  The excitations in the Kitaev spin liquid (KSL) can be described by Majorana
fermions, which have characteristic field dependence of bulk gap and
topological edge modes. In the high-field state of layered honeycomb magnet
$\alpha$-RuCl$_3$, experimental results supporting these Majorana features have
been reported recently. However, there are challenges due to sample dependence
and the impact of inevitable disorder on the KSL is poorly understood. Here we
study how low-energy excitations are modified by introducing point defects in
$\alpha$-RuCl$_3$ using electron irradiation, which induces site vacancies and
exchange randomness. High-resolution measurements of the temperature dependence
of specific heat $C(T)$ under in-plane fields $H$ reveal that while the
field-dependent Majorana gap is almost intact, additional low-energy states
with $C/T=A(H)T$ are induced by introduced defects. At low temperatures, we
obtain the data collapse of $C/T\sim H^{-\gamma}(T/H)$ expected for a
disordered quantum spin system, but with an anomalously large exponent
$\gamma$. This leads us to find a power-law relationship between the
coefficient $A(H)$ and the field-sensitive Majorana gap. These results are
consistent with the picture that the disorder induces low-energy linear
Majorana excitations, which may be considered as a weak localization effect of
Majorana fermions in the KSL.
