Superconductivity arises from two distinct quantum phenomena: electron pairing and long-range phase coherence. In conventional superconductors, the two quantum phenomena generally take place simultaneously, while the electron pairing occurs at higher temperature than the long-range phase coherence in the underdoped high-Tc cuprate superconductors. Recently, whether electron pairing is also prior to long-range phase coherence in single-layer FeSe film on SrTiO3 substrate is under debate. Here, by measuring Knight shift and nuclear spin-lattice relaxation rate, we unambiguously reveal a pseudogap behavior below Tp ~ 60 K in two layered FeSe-based superconductors with quasi-two-dimension. In the pseudogap regime, a weak diamagnetic signal and a remarkable Nernst effect are also observed, which indicate that the observed pseudogap behavior is related to superconducting fluctuations. These works confirm that strong phase fluctuation is an important character in the two-dimensional iron-based superconductors as widely observed in high-Tc cuprate superconductors.
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