  Both impurity- and magnetic-field-induced quasiparticle states in chiral
$p$-wave superconductors are investigated theoretically by solving the
Bogoliubov--de Gennes equations self-consistently. At the strong scattering
limit, we find that a universal state bound to the impurity can be induced for
both a single nonmagnetic impurity and a single magnetic impurity. Furthermore,
we find that different chiral order parameters and the corresponding
supercurrents have uniform distributions around linear impurities. Calculations
of the local density of states in the presence of an external magnetic field
show that the intensity peak of the zero-energy Majorana mode in the vortex
core can be enhanced dramatically by tuning the strength of the external
magnetic field or pairing interaction.
