Superperiods and quantum statistics of Laughlin quasiparticles

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 5he 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 e3 Laughlin quasielectron circling the island and the concurrent excitation of ten e5 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.