  The fermion-doubling problem can be an obstacle to getting half-a-qubit in
two-dimensional fermionic tight-binding models in the form of Majorana zero
modes bound to the core of superconducting vortices. We argue that the number
of such Majorana zero modes is determined by a Z_2 x Z_2 topological charge for
a family of two-dimensional fermionic tight-binding models ranging from
noncentrosymmetric materials to graphene. This charge depends on the dimension
of the representation (i.e., the number of species of Dirac fermions -- where
the doubling problem enters) and the parity of the Chern number induced by
breaking time-reversal symmetry. We show that in graphene there are as many as
ten order parameters that can be used in groups of four to change the
topological number from even to odd.
