We calculate the tunneling current through a Fabry-Pérot interferometer in the fractional quantum Hall regime. Within linear response theory (weak tunneling but arbitrary source-drain voltage), we find a general expression for the current due to tunneling of quasiparticles in terms of Carlson's $R$ function. Our result is valid for fractional quantum Hall states with an edge theory consisting of a charged channel and any number of neutral channels, with possibly different edge velocities and different chiralities. We analyze the case with a single neutral channel in detail, which applies for instance to the edge of the Moore-Read state. In addition, we consider an asymmetric interferometer with different edge lengths between the point contacts on opposite edges, and we study the behavior of the current as a function of varying edge length. Recent experiments attempted to measure the Aharanov-Bohm effect by changing the area inside the interferometer using a plunger gate. Theoretical analyses of these experiments have so far not taken into account the accompanying change in the edge lengths. We show that the tunneling current exhibits multiple oscillations as a function of this edge length, with frequencies proportional to the injected edge current and inversely proportional to the edge velocities. In particular, the edge velocities can be measured by looking at the Fourier spectrum of the edge current. We provide a numerical scheme to calculate and plot the $R$ function, and include sample plots for a variety of edge states with parameter values, which are experimentally relevant.

• Received 6 June 2013

DOI:https://doi.org/10.1103/PhysRevB.89.045308