  Recently, the connection between Majorana fermions bound to defects in
arbitrary dimensions, and complex momentum roots of the vanishing determinant
of the corresponding bulk Bogoliubov-de Gennes (BdG) Hamiltonian, has been
established (EPL, 2015, $\textbf{110}$, 67005). Based on this understanding, a
formula has been proposed to count the number ($n$) of the zero energy Majorana
bound states, which is related to the topological phase of the system. In this
paper, we provide a proof of the counting formula and we apply this formula to
a variety of 1d and 2d models belonging to the classes BDI, DIII and D. We show
that we can successfully chart out the topological phase diagrams. Studying
these examples also enables us to explicitly observe the correspondence between
these complex momentum solutions in the Fourier space, and the localized
Majorana fermion wavefunctions in the position space. Finally, we corroborate
the fact that for systems with a chiral symmetry, these solutions are the
so-called "exceptional points", where two or more eigenvalues of the
complexified Hamiltonian coalesce.
