Exactly Solved Model for an Electronic Mach-Zehnder Interferometer

TL;DR

This paper presents an exact solution for the nonequilibrium behavior of an electronic Mach-Zehnder interferometer in quantum Hall systems, revealing interaction effects on visibility and phase that align with experimental observations.

Contribution

It provides the first exact analytical model for the interferometer's visibility and phase under finite bias, considering electron interactions only within the device.

Findings

Visibility exhibits a lobe structure as a function of bias.

Fringe phase remains bias-independent except near zeros of visibility.

Results agree with recent experimental data.

Abstract

We study nonequilibrium properties of an electronic Mach-Zehnder interferometer built from integer quantum Hall edge states at filling fraction $\nu{=}1$. For a model in which electrons interact only when they are inside the interferometer, we calculate exactly the visibility and phase of Aharonov-Bohm fringes at finite source-drain bias. When interactions are strong, we show that a lobe structure develops in visibility as a function of bias, while the phase of fringes is independent of bias, except near zeros of visibility. Both features match the results of recent experiments [Neder \textit{et al.} Phys. Rev. Lett. \textbf{96}, 016804 (2006)].