  We study the possibility to realize Majorana zero mode that's robust and may
be easily manipulated for braiding in quantum computing in the ground state of
the Kitaev model in this work. To achieve this we first apply a uniform [111]
magnetic field to the gapless Kitaev model and turn the Kitaev model to an
effective p + ip topological superconductor of spinons. We then study possible
vortex binding in such system to a topologically trivial spot in the ground
state. We consider two cases in the system: one is a vacancy and the other is a
fully polarized spin. We show that in both cases, the system binds a vortex
with the defect and a robust Majorana zero mode in the ground state at a weak
uniform [111] magnetic field. The distribution and asymptotic behavior of these
Majorana zero modes is studied. The Majorana zero modes in both cases decay
exponentially in space, and are robust against local perturbations and other
Majorana zero modes far away, which makes them promising candidate for braiding
in topological quantum computing.
