Spectral Density of Cooper Pairs in Parallel Double Coupled Quantum Dots –Superconductor Josephson Junction: A Model Study

Abstract

The present work deals with the theoretical model analysis of spectral density of Cooper pairs in double T-shape coupled quantum dots sandwiched between two conventional superconducting leads i.e. (S-DQD-S) Josephson junction. We have considered two single level quantum dots coupled with each other in T-shape and have modelled the Hamiltonian for (S-DQD-S) junction as extended two impurity Anderson model. For this purpose, we have considered an attractive BCS-type effective interaction in superconducting lead to give rise bound Cooper pairs, coupled dots states, and also coupling between superconducting leads and one of the quantum dot state. The expression of spectral density of Cooper pairs have been obtained with the help of model Hamiltonian within BCS mean field Green’s function equation of motion approach. It is pointed that the spectral density of Cooper pairs mimic the zero bias conductance and exhibit tuneable Josephson effect in such (S-DQD-S) junction. On the basis of numerical computation, it is found that the spectral density depend on  binding energy of Cooper pairs in the leads, coupling of  energy level of the dots, dots level energy with respect to Fermi energy, and also on the coupling parameter between superconducting leads and  one of the quantum dot states in an essential way. The rich physics of spectral density in S-DQD-S junctions can provide clues to experimentalist to exhibit controllable Josephson effect leading to maximum Josephson super-current in such S-DQD-S junctions to underline potential applications in quantum devices.