  The BiS2-based superconductors were discovered recently. The
superconductivity has been proved by many other groups. Since the previous
experiments were all done on polycrystalline samples, therefore there remains a
concern whether the superconductivity is really derived from the materials
intrinsically or from some secondary phases. Experiments on single crystals are
highly desired. In this paper, we report the successful growth of the
NdO1-xFxBi1-yS2 single crystals. Resistive and magnetic measurements reveal
that the bulk superconducting transition occurs at about 5 K, while an
unexpected giant superconducting fluctuation appears at temperatures as high as
2-4 kBTC. Analysis based on the anisotropic Ginzbaug-Landau theory gives an
anisotropy of 30-45. Two gap features with magnitudes of about 3.5+-0.3 meV and
7.5+-1 meV were observed by scanning tunneling spectroscopy. The smaller gap is
associated with the bulk superconducting transition at about 5 K yielding a
huge ratio 2Delta_s/kBTc =16.8, the larger gap remains up to about 26 K. The
normal state recovered by applying a high magnetic field shows an anomalous
semiconducting behavior. All these suggest that the superconductivity in this
newly discovered superconductor cannot be formatted into the BCS theory.
