Fractional quantum Hall effect at the filling factor $\nu =5/2$

Abstract

The fractional quantum Hall (FQH) effect at the filling factor $\nu =5/2$ was discovered in GaAs heterostructures more than 35 years ago. Various topological orders have been proposed as possible candidates to describe this FQH state. Some of them possess non-Abelian anyon excitations, an entirely new type of quasiparticle with fascinating properties. If observed, non-Abelian anyons could offer fundamental building blocks of a topological quantum computer. Nevertheless, the nature of the FQH state at $\nu =5/2$ is still under debate. In this chapter, we provide an overview of the theoretical background, numerical results, and experimental measurements pertaining to this special FQH state. Furthermore, we review some recent developments and their possible interpretations. Possible future directions toward resolving the nature of the $5/2$ state are also discussed.

arXiv commentUpdated version; A chapter for Encyclopedia of Condensed Matter Physics, 2nd edition (Elsevier)

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• Aharonov-Bohm Interference in Even-Denominator Fractional Quantum Hall States
• Half-integer thermal conductance in the absence of Majorana mode
• Cascade of fractional quantum Hall states in 2D system
• Shot noise signatures of candidate states for the fractional quantum Hall $\nu =12/5$ state