Feedback of the electromagnetic environment on current and voltage fluctuations out of equilibrium

TL;DR

This paper develops a microscopic Keldysh field theory to analyze how a macroscopic electromagnetic environment influences low-frequency current and voltage fluctuations in mesoscopic conductors, explaining experimental observations and extending previous models.

Contribution

It introduces a microscopic Keldysh field theory for environmental feedback effects on current and voltage correlators, including Coulomb blockade corrections, advancing understanding of out-of-equilibrium mesoscopic systems.

Findings

Environmental feedback mixes correlators of different orders.

Temperature affects the relation between higher-order current and voltage correlators.

Coulomb blockade corrections relate to derivatives of higher-order cumulants.

Abstract

A theory is presented for low-frequency current and voltage correlators of a mesoscopic conductor embedded in a macroscopic electromagnetic environment. This Keldysh field theory evaluated at its saddle-point provides the microscopic justification for our earlier phenomenological calculation (using the cascaded Langevin approach). The nonlinear feedback from the environment mixes correlators of different orders, which explains the unexpected temperature dependence of the third moment of tunneling noise observed in a recent experiment. At non-zero temperature, current and voltage correlators of order three and higher are no longer linearly related. We show that a Hall bar measures voltage correlators in the longitudinal voltage and current correlators in the Hall voltage. We go beyond the saddle-point approximation to consider the environmental Coulomb blockade. We derive that the leading order Coulomb blockade correction to the n-th cumulant of current fluctuations is proportional to the voltage derivative of the (n+1)-th cumulant, generalizing to any n the earlier results for n=1,2.