Pairing Effects at the Edge of Paired Quantum Hall States

Abstract

We study pairing effects at the edge of paired fractional quantum Hall states using persistent edge currents as a probe. We give the grand partition functions for edge excitations of paired states (Haldane-Rezayi, Pfaffian, 331) coupled to an Aharanov-Bohm flux and derive the exact 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 ${\ensuremath{\varphi}}_{0}/2$ at zero temperature, which indicates pair condensation. This phenomenon provides an interesting bridge between superconductivity in $2+1$ dimensions and superconductivity in $1+1$ dimensions.