Magnetization of multiply connected superconductors with and without  -junctions loops

Abstract

The magnetic behavior of Multiply Connected Superconductors (MCS) can be described analyzing the simplest loop structures containing Josephson junctions: conventional loops with all conventional Josephson junctions and π-loops with an odd subset of πjunctions. These last are unconventional Josephson junctions in which the coupling has the reversed sign and appears in the ceramic materials as consequence of d-pairing. Among MCS the magnetic behavior of large β two-dimensional Josephson Junction Arrays (JJA) is based on the single loop behavior. Solving full mutual inductance Josephson junction square array equations with and without π-loops show that the mutual inductance coupling influence the distribution of π/conventional loops without altering substantially their single loop magnetization. The JJA mean magnetic behavior in low field can be recovered using a simple energy approach based on the single loop solutions avoiding the solution of the array full equations. Also we draw some consequences on the behavior of more complex MCS as high-T C ceramics and their observed paramagnetic susceptibilities (Paramagnetic Meissner Effect).

Induced paramagnetic states by localizedπloops in grain boundaries

“…We note that magnetization of paramagnetic state is zero at a threshold field η * ≃ 0.29. The linear decrease of mean is similar to that observed for (large β) single loops [18]. For the parameters of Fig.…”

“…In general a loop containing p Josephson junctions will have different magnetization states when a magnetic field is applied. If the junctions are identical the loop current I n is a solution of the following equation [18]:…”

“…For any p the lowest energy solutions of Eq. ( 1) are diamagnetic for conventional loops and paramagnetic for π-loops [18]. When β < 1 we have only one solution in the p = 1 loop which is diamagnetic in conventional loop and paramagnetic in π-loop without spontaneous currents [3].…”

Mobile π-kinks and half-integer zero-field-like steps in highly discrete alternating 0–π Josephson junction arrays

“…The usage of π−JJs as passive π−shifters in RSFQ circuits was recently suggested in reference [18], and realized in [19]. Moreover, recent studies (both theoretical and experimental) of JJ arrays with π−JJs have shown some novel features arising out of the interplay between 0− and π−JJs [20,21,22,23,24,25,26,27,28,29,30]. For instance, when a 2π kink is introduced in a hypothetical parallel array with alternating 0− and π−JJs [31], it will break up into two separate π−kinks.…”