Interference measurements of non-Abelian e/4 & Abelian e/2 quasiparticle braiding

Abstract

The quantum Hall states at filling factors $\nu =5/2$ and $7/2$ are expected to have Abelian charge $e/2$ quasiparticles and non-Abelian charge $e/4$ quasiparticles. The non-Abelian statistics of the latter has been predicted to display a striking interferometric signature, the even-odd effect. By measuring resistance oscillations as a function of magnetic field in Fabry-Pérot interferometers using new high purity heterostructures, we for the first time report experimental evidence for the non-Abelian nature of excitations at $\nu =7/2$. At both $\nu =5/2$ and $7/2$ we also examine, for the first time, the fermion parity, a topological quantum number of an even number of non-Abelian quasiparticles. The phase of observed $e/4$ oscillations is reproducible and stable over long times (hours) near both filling factors, indicating stability of the fermion parity. At both fractions, when phase fluctuations are observed, they are predominantly $\pi$ phase flips, consistent with either fermion parity change or change in the number of the enclosed $e/4$ quasiparticles. We also examine lower-frequency oscillations attributable to Abelian interference processes in both states. Taken together, these results constitute new evidence for the non-Abelian nature of $e/4$ quasiparticles; the observed life-time of their combined fermion parity further strengthens the case for their utility for topological quantum computation.

arXiv commentFinal version, nearly identical to the one published in Phys. Rev. X sans some questionable superficial changes insisted upon by the PRX editors and with Supplementary Materials included after the main text

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• Anyons in Quantum Hall Interferometry
• Edge Probes of Topological Order
• Strongly coupled edge states in a graphene quantum Hall interferometer
• Topological phase transition between composite-fermion and Pfaffian daughter states near ν = 1/2 FQHS
• Aharonov-Bohm interference and the evolution of phase jumps in fractional quantum Hall Fabry-Perot interferometers based on bi-layer graphene
• Valley-tunable, even-denominator fractional quantum Hall state in the lowest Landau level of an anisotropic system
• Even-denominator fractional quantum Hall state in conventional triple-gated quantum point contact