Magnetic field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at v=5/2

We show that the resistance of the v=5/2 quantum Hall state, confined to an interferometer, oscillates with magnetic field consistent with an Ising-type non-Abelian state. In three quantum Hall interferometers of different sizes, resistance oscillations at v=7/3 and integer filling factors have the magnetic field period expected if the number of quasiparticles contained within the interferometer changes so as to keep the area and the total charge within the interferometer constant. Under these conditions, an Abelian state such as the (3,3,1) state would show oscillations with the same period as at an integer quantum Hall state. However, in an Ising-type non-Abelian state there would be a rapid oscillation associated with the "even-odd effect" and a slower one associated with the accumulated Abelian phase due to both the Aharonov-Bohm effect and the Abelian part of the quasiparticle braiding statistics. Our measurements at v=5/2 are consistent with the latter.Comment: 10 pages, 8 figures, includes Supplemental Material

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

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. For the first time we report experimental evidence for the non-Abelian nature of excitations at $\nu=7/2$ and examine the fermion parity, a topological quantum number of an even number of non-Abelian quasiparticles, by measuring resistance oscillations as a function of magnetic field in Fabry-P\'erot interferometers using new high purity heterostructures. The phase of observed $e/4$ oscillations is reproducible and stable over long times (hours) near $\nu=5/2$ and $7/2$, indicating stability of the fermion parity. When phase fluctuations are observed, they are predominantly $\pi$ phase flips, consistent with fermion parity change. 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.Comment: A significantly revised version; 54 double-column pages containing 14 pages of main text + Supplementary Materials. The figures, which include a number of new figures, are now incorporated into the tex

A Fermi Fluid Description of the Half-Filled Landau Level

We present a many-body approach to calculate the ground state properties of a system of electrons in a half-filled Landau level. Our starting point is a simplified version of the recently proposed trial wave function where one includes the antisymmetrization operator to the bosonic Laughlin state. Using the classical plasma analogy, we calculate the pair-correlation function, the static structure function and the ground state energy in the thermodynamic limit. These results are in good agreement with the expected behavior at $\nu=\frac12$.Comment: 4 pages, REVTEX, and 4 .ps file

Diffusion Thermopower at Even Denominator Fractions

We compute the electron diffusion thermopower at compressible Quantum Hall states corresponding to even denominator fractions in the framework of the composite fermion approach. It is shown that the deviation from the linear low temperature behavior of the termopower is dominated by the logarithmic temperature corrections to the conductivity and not to the thermoelectric coefficient, although such terms are present in both quantities. The enhanced magnitude of this effect compared to the zero field case may allow its observation with the existing experimental techniques.Comment: Latex, 12 pages, Nordita repor

Effective Mass of the Four Flux Composite Fermion at ν=1/4\nu = 1/4

We have measured the effective mass ($m^*$) of the four flux composite fermion at Landau level filling factor $\nu = 1/4$ ($^4$CF), using the activation energy gaps at the fractional quantum Hall effect (FQHE) states $\nu$ = 2/7, 3/11, and 4/15 and the temperature dependence of the Shubnikov-de Haas (SdH) oscillations around $\nu = 1/4$. We find that the energy gaps show a linear dependence on the effective magnetic field $B_{eff}$ ($\equiv B-B_{\nu=1/4}$), and from this linear dependence we obtain $m^* = 1.0 m_e$ and a disorder broadening $\Gamma \sim$ 1 K for a sample of density $n = 0.87 \times 10^{11}$ /cm$^2$. The $m^*$ deduced from the temperature dependence of the SdH effect shows large differences for $\nu > 1/4$ and $\nu < 1/4$. For $\nu > 1/4$, $m^* \sim 1.0 m_e$. It scales as $\sqrt{B_{\nu}}$ with the mass derived from the data around $\nu =1/2$ and shows an increase in $m^*$ as $\nu \to 1/4$, resembling the findings around $\nu =1/2$. For $\nu < 1/4$, $m^*$ increases rapidly with increasing $B_{eff}$ and can be described by $m^*/m_e = -3.3 + 5.7 \times B_{eff}$. This anomalous dependence on $B_{eff}$ is precursory to the formation of the insulating phase at still lower filling.Comment: 5 pages, 3 figure