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In conventional superconductors, very narrow superconducting fluctuationregions are observed above $T_c$ because of the strong overlapping of Cooperpairs in a coherence volume. In the bulk form of iron chalcogenidesuperconductor FeSe, it is argued that the system may locate in the crossoverregion of BCS to BEC, indicating a strong superconducting fluctuation. In thisrespect, we have carried out measurements of magnetization, specific heat andNernst effect on FeSe single crystals in order to investigate thesuperconducting fluctuation effect near $T_c$. The region of diamagnetizationinduced by superconducting fluctuation seems very narrow above $T_c$. Thecrossing point of temperature dependent magnetization curves measured atdifferent magnetic fields, which appears in many systems of cupratesuperconductors and is regarded as indication of strong critical fluctuation,is however absent. The magnetization data can be scaled based on theGinzburg-Landau fluctuation theory for a quasi-two-dimensional system, but thescaling result cannot be described by the theoretical function of thefluctuation theory because of the limited fluctuation regions. The specificheat jump near $T_c$ is rather sharp without the trace of strongsuperconducting fluctuation. This is also supported by the Nernst effectmeasurements which indicate a very limited region for vortex motion above$T_c$. Associated with very small value of Ginzburg number and furtheranalyses, we conclude that the superconducting fluctuation is very weak above$T_c$ in this material. Our results are strongly against the picture ofsignificant phase fluctuation in FeSe single crystals, although the system hasa very limited overlapping of Cooper pairs in the coherence volume. Thisdichotomy provides new insights into the superconducting mechanism when thesystem is with a dilute superfluid density.

BCS-like critical fluctuations with limited overlap of Cooper pairs in FeSe