of a free group with two generators. When $N B /2 π$ is rationnal, the relevant space becomes a puncturated Riemann surface. We finally discuss our results from a phenomenological viewpoint.

21 pages, 7 figures, LaTeX