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Recent reports of interface-induced superconductivity in the unit-cell filmsof FeSe on SrTiO3 with a Tc up to ~ 65+-5 K, highest among the Fe-basedsuperconductors and second only to that of the cuprates, have generated greatexcitement. Here we show results of the first magnetic and resistiveinvestigation on the 1-4 unit-cell FeSe-films on SrTiO3. The samples displaythe Meissner state below ~ 20 K with a penetration field as low as 0.1 Oe dueto large edge effect at 2 K, a mesoscopic superconducting state comprisingpatches of dimension < 1 micrometer up to 45~55 K and an unusual relaxation ofthe diamagnetic signal up to 80 K, suggesting possible superconductivity atthis high temperature. The observations demonstrate the heterogeneous nature ofthe superconducting state in these films and offer new insights into the roleof interfaces in high temperature superconductivity proposed and futuresuperconducting electronics fabricated.

The Meissner and Mesoscopic Superconducting States in 1-4 Unit-Cell FeSe-Films up to 80 K