No-go results of flux trapping in Josephson junction networks in unconventional superconductors

A network of Josephson junctions consists of superconducting islands weakly coupled through coherent Cooper-pair tunneling. It can appear in superconducting polycrystals as well as single crystals. The interplay among the pairing symmetry, Josephson coupling, charging energy, and vortices can give rise to flux quantization and flux trapping, producing fluxoid states. We examine the no-go conditions under which a Josephson junction network cannot spontaneously trap a flux in unconventional superconductors and how this encodes the underlying superconducting pairing symmetry.