  Despite extensive investigations, a topological state that hosts Majorana
edge modes in the magnetic field-induced quantum disordered state of the Kitaev
candidate material $\alpha$-RuCl$_3$ has been hotly debated. To gain more
insight into this issue, we measured the thermal Hall conductivity
$\kappa_{xy}$ of various samples grown by the Bridgman method. The results show
that the half-integer quantum thermal Hall effect is intimately related to the
magnitude of longitudinal thermal conductivity and the N\'{e}el temperature at
zero field, both of which are sample dependent. Samples exhibiting the
half-integer quantum thermal Hall effect have larger zero-field thermal
conductivity values than a threshold value, implying that a long mean free path
of heat carriers is an important prerequisite. In addition, we find that
samples with a higher N\'{e}el temperature exhibit a higher magnetic field at
which quantization starts to occur. These results indicate that the
quantization phenomenon is significantly affected by the impurity scatterings
and the non-Kitaev interactions.
