  We study the dynamical response of vacancy-induced quasiparticle excitations
in the site-diluted Kitaev spin liquid with a magnetic field. Due to the
flux-binding effect and the emergence of dangling Majorana fermions around each
spin vacancy, the low-energy physics is governed by a set of vacancy-induced
quasi-zero-energy modes. These localized modes result in unique characteristics
of the dynamical spin correlation functions, which intriguingly mimic the
single-quasiparticle density of states and further exhibit a
quasi-zero-frequency peak. By recognizing the potential observability of these
local correlation functions via scanning tunneling microscopy (STM), we show
how the STM response is sensitive to the local flux configuration, the magnetic
field strength, and the vacancy concentration. Constructing a simple model of
the localized modes, we also elucidate how the local correlation functions can
be interpreted in terms of the hybridization between these modes.
