Irreducible Green Functions Method applied to nanoscopic systems

TL;DR

This paper introduces a modified equation of motion approach using irreducible Green functions to analyze quantum dot systems, successfully capturing the Abrikosov-Suhl resonance in various cases and providing results consistent with experimental data.

Contribution

It presents a novel application of irreducible Green functions within the EOM framework to effectively analyze quantum dots coupled to metallic and superconducting leads, including asymmetric cases.

Findings

Successfully reproduces the Abrikosov-Suhl resonance in symmetric and asymmetric cases.

Calculates density of states and differential conductance matching experimental data.

Provides a decoupling scheme for infinite Green function equations.

Abstract

The equation of motion method (EOM) for Green functions is one of the tools used in the analysis of quantum dot system coupled with metallic and superconducting leads. We investigate modified EOM, based on differentiation of double-time temperature dependent Green functions both after primary time t and secondary time t'. Our EOM approach allows us to obtain the Abrikosov-Suhl resonance both in the particle-hole symmetric case but also in the asymmetric cases. We will apply the irreducible Green functions technique to analyses the EOM for dot system. This method give a workable decoupling scheme breaking the infinite set of Green function equations. We apply this technique for calculating the density of the states and the differential conductance of single-level quantum dot with Coulomb repulsion attached to one metallic and one superconducting leads (N-QD-SC). Our results are compared with the experimental data and previous calculations.