RESUMEN
Monolayer FeSe grown on SrTiO3 (FeSe/STO) is an interfacial high-temperature superconductor distinctively different from bulk FeSe. However, the superconducting phase coherence of the interface is challenging to probe due to its fragility in the atmosphere. Here, we perform in situ mutual inductance under ultrahigh vacuum on FeSe/STO in combination with band mapping by angle-resolved photoemission spectroscopy. We find that even though the monolayer shows a gap-closing temperature above 50 K, no diamagnetism is visible down to 5 K. This is the case for few-layer FeSe/STO until it exceeds a critical number of five layers, where diamagnetism suddenly appears. The suppression of diamagnetism in the monolayer is also lifted by depositing a top FeTe layer. However, Tc and superfluid density both decrease with thicker FeTe, suggesting unconventional electron pairing and phase coherence competition. Our observation may be understood by a scenario in which the interfacial superconducting phase coherence is highly anisotropic.