Unusual paramagnetic phenomena in granular high-temperature superconductors—A consequence of $d$- wave pairing?

This colloquium reviews some unusual paramagnetic phenomena in granular high-temperature superconductors. These are consistently explained by assuming that there is frustration in the coupling patterns between the neighboring grains. Such frustration effects occur in a natural way in a multiply connected superconductor with Josephson junctions if the order parameter has unconventional symmetry due to Cooper pairing in a higher angular momentum channel, e.g., $d$- wave pairing. A simple model is introduced to describe the magnetic properties of a frustrated granular superconductor. Large orbital magnetic moments are spontaneously created, leading to superparamagnetic behavior. These results suggest that the unusual paramagnetic phenomena are a consequence of unconventional symmetry of the pairing state in the high-temperature superconductors.