dc and ac Josephson effect in a superconductor{endash}Luttinger-liquid{endash}superconductor system

Journal Article · Fri Mar 01 04:00:00 EST 1996 · Physical Review, B: Condensed Matter

DOI:https://doi.org/10.1103/PhysRevB.53.6653· OSTI ID:282820

Fazio, R ^[1]; Hekking, F W ^[2]; Odintsov, A A ^[3]

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1. Institut fuer Theoretische Festkoerperphysik, Universtitaet Karlsruhe, 76128 Karlsruhe (Germany)
2. Theoretical Physics Institute, University of Minnesota, 116 Church Street SE, Minneapolis, Minnesota 55455 (United States)
3. Department of Applied Physics, Delft University of Technology, P.O. Box 5046, 2600 GA Delft (The Netherlands)

We calculate both the dc and the ac Josephson current through a 1-D system of interacting electrons, connected to two superconductors by tunnel junctions. We treat the (repulsive) Coulomb interaction in the framework of the one-channel, spin-1/2 Luttinger model. The Josephson current is obtained for two geometries of experimental relevance: a quantum wire and a ring. At T=0, the critical current is found to decay algebraically with increasing distance {ital d} between the junctions. The decay is characterized by an exponent which depends on the strength of the interaction. At finite temperatures {ital T}, lower than the superconducting transition temperature {ital T}{sub {ital c}}, there is a crossover from algebraic to exponential decay of the critical current as a function of {ital d}, at a distance of the order of {h_bar}{ital v}{sub {ital F}}/{ital k}{sub {ital BT}}. Moreover, the dependence of critical current on temperature shows nonmonotonic behavior. If the Luttinger liquid is confined to a ring of circumference {ital L}, coupled capacitively to a gate voltage and threaded by a magnetic flux, the Josephson current shows remarkable parity effects under the variation of these parameters. For some values of the gate voltage and applied flux, the ring acts as a {pi} junction. These features are robust against thermal fluctuations up to temperatures on the order of {h_bar}{ital v}{sub {ital F}}/{ital k}{sub {ital BL}}. For the wire geometry, we have also studied the ac-Josephson effect. The amplitude and the phase of the time-dependent Josephson current are affected by electron-electron interactions. Specifically, the amplitude shows pronounced oscillations as a function of the bias voltage due to the difference between the velocities of spin and charge excitations in the Luttinger liquid. Therefore, the ac-Josephson effect can be used as a tool for the observation of {ital spin}-{ital charge} separation. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 282820
• Journal Information: Physical Review, B: Condensed Matter, Journal Name: Physical Review, B: Condensed Matter Journal Issue: 10 Vol. 53; ISSN PRBMDO; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
COULOMB FIELD
CRITICAL CURRENT
ELECTRON-ELECTRON INTERACTIONS
JOSEPHSON EFFECT
MAGNETIC FLUX
ONE-DIMENSIONAL CALCULATIONS
SUPERCONDUCTORS
TRANSITION TEMPERATURE