Superperiods and quantum statistics of Laughlin quasiparticles

TL;DR

This paper explains the origin of superperiodic conductance oscillations in fractional quantum Hall systems using a microscopic model based on hierarchical fractional statistics, confirming anyonic braiding properties of quasiparticles.

Contribution

It introduces a microscopic model for the 5h/e flux superperiod in fractional quantum Hall interferometers, linking hierarchical theory with composite fermion representation.

Findings

The superperiod arises from neutral island reconstruction and quasiparticle excitations.

The Berry phase quantization confirms anyonic braiding statistics.

The composite fermion model aligns with hierarchical fractional quantum Hall theory.

Abstract

Superperiodic conductance oscillations were recently observed in the quasiparticle interferometer, where an edge channel of the 1/3 fractional quantum Hall fluid encircles an island of the 2/5 fluid. We present a microscopic model of the origin of the 5h/e flux superperiod based on the Haldane-Halperin fractional-statistics hierarchical construction of the 2/5 condensate. Since variation of the applied magnetic field does not affect the charge state of the island, the fundamental period comprises the minimal 2/5 island neutral reconstruction. The period consists of incrementing by one the state number of the e/3 Laughlin quasielectron circling the island and the concurrent excitation of ten e/5 quasiparticles out of the island 2/5 condensate. The Berry phase quantization condition yields anyonic quasiparticle braiding statistics consistent with the hierarchical construction. We further discuss a composite fermion representation of quasiparticles consistent with the superperiods. It is shown to be in one-to-one correspondence with the Haldane-Halperin theory, provided a literal interpretation of the 2/5 condensate as comprised of an integer multiple of two-composite fermion, one-vortex blocks is postulated.