Tunneling conductance in superconductor-hybrid double quantum dots Josephson junction

Abstract

The present work deals with the theoretical model study to analyse the tunneling conductance across a superconductor hybrid double quantum dots tunnel junction (S-DQD-S). Recently, there are many experimental works where the Josephson current across such nanoscopic junction is found to be dependent on nature of the superconducting electrodes, coupling of the hybrid double quantum dot’s electronic states with the electronic states of the superconductors and nature of electronic structure of the coupled dots. For this, we have attempted a theoretical model containing contributions of BCS superconducting leads, magnetic coupled quantum dot states and coupling of superconducting leads with QDs. In order to include magnetic coupled QDs the contributions of competitive Kondo and Ruderman–Kittel– Kasuya–Yosida (RKKY) interaction terms are also introduced through many body effects in the model Hamiltonian at low temperatures (where Kondo temperature TK < superconducting transition temperature TC). Employing non-equilibrium Green’s function approach within mean field approximation, we have obtained expressions for density of states (DOS) and analysed the same using numerical computation to underline the nature of DOS close to Fermi level in S-DQD-S junctions. On the basis of numerical computation, it is pointed out that indirect exchange interaction between impurities (QD) i.e. RKKY interaction suppresses the screening of magnetic QD due to Cooper pair electrons i.e. Kondo effect in the form of reduction in the magnitude of sharp DOS peak close to Fermi level which is in qualitative agreement with the experimental observations in such tunnel junctions. Tunneling conductance is proportional to DOS, hence we can analyse it’s behaviour with the help of DOS.