Field Theory on the von Neumann Lattice and the Quantized Hall Conductance of Bloch Electrons

Details Field Theory on the von Neumann Lattice and the Quantized Hall Conductance of Bloch Electrons Field Theory on the von Neumann Lattice and the Quantized Hall Conductance of Bloch Electrons

1998-06-16

arxiv.org/abs/cond-mat/9806185v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

16 pages, 6 figures, revtex, revised version to appear in Physica E

Scientific paper

10.1016/S1386-9477(98)00243-4

We construct useful sets of one-particle states in the quantum Hall system based on the von Neumann lattice. Using the set of momentum states, we develop a field-theoretical formalism and apply the formalism to the system subjected to a periodic potential. The topological formula of the Hall conductance written by the winding number of propagator is generalized to Bloch electrons. The relation between the winding number and the Chern number is clarified.

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