Josephson frequency of fractional charges from Shot Noise measurements

The determination of the quasiparticles charge e^* is crucial to understand the Fractional Quantum Hall Effect (FQHE) phases occurring at fractional filling factors ν. Among various attempts to measure e^*, the most reliable were based on the tiny shot noise produces by their granularity^1,2. However, for complex FQHE states such as ν=2/5 or 2/3, noise measurements may give unexpected charges depending on experimental conditions^3,4. Here, we present a novel fractional charge measurement based on the Josephson frequency fj=e^*V/h which manifests as singularities in the Photo-Assisted Shot Noise (PASN) when fj matches the microwave irradiation frequency f. Measurements are done on a QPC realized on high mobility GaAs/AlGaAs heterojunctions. Cross-correlated and auto-correlated current fluctuations are recorded to provide the shot noise. The Josephson frequency gives e*=e/5 for v=2/5, while for v=1/3 fj gives e*=e/3 even at low temperature.

[1] L. Saminadayar et al., Phys. Rev. Lett. 79, 2526 (1997)
[2] R. de-Picciotto et al., Nature 389,162-164 (1997)
[3] Y.C. Chung et al., Phys. Rev. Lett. 91 216804 (2003)
[4] A. Bid et al., Phys. Rev. Lett. 103 236802 (2009)