Quantum Hall interferometry at finite bias with multiple edge channels

TL;DR

This paper models quantum Hall interferometers with multiple edge channels, analyzing how edge mode velocities, interactions, and temperature affect current-voltage behavior and interference visibility, aligning with recent experimental observations.

Contribution

It provides a theoretical analysis of finite-bias quantum Hall interferometry with multiple edge modes, highlighting the effects of edge mode interactions and backscattering on interference patterns.

Findings

Resonance features at low temperatures when the inner mode is fully reflected.

Exponential suppression of interference visibility at high voltages due to charge fluctuations.

Agreement of theoretical results with experimental data on interference suppression.

Abstract

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 $\nu=2/5$, 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.