Josephson current of interacting electrons

Abstract

We study the Josephson current through a one-dimensional quantum wire or a ring connected to two superconductors by tunnel junctions (S-Sc-S system). The Coulomb interaction is treated by means of the Luttinger model and Haldane's concept of topological excitations. The Josephson current I c is found to be exponentially suppressed by the Coulomb interaction, I c ∝ d - 2 g p , where d is the distance between the junctions and g p is the usual parameter for the interaction strength in the Luttinger model. If the Luttinger liquid has a ring geometry, the Josephson current is sensitive to the number of electrons N modulo 4. The number of electrons can be controlled by a gate voltage and by a magnetic flux threading the ring. The Josephson current shows a periodic, quasicontinuous dependence on the gate voltage. The period corresponds to the addition of four electrons to the system. The flux dependence of the Josephson current has a stepwise form and shows h/e periodicity. The jumps are associated with the change in electron number. For strong interaction the number of electrons in the ring and consequently the Josephson current do not depend on the flux for virtually all values of the gate voltage.