Singlet-doublet transitions and Josephson currents in a superconducting ring with a quantum dot

We investigate the ground state properties of a superconducting ring embedded with a quantum dot (QD) by using a variational wave-function approach. A theoretical formulation for the treatment of the finite-U Anderson impurity coupled with a superconducting ring are presented. We demonstrate singlet-doublet transitions of the ground state for this system with the QD in the mixed valence regime. It is shown that the supercurrent in the superconductor ring shows oscillations with the external enclosed magnetic flux and exhibits abrupt jumps at the singlet-doublet phase transition points.