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

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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.