Charge and Statistics of Quasiholes in Pfaffian States of Composite Fermion Excitations

TL;DR

This paper investigates the charge and statistical properties of quasiholes in Pfaffian states of composite fermion excitations, revealing fractional charges and complex braiding statistics relevant to quantum Hall systems.

Contribution

It provides a detailed analysis of quasihole charge and statistics in Pfaffian states, including the role of Jain quasiparticles and potential Read-Rezayi states.

Findings

Quasihole charge is ± e/(2q) at filling fraction ν=p/q.

Quasihole statistics correspond to the spinor representation of a combined U(1)×SO(2N_qh) group.

The phase factor for quasihole braiding is e^{i(1/8+1/4m)π} with m=1+α.

Abstract

The charge of quasiparticles in Pfaffian states of composite fermion excitations (the presence of which is indicated by recent experiments) is found. At the filling fraction of the Pfaffian state $\nu=p/q$ (of the lowest Landau level) the charge is $\pm e/(2q)$. As in the case of the Pfaffian state of electrons the statistics of $N_{qh}$ quasiholes in the Pfaffian state corresponds to the spinor representation of $U(1)\times SO(2N_{qh})$ (the continuous extension of the braid group). Here U(1) is given by the phase factor $e^{i({1/8}+\frac{1}{4m})\pi}$ with $m=1+\alpha$, $\alpha$ -- the exclusion statistics parameter of Jain quasiparticles. The possiblity of Read-Rezayi states of Jain quasiparticles is also discussed.