Inhomogeneous Superconductivity in Comb-Shaped Josephson Junction Networks

TL;DR

This paper demonstrates that inhomogeneous Josephson junction networks with specific topologies exhibit enhanced critical currents due to non-perturbative renormalization effects, confirmed through theoretical modeling and experiments.

Contribution

It reveals a topology-dependent renormalization effect in Josephson networks, showing how network structure influences superconducting properties.

Findings

Critical currents are enhanced along specific directions in comb-shaped networks.

Theoretical predictions align well with experimental measurements.

Networks with hidden spectra exhibit non-perturbative renormalization effects.

Abstract

We show that some of the Josephson couplings of junctions arranged to form an inhomogeneous network undergo a non-perturbative renormalization provided that the network's connectivity is pertinently chosen. As a result, the zero-voltage Josephson critical currents $I_c$ turn out to be enhanced along directions selected by the network's topology. This renormalization effect is possible only on graphs whose adjacency matrix admits an hidden spectrum (i.e. a set of localized states disappearing in the thermodynamic limit). We provide a theoretical and experimental study of this effect by comparing the superconducting behavior of a comb-shaped Josephson junction network and a linear chain made with the same junctions: we show that the Josephson critical currents of the junctions located on the comb's backbone are bigger than the ones of the junctions located on the chain. Our theoretical analysis, based on a discrete version of the Bogoliubov-de Gennes equation, leads to results which are in good quantitative agreement with experimental results.