Abstract
The Josephson current through a one-dimensional (1D) interacting electron system of length L coupled with two superconductors is studied in the presence of a barrier potential at the junction interfaces. The 1D system is treated within the framework of the Tomonaga-Luttinger liquid, in which the interaction is characterized by correlation exponents K ρ and K σ . We pay attention to the influence of Andreev reflection, which modifies the low-energy property of the 1D electron system near the junction interfaces. It is found that the critical current at low temperatures decays with increasing L as j c ∝(1/ L ) 2/ K ρ -1 , which is in striking contrast to the previous result j c ∝(1/ L ) 1/ K ρ + K σ -1 , obtained by Fazio et al. taking no account of the influence of Andreev reflection.
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