  We study the solutions of generic Hamiltonians exhibiting particle-hole
mixing. We show that there exists a universal quantity that can describe
locally the Majorana nature of a given state. This pseudo-spin like
two-component quantity is in fact a generalization of the Majorana polarization
(MP) measure introduced in Sticlet et al. 2012, which was applicable only for
some models with specific spin and symmetry properties. We apply this to an
open two-dimensional Kitaev system, as well as to a one-dimensional topological
wire. We show that the MP characterization is a necessary and sufficient
criterion to test whether a state is a Majorana or not, and use it to
numerically determine the topological phase diagram.
