Anderson localization in fractional quantum Hall effect

Abstract

The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative consequences. We provide compelling theoretical evidence that the localization of a single quasiparticle of the fractional quantum Hall state at filling factor $\nu =n/(2n+1)$ has a striking {\it quantitative} correspondence to the localization of a single electron in the $(n+1)$th Landau level. By analogy to the dramatic experimental manifestations of Anderson localization in integer quantum Hall effect, this leads to predictions in the fractional quantum Hall regime regarding the existence of extended states at a critical energy, and the nature of the divergence of the localization length as this energy is approached. Within a mean field approximation these results can be extended to situations where a finite density of quasiparticles is present.

9 pages, 5 figures

References in corpus (3)

• Metal-insulator transition in two-dimensional electron systems
• Berry phases for composite fermions: effective magnetic field and fractional statistics
• Topology and many-body localization

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• Unveiling quantum criticality of disordered Aubry-André-Harper models via typical fidelity susceptibility
• Localization renormalization and quantum Hall systems
• Proposal for bulk measurement of braid statistics in fractional quantum Hall effect
• Noisy Cyclic Quantum Random Walk