Aharonov-Bohm effect and coherence length of charge e/4 quasiparticles at 5/2 filling factor measured in multiple small Fabry-Perot interferometers

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.