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

TL;DR

This paper reviews the history, theoretical models, numerical simulations, and experimental findings related to the fractional quantum Hall effect at filling factor 5/2, highlighting its potential for topological quantum computing.

Contribution

It provides a comprehensive overview of the current understanding, debates, and recent developments concerning the enigmatic 5/2 FQH state, including possible non-Abelian anyon excitations.

Findings

Multiple topological orders proposed for the 5/2 state

Experimental evidence suggests non-Abelian anyons may exist

Future research directions to clarify the state’s nature

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.