Y-junction of superconducting Josephson chains

Abstract

We show that, for pertinent values of the fabrication and control parameters, an attractive finite coupling fixed point emerges in the phase diagram of a Y-junction of superconducting Josephson chains. The new fixed point arises only when the dimensionless flux $f$ piercing the central loop of the network equals $\pi$ and, thus, does not break time-reversal invariance; for $f\ne \pi$, only the strongly coupled fixed point survives as a stable attractive fixed point. Phase slips (instantons) have a crucial role in establishing this transition: we show indeed that, at $f=\pi$, a new set of instantons -the W-instantons- comes into play to destabilize the strongly coupled fixed point. Finally, we provide a detailed account of the Josephson current-phase relationship along the arms of the network, near each one of the allowed fixed points. Our results evidence remarkable similarities between the phase diagram accessible to a Y-junction of superconducting Josephson chains and the one found in the analysis of quantum Brownian motion on frustrated planar lattices.

32 pages, 8 .eps figures. Accepted version

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• Junctions of three quantum wires for spin 1/2 electrons
• Frustration of Decoherence in Open Quantum Systems
• Frustration of decoherence in $Y$-shaped superconducting Josephson networks
• Density matrix renormalization group algorithms for Y-junctions
• Boundary Field Theory Approach to the Renormalization of SQUID Devices
• Regular networks of Luttinger liquids
• Renormalization group study of the Kondo problem at a junction of several Luttinger wires
• Quantum wire networks with local Z2 symmetry

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