Josephson Transport through a Hubbard Impurity Center

We investigate the Josephson transport through a thin semiconductor barrier containing impurity centers with the on-site Hubbard interaction u of an arbitrary sign and strength. We find that in the case of the repulsive interaction the Josephson current changes sign with the temperature increase if the energy of the impurity level ε (measured from the Fermi energy of superconductors) falls in the interval (-u,0). We predict strong temporal fluctuations of the current if only a few centers are present within the junction. In the case of the attractive impurity potential (u<0) and at low temperatures, the model is reduced to the effective two level Hamiltonian allowing thus a simple description of the nonstationary Josephson effect in terms of pair tunneling processes.