  We study the possibility to realize Majorana zero mode that is 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 conical
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 conical 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 promissing candidate for
braiding in topological quantum computing.
