Spin-flip effects on the Andreev bound states and supercurrents in a superconductor/quantum-dot/superconductor system

We investigate the spin-flip effects on the Andreev bound states and the supercurrent in a superconductor/quantum-dot/superconductor system theoretically. The spin-flip scattering in the quantum dot can reverse the supercurrent flowing through the system, and one $\pi$-junction transition occurs. By controlling the energy level of quantum dot, the supercurrent is reversed back and another $\pi$-junction transition appears. The different influences of the spin-flip scattering and the intradot energy level on the supercurrent are interpreted in the picture of Andreev bound states.