  We studied the correlation among structure and transport properties and
superconductivity in the different $A_x$Fe$_2$Se$_2$ single crystals ($A$ = K,
Rb, and Cs). Two sets of (00$l$) reflections are observed in the X-ray single
crystal diffraction patterns, and arise from the intrinsic inhomogeneous
distribution of the intercalated alkali atoms. The occurrence of
superconductivity is closely related to the {\sl c}-axis lattice constant, and
the $A$ content is crucial to superconductivity. The hump observed in
resistivity seems to be irrelevant to superconductivity. There exist many
deficiencies within the FeSe layers in $A_x$Fe$_2$Se$_2$, while their $T_{\rm
c}$ does not change so much. In this sense, superconductivity is robust to the
Fe and Se vacancies. Very high resistivity in the normal state should arise
from such defects in the conducting FeSe layers. $A_x$Fe$_2$Se$_2$ ($A$ = K,
Rb, and Cs) single crystals show the same susceptibility behavior in the normal
state, and no anomaly is observed in susceptibility at the hump temperature in
resistivity. The clear jump in specific heat for Rb$_x$Fe$_2$Se$_2$ and
K$_x$Fe$_2$Se$_2$ single crystals shows the good bulk superconductivity in
these crystals.
