Josephson effect in a Coulomb-blockaded SINIS junction

The problem of a Josephson current through a Coulomb-blocked nanoscale superconductor-normal-superconductor structure with tunnel contacts is reconsidered. Two different contributions to the phase-biased supercurrent I(ϕ) are identified, which are dominant in the limits of weak and strong Coulomb interaction. Full expression for the free energy valid at arbitrary Coulomb strength is found. The current derived from this free energy interpolates between known results for weak and strong Coulomb interaction as the phase bias changes from 0 to π. In the broad range of Coulomb strength, the current-phase relation is substantially nonsinusoidal and qualitatively different from the case of semiballistic SNS junctions. The Coulomb interaction leads to the appearance of a local minimum in the current at some intermediate value of the phase difference applied to the junction.