Effects of dephasing on shot-noise in an electronic Mach-Zehnder interferometer

TL;DR

This paper theoretically investigates how dephasing affects shot noise in an electronic Mach-Zehnder interferometer, highlighting differences from phenomenological models and identifying two regimes based on fluctuation speed.

Contribution

It introduces a microscopic model for dephasing in shot noise analysis, contrasting it with existing phenomenological approaches and exploring the impact of environmental fluctuation spectra.

Findings

Slow fluctuations lead to averaged partition noise T(1-T).

Fast fluctuations modify the noise expression with transmission amplitude averages.

The model provides explicit formulas and plots for different fluctuation regimes.

Abstract

We present a theoretical study of the influence of dephasing on shot noise in an electronic Mach-Zehnder interferometer. In contrast to phenomenological approaches, we employ a microscopic model where dephasing is induced by the fluctuations of a classical potential. This enables us to treat the influence of the environment's fluctuation spectrum on the shot noise. We compare against the results obtained from a simple classical model of incoherent transport, as well as those derived from the phenomenological dephasing terminal approach, arguing that the latter runs into a problem when applied to shot noise calculations for interferometer geometries. From our model, we find two different limiting regimes: If the fluctuations are slow as compared to the time-scales set by voltage and temperature, the usual partition noise expression T(1-T) is averaged over the fluctuating phase difference. For the case of ``fast'' fluctuations, it is replaced by a more complicated expression involving an average over transmission amplitudes. The full current noise also contains other contributions, and we provide a general formula, as well as explicit expressions and plots for specific examples.