Is Hall Conductance in Hall Bar Geometry a Topological Invariant?

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.

13 pages, 2 figures uuencoded, phyzzx, EPHOU-94-005