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Journal Article

Mean-field theory of fractional quantum Hall effect


Dzyaloshinskii,  I.
High Magnetic Field Laboratory, Former Departments, Max Planck Institute for Solid State Research, Max Planck Society;

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Dzyaloshinskii, I. (2002). Mean-field theory of fractional quantum Hall effect. Physical Review B, 65(20): 205325.

Cite as: https://hdl.handle.net/21.11116/0000-000E-F325-6
A phenomenological theory based on the Bloch-Zak waves
representation of electron motion in constant magnetic field
reduces all calculations to the standard operations of the
theory of electron spectra in a crystalline field in the
pseudopotential approximation. The theory automatically
predicts the Laughlin odd fraction fractional quantum Hall
effect (FQHE) but, like the gauge theory, stops short of
forbidding even fractions. Physical arguments involving
peculiarity of time-reversal symmetry breaking and the well-
known Mott criterion for stability of insulating states make
the absence of even fraction FQHE plausible. Clear physical
conditions ensure that the pseudopotentials that formally
describe effects of periodic density waves (Bravais-Zak
lattices) on electrons motion actually represent phenomena in a
genuine liquid (or a liquid crystal).