Title: Vortex formation and exotic superconducting states in field-cooled Sn-Pb solders

Abstract: Formation of vortices is a typical phenomenon of type-II superconductors under magnetic fields (H). In contrast, type-I superconductors do not host vortices because of their Meissner state. As rare cases, vortices have been observed in intermediate states of type-I superconductors; in addition, the recent observation of type-II superconductivity with vortices in a (originally type-I) Pb crystal film at extremely low temperature (T) under H has opened new pathway to study vortex physics. However, thermodynamic characteristics of such type-II-like superconducting states with vortices in originally type-I element superconductors have not been detected because of the lack of bulk example. In this study, we investigated superconducting states of phase-separated Sn-Pb solders using specific heat and magnetization to reveal magnetic-flux-trapping mechanisms. Here, we show that Sn islands in the Sn-Pb solders exhibit type-II-like superconducting states with vortices when the solders host extremely high magnetic fluxes after field cooling. Furthermore, with increasing T, the amount of trapped flux decreases, and the driving force of the magnetic flux changes from type-II superconducting states of Sn to supercurrent of Pb regions surrounding the Sn islands. The field-cooled Sn-Pb solders are rich in physics of bulk vortex formation and anomalously enhanced supercurrent in element (originally type-I) superconductors.