Quantum Hall interferometry at finite bias with multiple edge channels

In a quantum Hall interferometer, the dependence of the signal on source-drain voltage is controlled by details of the edge physics, such as the velocities of edge modes and the interaction between them and with screening layers. Such dependence of the signal has been seen in recent experiments at various integer and fractional filling factors, including $\nu =2$ and $2/5$, where two edge modes are present. Here we study theoretically the current-voltage curves for various values of the relative edge velocities, interaction strength, and the temperature, in a model containing two edge modes. We consider separate cases in which the inner mode or the outer mode is weakly backscattered at the tunneling contacts. When the inner mode is completely reflected and the outer mode is partially transmitted, we find striking features at very low temperatures related to resonance of excitations of the closed inner channel. Fluctuations in the charge of the closed inner mode, caused by sparse tunneling events, lead to an exponential suppression of the interference visibility at high voltages, in agreement with experiments.