Irreducible Green Functions Method applied to nanoscopic systems

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.