Cooper pairs localization in tree-like networks of superconducting islands

Abstract

We study inhomogeneous Cooper pairs distribution and localization effects in tree-like networks of superconducting islands coupled via Josephson weak links. Using a generalized Feynman’s approach, reminiscent of the Bose–Hubbard model, we demonstrate that the Cooper pairs fraction which localizes on a specific network’s island is limited by the network topology and, if present, by the repulsive interaction. These findings contribute to clarify the interplay between confinement effects induced by the network’s topology and interaction and shed some light on recent experiments dealing with networks of Josephson junctions.

Critical Temperature and Critical Current Enhancement in Arrays of Josephson Junctions: A Ginzburg–Landau Perspective

“…In particular, the observed effects are suggestive of a nontrivial interplay between the macroscopic long-range quantum coherence and the network topology. Such effects are captured by any level of theoretical description, from a GL formulation [59][60][61][62] to more microscopic treatments [69,70], so they certainly deserve further experimental and theoretical investigations.…”

Quantum Coherence in Loopless Superconductive Networks

“…A strong argument in favor of this intuition comes from noting that the Bose–Hubbard model, under the macroscopic occupation of the lattice sites, implies a non-linear Schrodinger equation (NSE) for the condensate wavefunction. The NSE, in turn, can be organized in the form of a generalized Feynman’s model [ 12 ] describing the Josephson coupling among the lattice sites (superconducting islands). The aforementioned observation suggests a close analogy between the hopping of bosons in optical networks and Cooper pair dynamics on networks of superconducting islands coupled by the Josephson effect.…”