The physics of the crossover between weak-coupling Bardeen–Cooper–Schrieffer (BCS) and strong-coupling Bose–Einstein condensate (BEC) limits gives a unified framework of quantum-bound (superfluid) states of interacting fermions. This crossover has been studied in the ultracold atomic systems, but is extremely difficult to be realized for electrons in solids. Recently, the superconducting semimetal FeSe with a transition temperature Tc=8.5 K has been found to be deep inside the BCS–BEC crossover regime. Here we report experimental signatures of preformed Cooper pairing in FeSe, whose energy scale is comparable to the Fermi energies. In stark contrast to usual superconductors, large non-linear diamagnetism by far exceeding the standard Gaussian superconducting fluctuations is observed below T*∼20 K, providing thermodynamic evidence for prevailing phase fluctuations of superconductivity. Nuclear magnetic resonance and transport data give evidence of pseudogap formation at ∼T*. The multiband superconductivity along with electron–hole compensation in FeSe may highlight a novel aspect of the BCS–BEC crossover physics.

We conducted77 Se-nuclear magnetic resonance studies of the iron-based superconductor FeSe in magnetic fields of 0.6 to 19 T to investigate the superconducting and normal-state properties. The nuclear spin-lattice relaxation rate divided by the temperature (T1T ) −1 increases below the structural transition temperature Ts but starts to be suppressed below T * , well above the superconducting transition temperature Tc(H), resulting in a broad maximum of (T1T ) −1 at Tp(H). This is similar to the pseudogap behavior in optimally doped cuprate superconductors. Because T * and Tp(H) decrease in the same manner as Tc(H) with increasing H, the pseudogap behavior in FeSe is ascribed to superconducting fluctuations, which presumably originate from the theoretically predicted preformed pair above Tc(H).The discovery of superconductivity in iron pnictide 1)provided new research systems in which the unconventional superconductivity realized in strongly correlated electron compounds can be studied. Among the Fe-based superconductors (FeSCs), FeSe, which exhibits superconductivity at T c ∼ 9 K, has the simplest crystalline structure, which is called the 11 structure,2) but it exhibits several properties unlike those of other FeSCs. A tetragonal-to-orthorhombic structural transition occurs at T s ∼ 90 K without long-range antiferromagnetic (AFM) ordering down to T c .3) This is in stark contrast with the other FeSCs, such as the 122 and 1111 systems, where static AFM ordering was observed at or slightly below T s . 4,5) We reported that the 77 Se nuclear magnetic resonance (NMR) spectrum splits below T s and that the nuclear spin-lattice relaxation rate divided by T , (T 1 T ) −1 , of 77 Se is enhanced below T s . 6) These results suggest that orbital ordering induces the electronic nematic state below T s and also triggers the development of AFM fluctuations with stripe correlations breaking the C 4 symmetry in FeSe.6, 7) This scenario is consistent with the results of angle-resolved photoemission spectroscopy, 8,9) but it seems to be inconsistent with the AFM-fluctuation-driven nematic scenario.10) In any case, FeSe is an ideal system for studying the origin of the electronic nematic state in FeSCs.It was recently suggested that the superconductivity in FeSe may be in the Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein condensate (BEC) crossover regime, as an extremely small Fermi energy comparable to the superconducting (SC) condensation energy was revealed by several measurements.11, 12) In a schematic phase diagram of the attractive Hubbard model, the interaction between two fermions (e.g., electrons in solids) is in the weak-coupling regime in the BCS state and in the strongcoupling regime in the BEC state. The characteristic pa-

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