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 ν=2 and ν=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 where 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 low temperature related to resonance of excitation of the closed inner channel. However, these features disappear rapidly with increasing temperatures. We argue that the effect of a two-dimensional screening layer can be best captured by a model with an additional chiral edge channel, rather than a model coupled to an ideal two-dimensional conductor. We compare our predictions for ν=2/5 with the experimental observation in Ref. [1] including screening effects.



[1] J. Nakamura, S. Liang, G. C. Gardner, and M. J. Manfra, Fabry-Perot interferometry at the ν = 2/5 fractional quantum Hall state, arXiv:2304.12415 (2023).