Observation of Interaction-Induced Modulations of a Quantum Hall Liquid's Area

Abstract

Studies of electronic interferometers, based on edge channel transport in the quantum Hall effect regime, have been stimulated by the search for evidence of abelian and non-abelian anyonic statistics of fractional charges.These studies found the ubiquitous electronic Fabry-Perot interferometer to be Coulomb dominated, thus masking coherent Aharonov-Bohm interference. Typically, the main signature of the Coulomb dominated regime is the lack of interference of the outer most edge channel as the magnetic field is varied. This seemingly surprising behavior is explained by the shrinkage of the interference area with increasing magnetic field, thus keeping the number of electrons and the enclosed flux constant. The model further stipulates, but with no experimental evidence thus far, that once the area shrinks by a size corresponding to an entire flux-quantum, it abruptly inflates to its original size leading to an unobservable 2{\pi} phase jump. Here we report on the observation of such area breathing by performing a partial screening of the Coulomb interactions. The novelty is that the variation of the phase induced by the external knobs is not fully cancelled by the area response. We infer the area variations (with a resolution on the order of ~50 nm$^{2}$) from conductance measurements. The latter are sensitive to the continuous phase variations, and reveal abrupt phase-jumps (smaller than 2{\pi}). Based on our results, we propose a new experimental tool for probing anyonic statistics.