We explore the electrical and magnetic properties of a fractal assembly of Josephson junctions with transparent interfaces. For this purpose, we employ an Mg/MgO/MgB2 nanocomposite with similar to 16 vol. % of MgB2 nanograins, which are distributed in a fractal manner in the normal matrix. Irrespective of the low volume fraction of MgB2 nanograins, the nanocomposite behaves as a bulk-like superconductor, i.e., zero resistivity, perfect diamagnetism, and strong vortex pinning. Thus, a global Josephson phase coherence is achieved in the nanocomposite. The lower (H-c1J) and higher (H-c2J) critical fields of the Josephson network are exceptionally high (H-c1J = 96 Oe and H-c2J = 83.5 kOe) as compared to those reported previously for granular superconductors. This will give an example of robust macroscopic superconducting coherence derived from long-range proximity coupling among fractally distributed superconducting nanograins through quantum interference of Andreev quasiparticles. Transverse-field muon spin rotation measurements reveal that the mean internal field in the superconducting mixed state increases with decreasing temperature below which the Josephson phase coherence sets in, opposite to the diamagnetic response observed in magnetization measurements. This unusual behavior implies a highly disordered and fluctuating nature of the Josephson vortices in the present superconducting nanocomposite.
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