PAIRING EFFECTS AT THE EDGE OF PAIRED QUANTUM HALL STATES

We study pairing effects at the edge of paired fractional quantum Hall states using persistent edge currents as a probe. We give the grand p artition functions for edge excitations of paired states (Haldane Reza yi, Pfaffian, 331) coupled to an Aharanov-Bohm fur and derive the exac t formulas of the persistent edge currents. At low temperatures, they exhibit anomalous oscillations in their flux dependence. They converge to the sawtooth function with period phi(o)/2 at zero temperature, wh ich indicates pair condensation. This phenomenon provides an interesti ng bridge between superconductivity in 2 + 1 dimensions and super-cond uctivity in 1 + 1 dimensions.