Growth and Characterization of Bi$_{2+x}$Sr$_{2-x}$CuO$_{6+\delta}$ Single Crystals

High-quality Bi$_{2+x}$Sr$_{2-x}$CuO$_{6+\delta}$(0$<$x$\leq$0.5) single crystals have been grown successfully using the travelling-solvent floating-zone(TSFZ) technique. The samples with $x >$ 0.05 are in the underdoped level. The structure of these crystals was investigated by X-ray diffraction. The evolution of c-axis lattice parameters with varied \emph{x} is displayed, which is strongly associated with the behavior of $T_{c}$. The crystals exhibit superconducting transitions with $T_c=9$ to 0.8 K for the samples with $x=0.05$ to 0.20, while for samples with $x=0.25$ and above no superconductivity was discovered down to 1.6 K. The resistivity of samples with $x$=0.31, 0.40 and 0.50 exhibits a drastic divergence as temperature approaches 0 K.