Magnetization of multiply connected superconductors with and without π-junctions loops

The magnetic behaviour of multiply connected superconductors (MCS) can be described by analysing the simplest loop structures containing Josephson junctions: conventional loops with all conventional Josephson junctions and π-loops with an odd subset of π-junctions. The latter are unconventional Josephson junctions in which the coupling has the reversed sign and appears in the ceramic materials as a consequence of d-pairing. Among MCS, the magnetic behaviour of large β two-dimensional Josephson junction arrays (JJA) is based on the single loop behaviour. Solving full mutual inductance Josephson junction square array equations with and without π-loops shows that the mutual inductance coupling influences the distribution of π/conventional loops without substantially altering their single loop magnetization. The JJA mean magnetic behaviour in a low field can be recovered using a simple energy approach based on the single loop solutions avoiding the solution of the array equations. Also, we draw some consequences on the behaviour of more complex MCS as high-Tc ceramics and their observed paramagnetic susceptibilities (paramagnetic Meissner effect).