Finite frequency current fluctuations and the self-consistent perturbation theory for electron transport through quantum dot

TL;DR

This paper develops a self-consistent perturbation theory framework for electron transport through quantum dots, ensuring current conservation and gauge invariance, and applies it to analyze finite frequency noise with interaction effects.

Contribution

It introduces a gauge-invariant, self-consistent perturbation approach for nonequilibrium electron transport, extending analysis of current noise to finite frequencies with interactions.

Findings

Derived general formulas for current and noise in time-dependent potentials.

Established the gauge invariance and current conservation in the perturbation theory.

Provided an analytical expression for interaction effects on finite frequency noise within Hartree approximation.

Abstract

We have formulated the problem of electron transport through interacting quantum dot system in the framework of self-consistent perturbation theory, and show that the current conservation condition is guaranteed due to the gauge invariant properties of the Green's functions and the generalized Ward identity. By using a generating functional for the statistics of the nonequilibrium system, we have obtained general formulae for calculating the current and the current fluctuations in the presence of arbitrary time-dependent potentials. As demonstration of application, we have studied the interaction effects on the finite frequency noise for electron resonant tunneling through an Anderson impurity, and obtained an analytical equation for the interaction effect on the finite frequency current noise within the Hartree approximation, which is an extension of the previous results obtained by Hershfield on zero frequency shot noise.