2 research outputs found
DC and AC Josephson Effect in a Superconductor-Luttinger Liquid-Superconductor System
We calculate both the DC and the AC Josephson current through a
one-dimensional 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- Luttinger model.
The Josephson current is obtained for two geometries of experimental relevance:
a quantum wire and a ring. At zero temperature, the critical current is found
to decay algebraically with increasing distance between the junctions. The
decay is characterized by an exponent which depends on the strength of the
interaction. At finite temperatures , lower than the superconducting
transition temperature , there is a crossover from algebraic to
exponential decay of the critical current as a function of , at a distance
of the order of . Moreover, the dependence of critical current
on temperature shows non-monotonic behavior. If the Luttinger liquid is
confined to a ring of circumference , 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 -junction. These features are
robust against thermal fluctuations up to temperatures on the order of . 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 o