Two point-contact interferometer for quantum Hall systems

We propose a device, consisting of a Hall bar with two weak barriers, that can be used to study quantum interference effects in a strongly correlated system. The objective of this research is to demonstrate how the device provides a method for measuring the fractional charge and fractional statistics of quasiparticles in the quantum Hall effect through an anomalous Aharonov-Bohm period. Our methodology includes discussions on disentangling the charge and statistics through measurements at fixed filling factor and density, along with exploration of another interference effect in the nonlinear regime as the source-drain voltage is varied. The results indicate that the oscillation period can also be leveraged to measure fractional charge, while the details of the oscillation patterns can help distinguish between Fermi-liquid and Luttinger-liquid behavior. We illustrate these findings by computing the conductance of the device within edge state theory and provide estimates for parameters relevant for the experimental realization of this device.