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• W2085223208 abstract "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-$1/2$ 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 $d$ between the junctions. The decay is characterized by an exponent which depends on the strength of the interaction. At finite temperatures $T$, lower than the superconducting transition temperature $T_c$, there is a crossover from algebraic to exponential decay of the critical current as a function of $d$, at a distance of the order of $hbar v_F/k_B T$. Moreover, the dependence of critical current on temperature shows non-monotonic behavior. If the Luttinger liquid is confined to a ring of circumference $L$, 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 $hbar v_F/k_B L$. 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" @default.
• W2085223208 created "2016-06-24" @default.
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• W2085223208 date "1996-03-01" @default.
• W2085223208 modified "2023-09-23" @default.
• W2085223208 title "dc and ac Josephson effect in a superconductor–Luttinger-liquid–superconductor system" @default.
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• W2085223208 doi "https://doi.org/10.1103/physrevb.53.6653" @default.
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