  We study the effects of vacancy disorder on the Kitaev model defined on a
hexagonal lattice. We show that the vacancy disorder induces a zero-mode that
is localized at the defect site. We derive analytical forms for these localized
wave functions in both the gapped and gapless phases of the Kitaev model. We
conjecture that the vacancy disorder can be utilized as a probe of the quantum
phase transition (from the gapped to gapless phases) in this model. The
behavior of the Inverse Participation Ratio (IPR) in the gapless phase and
across the transition is also studied numerically. Comments are made about the
behavior of site-site entanglement in the single particle states for the case
of a single vacancy.
