Charge and Statistics of Quasiparticles in Fractional Quantum Hall Effec

TL;DR

This paper investigates the charge and statistical properties of quasiparticles in fractional quantum Hall states using Berry phase methods, providing new insights into their quantization and numerical validation at specific filling factors.

Contribution

It introduces a Berry phase approach to determine quasiparticle charge and statistics, and numerically confirms these properties for certain fractional quantum Hall states.

Findings

Quasiparticle charge q=(n/(2pn+1))e

Statistical parameter θ=n/(2pn+1)

Statistics parameter well-defined for quasielectrons at ν=1/3

Abstract

We have studied here the charge and statistics of quasiparticle excitations in FQH states on the basis of the Berry phase approach incorporating the fact that even number of flux quanta can be gauged away when the Berry phase is removed to the dynamical phase. It is observed that the charge $q$ and statistical parameter $\theta$ of a quasiparticle at filling factor $\nu=\frac{n}{2pn+1}$ are given by $q=(\frac{n}{2pn+1})e$ and $\theta=\frac{n}{2pn+1}$, with the fact that the charge of the quasihole is opposite to that of the quasielectron. Using Laughlin wave function for quasiparticles, numerical studies have been done following the work of Kj{\o}nsberg and Myrheim \cite{KM} for FQH states at $\nu=1/3$ and it is pointed out that as in case of quasiholes, the statistics parameter can be well defined for quasielectrons having the value $\theta=1/3$.