Fractional charge and fractional statistics in the quantum Hall effects

Abstract

Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian quasiparticles in certain quantum Hall systems.

arXiv commentReview article; references added

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• Classification of Fermionic Topological Orders from Congruence Representations
• Molecular anyons in fractional quantum Hall effect
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Spin Seebeck Effect as a Probe for Majorana Fermions in Kitaev Spin Liquids
• Different fractional charges from auto- and cross-correlation noise in quantum Hall states without upstream modes
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• Adiabatic preparation of fractional Chern insulators from an effective thin-torus limit
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• Quantum Entanglement of Anyonic Charges and Emergent Spacetime Geometry
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