Persistent edge currents for paired quantum hall states

We study the behavior of the persistent edge current for paired quantum Hall states on the cylinder. We show that the currents are periodic with the unit flux ${\varphi }_0=hc\mathrm{/}e$. At low temperatures, they exhibit anomalous oscillations in their flux dependence.The shape of the functions converges to the sawtooth function periodic with ${\varphi }_0\mathrm{/}2$.