We argue that negative critical currents arise generically in Josephson junctions formed by single-channel conductors. Specifically, we theoretically study the Josephson coupling between two superconducting leads connected by a one-dimensional conductor in the Coulomb blockade regime. We show that in the clean regime the sign of the critical current alternates with the number of electrons in the normal region. For odd occupancy the critical current is negative even when the number of electrons on the conductor is large.

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• Josephson effect
• Mesoscopics
• Josephson junctions
• Nanostructures