Y-junction of superconducting Josephson chains

TL;DR

This paper investigates the phase diagram of a Y-junction of superconducting Josephson chains, revealing a new attractive fixed point at specific flux conditions and analyzing the role of instantons in this transition.

Contribution

It introduces the concept of a finite coupling fixed point emerging at flux $f = \pi$ and details the influence of W-instantons on the stability of fixed points.

Findings

A new attractive fixed point appears at $f=\pi$

W-instantons destabilize the strongly coupled fixed point at $f=\pi$

The phase diagram resembles that of quantum Brownian motion on frustrated lattices

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 $f \neq \pi$, 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.