Quasicrystal nanowires in SNS-junctions

Abstract: Quasicrystals are systems that are ordered but not periodic. They do however still have long-range order and well-defined diffraction peaks. This leads to interesting properties, like critical states which are neither extended nor localized, and to topological invariants and edge states. We study how these peculiar properties impact superconductivity in an SNS-junction, by attaching superconducting leads to a quasicrystal nanowire. We choose to investigate proximitzed superconductivity in Fibonacci quasicrystals, since their normal state has been thoroughly studied and understood. Using the Bogoliubov-de Gennes method and solving the order parameter self-consistently, we calculate the proximity effect as well as the Josephson current. We find that quasicrystals can enhance the proximity effect and significantly enhance the Josephson currents.