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 $T_{rm c}=8.5$ K has been found to be deep inside the BCS-BEC crossover regime. Here we report experimental signatures of preformed Cooper pairing in FeSe below $T^*sim20$ K, whose energy scale is comparable to the Fermi energies. In stark contrast to usual superconductors, large nonlinear diamagnetism by far exceeding the standard Gaussian superconducting fluctuations is observed below $T^*sim20$ K, providing thermodynamic evidence for prevailing phase fluctuations of superconductivity. Nuclear magnetic resonance (NMR) and transport data give evidence of pseudogap formation at $sim T^*$. The multiband superconductivity along with electron-hole compensation in FeSe may highlight a novel aspect of the BCS-BEC crossover physics.
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