Induced paramagnetic states by localized $π$-loops in grain boundaries

Recent experiments on high-temperature superconductors show paramagnetic behavior localized at grain boundaries (GB). This paramagnetism can be attributed to the presence unconventional d-wave induced $π$-junctions. By modeling the GB as an array of $π$ and conventional Josephson junction we determine the conditions of the occurrence of the paramagnetic behavior.

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