  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.
