Is Hall Conductance in Hall Bar Geometry a Topological Invariant?

K. Ishikawa; N. Maeda; K. Tadaki

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arXiv · cond-mat/9409109

Is Hall Conductance in Hall Bar Geometry a Topological Invariant?

K. Ishikawa·N. Maeda·K. Tadaki

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Abstract

A deep connection between the Hall conductance in realistic situation and a topological invariant is pointed out based on von-Neumann lattice representation in which Landau level electrons have minimum spatial extensions. We show that the Hall conductance has no finite size correction in quantum Hall regime, but a coefficient of induced Chern-Simons term in QED$_3$ has a small finite size correction, although both of them are similar topological invariant.

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K. Ishikawa, N. Maeda, K. Tadaki. 1994-09-26. Is Hall Conductance in Hall Bar Geometry a Topological Invariant?. https://arxiv.org/abs/cond-mat/9409109

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