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Persistent Edge Current In the Fractional Quantum Hall Effect

Kazusumi Ino
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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 $ϕ_0/m$ 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.

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Kazusumi Ino. 1998-09-19. Persistent Edge Current In the Fractional Quantum Hall Effect. https://doi.org/10.1103/physrevlett.81.5908

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