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.

Thermal Interferometry of Anyons in Spin Liquids

“…In Mach-Zehnder interferometry, the topological charge inside the device changes after each tunneling event [1,17]. Indeed, each anyon that tunnels into the inner edge of the device is eventually absorbed by a drain located inside the device.…”

“…The last three years have seen important developments in probing fractional statistics in the quantum Hall effect [1]. One development was a Fabry-Perot interferometry experiment [2] at the filling factor 1/3 (Fig.…”

Possible fractional quantum Hall effect and Wigner crystal states in two-dimensional Coulomb gases as a result of anyon correlations

“…In this effect xx and xy components of the semiconductor magneto-resistance exhibit deep minima and plateaus, respectively, at the fixed fractional numerical values of the Landau level filling factor (LLFF) [1]. Three physical factors: inter-particle Coulomb interaction, the strong magnetic field and an external disorder, are crucial for the formation of the FQHE [2,3]. It was suggested in the reviews [2,3] that above mentioned plateaus of the FQHE are results of a disorder and impurities in a sample.…”

“…Three physical factors: inter-particle Coulomb interaction, the strong magnetic field and an external disorder, are crucial for the formation of the FQHE [2,3]. It was suggested in the reviews [2,3] that above mentioned plateaus of the FQHE are results of a disorder and impurities in a sample. The effect of localization of the FQHE real space structure as well as of a 2D Wigner crystal (WC) in this disorder was demonstrated in the Ref.…”

“…In the present paper we show that the localization of the FQHE real space structure and of the WC without the disorder and impurities is possible. For the explanation of this effect, we use the finding (see reviews [2,3] and book [6]) that elementary excitations or quasiparticles, appearing from the system ground state at some fixed fractional values of the LLFF, are responsible for the FQHE, these quasi-particles are anyons, and the anyon factor equals to the LLFF fractional value. More clearly, we demonstrate in the present paper that the ground state energy of 2D Coulomb interacting anyons without magnetic field has a minimum at any fractional value of the LLFF and the physical origin of the FQHE and the WC is in this minimum, while the physical origin of the minimum is in the correlations of these anyons.…”