Map of superconducting and insulating states as a function of Josephson energy E J and temperature T . The wave impedance (Z=h/(4e^2)K_g^{-1}) satisfies 1/ Z 2 ∝ E J for constant E g . The dashed line marks the boundary between long-range and short-range behaviour, T ins , given by equation ( 1 ). Below T ins , the physics is governed by the long-range phase stiffness K g with a superconductor–insulator transition at π K g ≈ 3/2. Above T ins , physics is governed by the short-range phase stiffness K C with a superconductor–insulator transition as π K C ≈ 1. The solid black curve traces the crossover from local to global superconductor–insulator transition. The outlined box indicates superinductance region probed in this experiment.
