Abstract
We investigate the persistent edge currents for the parafermionic fractional quantum Hall (FQH) states on a cylinder. The currents are periodic with the unit flux ${\ensuremath{\varphi}}_{0}=hc/e$ at all temperatures. In the low temperature limit, a sequence of the parafermionic FQH states show additional oscillations. In these cases, the periods of the oscillations become ${\ensuremath{\varphi}}_{0}/k$ with $k=1,2,3,\dots{},$ indicating the collective motion of k particles.
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