Search

The quantum Hall states at filling factors ν=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 is predicted to display a striking interferometric signature, the even-odd effect. By measuring resistance oscillations as a function of the 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 ν=7/2. At both ν=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 π 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 lifetime of their combined fermion parity further strengthens the case for their utility for topological quantum computation.

What is the fate of the ground state of a two-dimensional electron system at very low Landau level filling factors (ν) where interaction reigns supreme? An ordered array of electrons, the so-called Wigner crystal, has long been believed to be the answer. It was in fact the search for the elusive Wigner crystal that led to the discovery of an unexpected, incompressible liquid state, namely the fractional quantum Hall state at ν=1/3. Understanding the competition between the liquid and solid ground states has since remained an active field of fundamental research. Here we report experimental data for a new two-dimensional system where the electrons are confined to an AlAs quantum well. The exceptionally high quality of the samples and the large electron effective mass allow us to determine the liquid-solid phase diagram for the two-dimensional electrons in a large range of filling factors near ≃1/3 and ≃1/5. The data and their comparison with an available theoretical phase diagram reveal the crucial role of Landau level mixing and finite electron layer thickness in determining the prevailing ground states.