Keldysh Functional Integral Theory of Non-equilibrium Kondo Bridge

TL;DR

This paper develops a Keldysh functional integral approach to calculate non-equilibrium Green's functions for a nano-sized quantum dot in the Kondo regime, revealing stepwise current increases related to phonon frequencies.

Contribution

It introduces a novel Keldysh functional integral method for analyzing non-equilibrium Kondo systems with vibrational modes, providing new insights into tunneling current behavior.

Findings

Current exhibits stepwise increases at biases exceeding multiples of phonon frequency

Method effectively captures non-equilibrium Green's functions in Kondo regime

Results enhance understanding of electron-phonon interactions in nano-scale devices

Abstract

We develop a consistent method for calculating non-equilibrium Green's functions for a nano-sized dot coupled to electron reservoirs by tunneling. The leads are generally at different chemical potentials (non-equilibrium), and the dot may be a single molecule characterized by its own vibrational frequency $\wph$. We carry out a Keldysh functional analysis of the effective Green's functions of the local electron in the dot, and also of the vibration mode, in the Kondo regime. Finally, the tunneling current is calculated as a function of bias using non-equilibrium Green's function. We find stepwise increase of the current when bias exceeds even multiples of the phonon frequency.