Visualising Majorana bound states in 1D and 2D using the generalized Majorana polarization

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.