Fractional charge and fractional statistics in the quantum Hall effects

TL;DR

This paper reviews the theoretical concepts and experimental evidence of fractional charge, fractional statistics, and non-Abelian quasiparticles in the fractional quantum Hall effect, highlighting recent advances and ongoing challenges.

Contribution

It provides a comprehensive overview of the definitions, theoretical background, and experimental status of fractional and non-Abelian quasiparticles in quantum Hall systems.

Findings

Experimental evidence for fractional charge and statistics

Discussion of non-Abelian quasiparticles in specific quantum Hall states

Summary of current experimental techniques and challenges

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.