Fractional Spin for Quantum Hall Effect Quasiparticles

Abstract

We investigate the issue of whether quasiparticles in the fractional quantum Hall effect possess a fractional intrinsic spin. The presence of such a spin $S$ is suggested by the spin-statistics relation $S=θ/2π$, with $θ$ being the statistical angle, and, on a sphere, is required for consistent quantization of one or more quasiparticles. By performing Berry-phase calculations for quasiparticles on a sphere we find that there are two terms, of different origin, that couple to the curvature and can be interpreted as parts of the quasiparticle spin. One, due to self-interaction, has the same value for both the quasihole and quasielectron, and fulfills the spin-statistics relation. The other is a kinematical effect and has opposite signs for the quasihole and quasielectron. The total spin thus agrees with a generalized spin-statistics theorem $(S_{qh} + S_{qe})/2 = θ/2π$. On the plane, we do not find any corresponding terms.