33 research outputs found
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 and are expected
to have Abelian charge quasiparticles and non-Abelian charge
quasiparticles. For the first time we report experimental evidence for the
non-Abelian nature of excitations at 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 oscillations is reproducible and stable over long times
(hours) near and , indicating stability of the fermion parity.
When phase fluctuations are observed, they are predominantly 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 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
Measurement of filling factor 5/2 quasiparticle interference: observation of charge e/4 and e/2 period oscillations
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 081259910
Current Path Properties of the Transport Anisotropy at Filling Factor 9/2
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 figure
Experimental Demonstration of Fermi Surface Effects at Filling Factor 5/2
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 figure
Composite Fermion Wavefunctions Derived by Conformal Field Theory
The Jain theory of hierarchical Hall states is reconsidered in the light of
recent analyses that have found exact relations between projected Jain
wavefunctions and conformal field theory correlators. We show that the
underlying conformal theory is precisely given by the W-infinity minimal models
introduced earlier. This theory involves a reduction of the multicomponent
Abelian theory that is similar to the projection to the lowest Landau level in
the Jain approach. The projection yields quasihole excitations obeying
non-Abelian fractional statistics. The analysis closely parallels the bosonic
conformal theory description of the Pfaffian and Read-Rezayi states.Comment: 4 pages, 1 figur