Pairing Effects in the Edge of Paired Quantum Hall States

TL;DR

This paper investigates the edge state pairing effects in fractional quantum Hall systems using persistent edge currents, revealing flux periodicity, anomalous oscillations, and signatures of pair condensation linked to bulk topological order.

Contribution

It provides exact formulas for edge currents in paired quantum Hall states and predicts observable flux periodicity and oscillations, connecting topological order with superconductivity phenomena.

Findings

Edge currents are flux periodic with period $\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,",

At low temperatures, the edge currents show anomalous flux oscillations.

The zero-temperature limit indicates pair condensation, linking to topological order and superconductivity phenomena.

Abstract

We study pairing effects in the edge states of paired fractional quantum Hall states by using persistent edge currents as a probe. We give the grand partition functions for edge excitations of paired states (Pfaffian, Haldane-Rezayi, 331) coupling to an Aharanov-Bohm flux and derive the exact formulas of the persistent edge current. We show that the currents are flux periodic with the unit flux $\phi_0=hc/e$. At low temperatures, they exhibit anomalous oscillations in their flux dependence. The shapes of the functions depend on the bulk topological order. They converge to the sawtooth function with period $\phi_0/2$ 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. We propose experiments of measuring the persistent current at even denominator plateau in single or double layer systems to test our predictions.