Abstract
We consider the charge and spin effects in low-dimensional superconducting weak links. The first part of the review deals with the effects of electron–electron interaction in Superconductor/Luttinger liquid/Superconductor junctions. The experimental realization of this mesoscopic hybrid system can be an individual single-wall carbon nanotube that bridges a gap between two bulk superconductors. The dc Josephson current through a Luttinger liquid is evaluated in the limits of perfectly and poorly transmitting junctions. The relationship between the Josephson effect in a long SNS junction and the Casimir effect is discussed. In the second part of the paper we review the recent results concerning the influence of the Zeeman and Rashba interactions on the thermodynamic properties of ballistic S–QW–S junction fabricated in a two-dimensional electron gas. It is shown that in a magnetically controlled junction there are conditions for a resonant Cooper pair transition which results in a giant supercurrent through a tunnel junction and a giant magnetic response of a multichannel SNS junction. The supercurrent induced by the joint action of the Zeeman and Rashba interactions in 1D quantum wires connected to bulk superconductors is predicted.
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