Recently, the detection of non-bulk superconductivity with unexpectedly high onset-Tcs up to 49 K in Pr-doped CaFe2As2 [(Ca,Pr)122] single crystals and the report of a Tc up to 65 K in one-unit-cell (1UC) FeSe epi-films, offer an unusual opportunity to seek an answer to the question posed in the title. Through systematic compositional, structural, resistive, and magnetic investigations on (Ca,Pr)122 single crystals, we have observed a doping-level-independent Tc, the simultaneous appearance of superparamagnetism and superconductivity, large magnetic anisotropy, and the existence of mesoscopic-2D structures in these crystals, thus providing clear evidence consistent with the proposed interface-enhanced Tc in these naturally occurring rareearth-doped Fe-based superconductors, (Ca,R)122. Similar resistive and magnetic measurements were also made on the 3-4UC FeSe ultrathin epi-films. We have detected weak links in the Meissner state below 20 K, weakly coupled small superconducting patches between 20-45 K, and collective excitations of spin and/or superconducting nature between 45-80 K. The unusual frequency dependences of the diamagnetic moment observed in the films in different temperature ranges will be presented and their implications discussed.
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