  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.
