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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-P\'erot 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., Comment: Final 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

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 Materials

Design of a Fabry-Perot (double point contact) interferometer to measure fractional quantum Hall effect quasiparticle charge properties, and in particular the 5/2 excitations, poses an important trade-off: the device size should be minimized to allow two path interference, since the coherence length of the quasiparticles in the correlated states are expected be limited, yet a small device promotes the dominance of Coulomb charging effects which would overwhelm the Aharonov-Bohm interference effect. In this study a series of small but different size interferometers from the same high density heterostructure wafer are examined for the presence of Coulomb effects versus Aharonov-Bohm (A-B) interference effect when operated in gate configurations that support the 5/2, 7/3, and 8/3 fractional quantum Hall effects. The device sizes vary by more than a factor of three, and over this range explicitly show specific properties of A-B interference, but not Coulomb dominated effects. Given these A-B interference results, the coherence length of the charge e/4 interference is extracted. The coherence length of non-Abelian e/4 quasiparticles is an important parameter for design and development of complex interference devices used to study and apply this exotic excitation. As in prior observations of e/4 excitations, A-B e/4 and e/2 oscillations in alternation are observed in these multiple devices. The amplitudes of the e/4 oscillations are observed to be dramatically reduced for larger area interferometers. Path-length limits are derived from interferometer areas determined directly by A-B measurements, and the attenuation lengths of the e/4 oscillations are shown to be micron to sub-micron scale. This coherence length is consistent with that of the 7/3 excitations measured here, and consistent with theoretical models., Comment: 31 pages, 14 figures. arXiv admin note: text overlap with arXiv:1204.1993

Non-Abelian e/4 quasiparticles at 5/2 filling factor in a correlated two-dimensional electron gas have a proposed specific property in an interference measurement of their edge propagation: encircling an even number of localized e/4 quasiparticles allows expression of e/4 Aharonov-Bohm (A-B) oscillations, but suppression of these oscillations will occur with an odd number encircled. This picture is tested explicitly here in multiple interferometers of different areas. The encircled localized e/4 quasiparticle number near 5/2 filling factor is changed by sweeping B-field, and oscillations are observed in resistance near 5/2 of period specific to that device area for each interferometer. The product of the measured interferometric area of each device and the respective 5/2 resistance oscillation period is found to agree with the expected flux quanta addition needed for parity change in the localized e/4 number. This result shows a highly specific non-Abelian property of the quasiparticle excitations at 5/2 filling expressed in multiple interferometers., Comment: 18 pages, 5 figures

It is a theoretical conjecture that 5/2 fractional quantum Hall state charge e/4 excitations may obey exotic non-Abelian statistics. In edge state interference these purported non-Abelian quasiparticles should display period e/4 Aharonov-Bohm oscillations if the interfering quasiparticle encircles an even number of localized e/4 charges, but suppression of oscillations if an odd number is encircled. To test this hypothesis, here we perform swept area interference measurements at 5/2. We observe an alternating pattern of e/4 and e/2 period oscillations in resistance. This aperiodic alternation is consistent with proposed non-Abelian properties: the e/4 oscillations occur for encircling an even number of localized quasiparticles, e/2 oscillations are expressed when encircling an odd number. Aperiodic alternation corresponds to the expected area sweep sampling the localized quasiparticles. Importantly, adding localized quasiparticles to the encircled area by changing magnetic field induces interchange of the e/4 and e/2 oscillation periods, specifically consistent with non-Abelian e/4 quasiparticles., Comment: 27 pages, 10 figures; revised version contains additional new data

A standing problem in low dimensional electron systems is the nature of the 5/2 fractional quantum Hall state: its elementary excitations are a focus for both elucidating the state's properties and as candidates in methods to perform topological quantum computation. Interferometric devices may be employed to manipulate and measure quantum Hall edge excitations. Here we use a small area edge state interferometer designed to observe quasiparticle interference effects. Oscillations consistent in detail with the Aharanov-Bohm effect are observed for integer and fractional quantum Hall states (filling factors 2, 5/3, and 7/3) with periods corresponding to their respective charges and magnetic field positions. With these as charge calibrations, at 5/2 filling factor and at lowest temperatures periodic transmission through the device consistent with quasiparticle charge e/4 is observed. The principal finding of this work is that in addtion to these e/4 oscillations, periodic structures corresponding to e/2 are also observed at 5/2 and at lowest temperatures. Properties of the e/4 and e/2 oscillations are examined with the device sensitivity sufficient to observe temperature evolution of the 5/2 quasiparticle interference. In the model of quasiparticle interference, this presence of an effective e/2 period may empirically reflect an e/2 quasiparticle charge, or may reflect multiple passes of the e/4 quasiparticle around the interferometer. These results are discussed within a picture of e/4 quasiparticle excitations potentially possessing non-Abelian statistics. These studies demonstrate the capacity to perform interferometry on 5/2 excitations and reveal properties important for understanding this state and its excitations., Comment: version 3 contains additional data beyond version 2, 26 pages, 8 figures PNAS 0812599106

