Flux State in von Neumann lattice and Fractional Hall Effect

Abstract

Formulation of quantum Hall dynamics using von Neumann lattice of guiding center coordinates is presented. A topological invariant expression of the Hall conductance is given and a new mean field theory of the fractional Hall effect based on flux condensation is proposed. Because our mean field Hamiltonian has the same form as Hofstadter Hamiltonian, it is possible to understand characteristic features of the fractional Hall effect from Hofstadter's spectrum. Energy gap and other physical quantities are computed and are compared with the experiments. A reasonable agreement is obtained.

arXiv comment28 pages, LaTeX, 4 figures

Cited by in corpus (6)

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• Effective Hamiltonian for striped and paired states at the half-filled Landau level
• Robust translational invariance in topological bands against lattice potentials and disorders