  In conventional superconductors, very narrow superconducting fluctuation
regions are observed above $T_c$ because of the strong overlapping of Cooper
pairs in a coherence volume. In the bulk form of iron chalcogenide
superconductor FeSe, it is argued that the system may locate in the crossover
region of BCS to BEC, indicating a strong superconducting fluctuation. In this
respect, we have carried out measurements of magnetization, specific heat and
Nernst effect on FeSe single crystals in order to investigate the
superconducting fluctuation effect near $T_c$. The region of diamagnetization
induced by superconducting fluctuation seems very narrow above $T_c$. The
crossing point of temperature dependent magnetization curves measured at
different magnetic fields, which appears in many systems of cuprate
superconductors and is regarded as indication of strong critical fluctuation,
is however absent. The magnetization data can be scaled based on the
Ginzburg-Landau fluctuation theory for a quasi-two-dimensional system, but the
scaling result cannot be described by the theoretical function of the
fluctuation theory because of the limited fluctuation regions. The specific
heat jump near $T_c$ is rather sharp without the trace of strong
superconducting fluctuation. This is also supported by the Nernst effect
measurements which indicate a very limited region for vortex motion above
$T_c$. Associated with very small value of Ginzburg number and further
analyses, we conclude that the superconducting fluctuation is very weak above
$T_c$ in this material. Our results are strongly against the picture of
significant phase fluctuation in FeSe single crystals, although the system has
a very limited overlapping of Cooper pairs in the coherence volume. This
dichotomy provides new insights into the superconducting mechanism when the
system is with a dilute superfluid density.
