Monte Carlo study on phase transitions of two-band Josephson networks with superconducting grains

Based on the two-band free-energy functional, we have investigated phase transitions of a three-dimensional granular superconductor through the Monte Carlo method and finite-size scaling analysis. In the ordered lattices for this superconductor consisting of Josephson-coupled grains, we obtain an intermediate phase above the critical intraband coupling strength while maintaining a constant interband coupling coefficient. This phase is distinct from both the low-temperature superconducting phase and the high-temperature normal phase, characterized by the absence of long-range phase coherence solely for the first band. This numerical prediction can be confirmed through magnetic susceptibility calculations, and the phase diagram is qualitatively consistent with the mean-field theoretical analysis. Additionally, we have considered the effects of interband interaction between the nearest-neighbor grains and random disorders in diluted lattices with three different site occupancies. When the occupation probability exceeds the percolation threshold, the results are qualitatively similar to those of ordered lattices, and the intermediate phase likewise appears by adjusting the intraband Josephson coupling coefficient. In contrast, below the percolation threshold, such a phase does not exist because the long-range phase coherence for both bands disappears.