We present a two-dimensional electron heterostructure field effect device of simplistic design and ease of fabrication that displays high mobility electron transport. This is accomplished using a high efficacy contacting scheme and simple metallic overlapping gate, obviating dopant layers. The resultant devices demonstrate adjustable electron densities and mobilities larger than 8x106 cm2/V-sec at the highest densities of 2.4x1011/cm2. This device type provides an experimental avenue for studying electron correlations and may answer demands for routine fabrication of practical HEMTs.

Two fundamental extensions to the function of previously described fully field effect two-dimensional (2D) electron heterostructures are presented: First, using the same basic heterostructure design of lithographically defined contacts overlain by both an insulating layer and top-gate employed for electron systems, appropriate contact material allows a high mobility 2D hole layer to be populated. Second, a simple method for producing mesoscopic structures in these devices is presented in which small-scale metallic patterns are placed on the heterostructure under the insulating and global gate layers which allows local carrier density tuning via the overlapping gate arrays. Example devices using these generally applicable methods are demonstrated.

Confinement of small-gapped fractional quantum Hall states facilitates quasiparticle manipulation and is an important step towards quasiparticle interference measurements. Demonstrated here is conduction through top gate defined, narrow channels in high density, ultra-high mobility heterostructures. Transport evidence for the persistence of a correlated state at filling fraction 5/3 is shown in channels of 2micron length but gated to near 0.3micron in width. The methods employed to achieve this confinement hold promise for interference devices proposed for studying potential non-Abelian statistics at filling fraction 5/2.

We report experimental results of low temperature magnetotransport in high mobility 2D electron systems exposed to radiation up to 20GHz frequency using a simple dipole configuration. Magnetoresistance oscillations are observed as in previously reported higher frequency radiation on 2D systems, however minima here can be seen to extend to negative biases, and zeroes previously reported are not observed persistently around the full sample perimeters. In addition, under radiation, voltages are observed from internal to external contacts in the absence of applied driving currents not due to simple rectification. These findings are consistent with micro- and macroscopic theoretical pictures of radiation induced transport and current instabilities due to local negative resistivities. However, the temperature dependent development of minima is shown to be severely power dependent, and outside of present theoretical understanding., Comment: 11 pages, 5 figures

To establish the presence and orientation of the proposed striped phase in ultra-high mobility 2D electron systems at filling factor 9/2, current path transport properties are determined by varying the separation and allignment of current and voltage contacts. Contacts alligned orthogonal to the proposed intrinsic striped phase produce voltages consistent with current spreading along the stripes; current driven along the proposed stripe direction results in voltages consistent with channeling along the stripes. Direct comparison is made to current spreading/channeling properties of artificially induced 1D charge modulated systems, which indicates the 9/2 direction., Comment: 10 pages, 4 figures

Using small wavelength surface acoustic waves (SAW) on ultra-high mobility heterostructures, Fermi surface properties are detected at 5/2 filling factor at temperatures higher than those at which the quantum Hall state forms. An enhanced conductivity is observed at 5/2 by employing sub 0.5 micron wavelength SAW, indicating a quasiparticle mean-free-path substantially smaller than that in the lowest Landau level. These findings are consistent with the presence of a filled Fermi sea of composite fermions, which may pair at lower temperatures to form the 5/2 ground state., Comment: 11 pages, 4 figures

Surface morphology of high mobility heterostructures is examined and correlated with d.c. transport. {\it All} samples examined show evidence of lines in the [1$\bar{1}$0] direction with roughness ranging from small amplitude features to severe anisotropic ridges. Transport in these samples is consistent with that in samples having artificially induced 1D charge modulations. The native surface properties reflect a prevalent, anisotropic disorder affecting 2D electron conduction. Importantly, the native lines are orthogonal to the stripes theoretically proposed to explain high Landau level transport anisotropies., Comment: 4 pages, 4 color figures; reduced length, softened conclusions

Temperature dependent weak localization is measured in metallic nanowires in a previously unexplored size regime down to width $w=5$ nm. The dephasing time, $\tau_{\phi}$, shows a low temperature $T$ dependence close to quasi-1D theoretical expectations ($\tau_{\phi} \sim T^{-2/3}$) in the narrowest wires, but exhibits a relative saturation as $T \to 0$ for wide samples of the same material, as observed previously. As only sample geometry is varied to exhibit both suppression and divergence of $\tau_{\phi}$, this finding provides a new constraint on models of dephasing phenomena., Comment: 6 pages, 3 figures