Strong phase coherence and vortex matter in a fractal system with proximity-induced superconductivity

We investigate vortex matter in a proximity-coupled $\mathrm{Mg}/\mathrm{MgO}/\mathrm{Mg}{\mathrm{B}}_{2}$ nanocomposite with $\ensuremath{\sim}30$ vol. % of $\mathrm{Mg}{\mathrm{B}}_{2}$ using magneto-optical imaging, scanning superconducting quantum interface device microscopy, and pinning-force analysis. This nanocomposite was prepared by spark plasma sintering (SPS) of the MgO/$\mathrm{MgO}/\mathrm{Mg}{\mathrm{B}}_{2}$ mixture powders obtained from a solid-phase reaction between Mg and ${\mathrm{B}}_{2}{\mathrm{O}}_{3}$ [Uchino et al., Phys. Rev. B 101, 035146 (2020)]. The resulting nanocomposite is characterized by scale-free (or fractal) distributions of $\mathrm{Mg}{\mathrm{B}}_{2}$ components and the atomically clean $\mathrm{MgO}/\mathrm{Mg}{\mathrm{B}}_{2}$ interfaces. It is also found that high SPS temperature ($1200{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$) is the key to improve the proximity-induced superconducting properties of the $\mathrm{Mg}/\mathrm{MgO}/\mathrm{Mg}{\mathrm{B}}_{2}$ nanocomposite. This proximity-coupled system acts as a fully phase-coherent superconductor with isotropic pinning and strong superfluid phase stiffness irrespective of the low volume fraction of $\mathrm{Mg}{\mathrm{B}}_{2}$. Our results demonstrate that in contrast to the case of conventional granular superconductors, the grain boundaries in the present system carry high critical currents and have high vortex-pinning efficiency, implying an excellent phase-coherent capability of the proximity-coupled fractal network.