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The Josephson current in Luttinger liquid-superconductor junctions

J. -S. Caux·H. Saleur·F. Siano
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Abstract

We study the Josephson current through a Luttinger liquid in contact with two superconductors. We show that it can be deduced from the Casimir energy in a two-boundary version of the sine-Gordon model. We develop a new thermodynamic Bethe Ansatz, which, combined with a subtle analytic continuation procedure, allows us to calculate this energy in closed form, and obtain the complete current-crossover function from the case of complete normal to complete Andreev reflection.

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J. -S. Caux, H. Saleur, F. Siano. 2001-09-06. The Josephson current in Luttinger liquid-superconductor junctions. https://doi.org/10.1103/physrevlett.88.106402

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