The Properties of “Quasi-Reentrant” Behavior in Granular System

We have investigated the superconductor-insulator transition (SIT) induced by a disorder of a granular system. The effective energy gap model based on localized Cooper pairs and hopping quasiparticles has been used. The “quasi-reentrant” behavior appears when the metal volume fraction is slightly smaller than the percolation threshold. In particular, we have found the double “quasi-reentrant” behavior with the increased superconducting transition width. This result indicates that the double “quasi-reentrant” behavior should have been observed in a granular system with a large transition width. Besides, the “quasi-reentrant” behavior has been flattened when applying the magnetic field. In order to clarify the method is suitable for a granular system, the theoretical result has been compared with the experimental value of Pb \(_x\) $_x^{}$ (SiO \(_2\) $_2^{}$ ) \(_{1-x}\) $_{1-x}^{}$ granular film. It has almost no difference near the minimum value and the differences onset at lower temperatures due to the negative electroresistance effect. The “quasi-reentrant” behavior becomes unobvious due to the Copper pairs destroyed by the magnetic field.