Full Set of Superconducting Parameters of K$_3$C$_{60}$

The superconducting parameters are the key for building or identifying the theory responsible for the mechanism of superconductivity. Such parameters for fulleride superconductors have not been well established despite the tremendous efforts over the past 30 years. Here we provide a full set of parameters through a systematic study on a well-characterized K$_{3}$C$_{60}$ sample. The obtained high upper critical field of 33.0$\pm$0.5 T from the direct electrical transport measurements together with the relatively high critical temperature and large critical current density classifies K$_{3}$C$_{60}$ as a promising three-dimensional superconducting magnet material with the advantage of the rich carbon abundance on the Earth. This high upper critical field along with the large reduced superconducting energy gap and strong phonon self-energy effect supports the strong electron-phonon coupling interactions in this superconductor. The evaluation of all self-consistently obtained parameters suggests the unconventional nature of the superconductivity for K$_3$C$_{60}$ with the joint contributions from the strong electron-phonon coupling and electron correlations. These results and findings are important not only for fundamentally understanding the superconductivity in fullerides but also for future superconducting magnet developments and applications.