  We study the vortex lattice in a two-dimensional s-wave topological
superconductor with Rashba spin-orbit coupling and Zeeman field by solving the
Bogoliubov-de Gennes equations self-consistently for the superconducting order
parameter. We find that when spin-orbit coupling is relatively weak, one of the
two underlying chiralities in the topological superconducting state can be
strongly manifest in the vortex core structure and govern the response of the
system to vorticity and a nonmagnetic impurity where the vortex is pinned. The
Majorana zero mode in the vortex core is found to be robust against the
nonmagnetic impurity in that it remains effectively a zero-energy bound state
regardless of the impurity potential strength and the major chirality. The spin
polarization of the Majorana bound state depends on the major chirality for
weak spin-orbit coupling, while it is determined simply by the vorticity when
spin-orbit coupling is relatively strong.
