Transport through superconductor/magnetic dot/superconductor structures

The coupling of two s-wave superconductors through a small magnetic dot is discussed. Assuming that the dot charging energy is small compared to the superconducting gap, $E_c\ll \Delta$, and that the moment of the dot is classical, we develop a simple theory of transport through the dot. The presence of the magnetic dot will position Andreev bound states within the superconducting gap at energies tunable with the magnetic properties of the dot. Studying the Josephson coupling it is shown that the constructed junction can be tuned from a "0" to a "$\pi$"-junction via a degenerate two-level state either by changing the magnetic moment of the dot or by changing temperature. Furthermore, it is shown that details of the magnetic dot can be extracted from the sub-harmonic structure in the current-voltage characteristics of the junction.