A note contrasting two microscopic theories of the fractional quantum Hall effect

Abstract

Two microscopic theories have been proposed for the explanation of the fractional quantum Hall effect, namely the Haldane-Halperin hierarchy theory and the composite fermion theory. Contradictory statements have been made regarding the relation between them, ranging from their being distinct to their being completely equivalent. This article attempts to provide a clarification of the issue. It is shown that the two theories postulate distinct microscopic mechanisms for the origin of the fractional quantum Hall effect, and make substantially different predictions that have allowed experiments to distinguish between them.

arXiv comment14 pages, 5 figures

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Cited by in corpus (12)

• Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
• Fermi wave vector for the non-fully spin polarized composite-fermion Fermi sea
• Interplay between fractional quantum Hall liquid and crystal phases at low filling
• Positions of the magnetoroton minima in the fractional quantum Hall effect
• Microscopic Model for Fractional Quantum Hall Nematics
• Devil's staircase phase diagram of the fractional quantum Hall effect in the thin-torus limit
• Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect
• Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in fractional quantum Hall effect
• Abelian Chern-Simons Theory for the Fractional Quantum Hall Effect in Graphene
• Composite Fermions and the First-Landau-Level Fine Structure of the Fractional Quantum Hall Effect
• Generalization of Laughlin's Theory for the Fractional Quantum Hall Effect
• Particle-Hole Mirror Symmetries around the Half-Filled Shell: The Quantum Numbers and Algebraic Structure of Composite Fermions