Analytically solvable model of an electronic Mach-Zehnder interferometer

TL;DR

This paper presents an exact analytical model for electronic Mach-Zehnder interferometers in quantum Hall systems, linking the interference visibility to singular integral determinants and matching experimental observations.

Contribution

It introduces an exactly solvable model with arbitrary transmission coefficients and strong interactions, connecting the interference pattern to advanced mathematical determinants.

Findings

Analytic expression for interference current and visibility.

Good agreement with experimental data.

Connection between lobe structure and singular integral determinants.

Abstract

We consider a class of models of non-equilibrium electronic Mach-Zehnder interferometers built on integer quantum Hall edges states. The models are characterized by the electron-electron interaction being restricted to the inner part of the interferometer and transmission coefficients of the quantum quantum point contacts, defining the interferometer, which may take arbitrary values from zero to one. We establish an exact solution of these models in terms of single-particle quantities --- determinants and resolvents of Fredholm integral operators. In the general situation, the results can be obtained numerically. In the case of strong charging interaction, the operators acquire the block Toeplitz form. Analyzing the corresponding Riemann-Hilbert problem, we reduce the result to certain singular single-channel determinants (which are a generalization of Toeplitz determinants with Fisher-Hartwig singularities), and obtain an analytic result for the interference current (and, in particular, for the visibility of Aharonov-Bohm oscillations). Our results, which are in good agreement with experimental observations, show an intimate connection between the observed "lobe" structure in the visibility of Aharonov-Bohm oscillations and multiple branches in the asymptotics of singular integral determinants.