Josephson current and proximity effect in Luttinger liquids

Dmitrii L. Maslov, Michael Stone

Research output: Contribution to journalArticlepeer-review


A theory describing a one-dimensional Luttinger liquid in contact with a superconductor is developed. Boundary conditions for the fermion fields describing Andreev reflection at the contacts are derived and used to construct a bosonic representation of the fermions. The Josephson current through a superconductor/Luttinger liquid/superconductor junction is considered for both perfectly and poorly transmitting interfaces. In the former case, the Josephson current at low temperatures is found to be essentially unaffected by electron-electron interactions. In the latter case, significant renormalization of the Josephson current occurs. The profile of the (induced) condensate wave function in a semi-infinite Luttinger liquid in contact with a superconductor is shown to decay as a power law, the exponent depending on the sign and strength of the interactions. In the case of repulsive (attractive) interactions the decay is faster (slower) than in their absence. An equivalent method of calculating the Josephson current through a Luttinger liquid, which employs the bosonization of the system as a whole (i.e., superconductor, as well as Luttinger liquid) is developed and shown to give the results equivalent to those obtained via boundary conditions describing Andreev reflection.

Original languageEnglish (US)
Pages (from-to)1548-1557
Number of pages10
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number3
StatePublished - 1996

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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