Quantum Hall effect with realistic boundary conditions

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Abstract
Earlier theories of the quantum Hall effect depend on boundary conditions (cylindrical, toroidal, etc.) which are very different from that of the experimental devices (essentially striplike). To remove this discrepancy, we show that the Hall conductivity has an exponential locality property whenever the Fermi energy lies between the levels of the bulk extended states, and that this is true in spite of the edge states at the Fermi energy. We describe in detail how this locality property can be used to adapt the gauge-symmetry argument of Laughlin and the topological-invariant approach of Niu, Thouless, and Wu to conditions that are much closer to real experimental ones. The resulting conclusion is that the boundary correction to the quantization of the Hall conductance is exponentially small when the system size is large compared with a microscopic length (typically the magnetic length).