Telegraph Noise and Fractional Statistics in the Quantum Hall Effect

Abstract

We study theoretically nonequilibrium noise in the fractional quantum Hall regime for an Aharonov Bohm ring which has a third contact in the middle of the ring. We show that as a consequence of their fractional statistics the tunneling of a Laughlin quasiparticle between the inner and outer edge of the ring changes the effective Aharonov Bohm flux experienced by quasiparticles going around the ring, leading to a change in the conductance across the ring. A small current in the middle contact therefore gives rise to fluctuations in the current flowing across the ring which resemble random telegraph noise. We analyze this noise using the chiral Luttinger liquid model. At low frequencies the telegraph noise varies inversely with the quasiparticle tunneling current, and can be much larger than the shot noise. We propose that combining the Aharonov Bohm effect with a noise measurement provides a direct method for observing fractional statistics.