Modulating the Electrical Transport in Superconducting NbC Crystals by Fractal Morphology

The self-similar fractal morphology mediated by nonequilibrium processes is widely observed in low-dimensional materials grown by various techniques. Understanding how these fractal geometries affect the physical and chemical properties of materials and devices is crucial for both fundamental studies and various applications. In particular, the interplay between superconducting phase fluctuations and disorder can give rise to intriguing phenomena depending on the dimensionality. However, current experimental studies on low-dimensional superconductors are limited to two- and one-dimensional systems, leaving fractional dimensional systems largely unexplored. Here, we use chemical vapor deposition to successfully synthesize ultrathin NbC crystals with a well-defined fractal geometry at the nanoscale. By performing electrical transport measurements, we find that both the superconducting and normal-state properties are strongly affected in the fractal samples, where the intrinsic and geometric disorder is induced. In contrast to the 2D crystal, the fractal NbC crystals show a significant low-temperature resistive upturn before the onset of superconducting transition, which can be attributed to the disorder-enhanced electron-electron interaction effect. From transport data analysis, we demonstrate that the superconducting transition in NbC is correlated to the strength of disorder and the fractional dimensions, revealing that nanoscale fractal structures can significantly modify the electronic properties of low-dimensional superconductors. Our work paves the way for the explorations of mesoscopic transport and intriguing superconducting phenomena in fractional dimensions.