Proposal for unambiguous measurement of braid statistics in fractional quantum Hall effect

The quasiparticles (QPs) or quasiholes (QHs) of fractional quantum Hall states have been predicted to obey fractional braid statistics, which refers to the Berry phase (in addition to the usual Aharonov-Bohm phase) associated with an exchange of two QPs or two QHs, or equivalently, to half of the phase associated with a QP / QH going around another. Certain phase slips in interference experiments in the fractional quantum Hall regime have been interpreted as arising from the statistics associated with a QP moving along the edge of the sample around another QP in the interior. A conceptual difficulty with this interpretation is that the edge, being compressible, does not support a QP or a QH with a sharply quantized fractional charge or fractional statistics. We analyze the experiment in terms of composite fermions (CFs) obeying integral braid statistics and suggest that the observed phase slips can be naturally understood as a measure of the relative braid statistics of a CF in the ground state at the edge and a fractionally charged QP / QH in the interior; in contrast to fractionally charged excitations, the CFs are known to remain sharply defined even in compressible regions such as the edge or the CF Fermi liquid state at half filled Landau level. We further propose that transport through a closed tunneling loop confined entirely in the bulk can, in principle, allow an unambiguous measurement of the relative braid statistics of a fractionally charged QP / QH braiding around another fractionally charged QP / QH. Optimal parameters for this experimental geometry are determined from quantitative calculations.