Effects of voltage fluctuations on the current correlations in mesoscopic Y-shaped conductors

TL;DR

This paper investigates how voltage fluctuations influence current correlations in mesoscopic Y-shaped conductors, revealing that external impedances can induce positive cross correlations, a departure from behavior in simpler two-terminal systems.

Contribution

It introduces a theoretical framework for analyzing feedback effects of voltage fluctuations on current correlations in Y-shaped conductors with finite impedance probes.

Findings

External impedances can cause positive cross correlations in Y-shaped conductors.

Current moments cannot be simply rescaled from bare moments due to impedance effects.

Formulas are provided for parameter ranges leading to positive correlations.

Abstract

We study current fluctuations in a phase coherent Y-shaped conductor connected to external leads and voltage probes. The voltage probes are taken to have finite impedances and thus can cause voltage fluctuations in the circuit. Applying the Keldysh formulation and a saddle point approximation appropriate for slow fluctuations, we examine at zero temperature the feedback effects on the current fluctuations due to the fluctuating voltages. We consider mesoscopic Y-shaped conductors made of tunnel junctions and of diffusive wires. Unlike two-terminal conductors, we find that for the Y-shaped conductors the current moments in the presence of external impedances cannot be obtained from simple rescaling of the bare moments already in the second moments. As a direct consequence, we find that the cross correlation between the output terminals can become positive due to the impedances in the circuit. We provide formulas for the range of parameters that can cause positive cross correlations.