Persistent Edge Current In the Fractional Quantum Hall Effect

TL;DR

This paper analyzes the persistent edge current in fractional quantum Hall states, deriving exact formulas and revealing anomalous flux oscillations that support the existence of hierarchical states.

Contribution

It provides the first exact formula for the persistent edge current in hierarchical fractional quantum Hall states and predicts anomalous flux oscillations at low temperatures.

Findings

Persistent edge current exhibits anomalous flux oscillations at low temperatures.

The current approaches a sawtooth function with period /m as temperature approaches zero.

The results support the existence of hierarchical states in the fractional quantum Hall effect.

Abstract

We study the persistent edge current in the fractional quantum Hall effect. We give the grand partition functions for edge excitations of hierarchical states coupled to an Aharanov-Bohm flux and derive the exact formula of the persistent edge current. For $m$-th hierarchical states with $m>1$, it exhibits anomalous oscillations in its flux dependence at low temperatures. The current as a function of flux goes to the sawtooth function with period $\phi_0/m$ in the zero temperature limit. This phenomenon provides a new evidence for exotic condensation in the fractional quantum Hall effect. We propose experiments of measuring the persistent edge current to confirm the existence of the hierarchy.