Spectral density of Cooper pairs in two level quantum dot–superconductors Josephson junction

• The present work deals with the study of the electronic spectral density of electron pairs and its effect in charge transport in superconductor-quantum dot-superconductor junctions.
• The charge transfer across such junctions can be controlled by changing the positions of the dot level.
• The Josephson supercurrent can also be tuned by controlling the position of quantum dot energy levels.

In the present paper, we report the role of quantum dot energy levels on the electronic spectral density for a two level quantum dot coupled to s-wave superconducting leads. The theoretical arguments in this work are based on the Anderson model so that it necessarily includes dot energies, single particle tunneling and superconducting order parameter for BCS superconductors. The expression for single particle spectral function is obtained by using the Green's function equation of motion technique. On the basis of numerical computation of spectral function of superconducting leads, it has been found that the charge transfer across such junctions can be controlled by the positions and availability of the dot levels.