State Space for Planar Majorana Zero Modes

Zero modes arising from a planar Majorana equation in the presence of $N$ vortices require an $mathcal{N}$-dimensional state-space, where $mathcal{N} = 2^{N/2}$ for $N$ even and $mathcal{N} = 2^{(N + 1)/2}$ for $N$ odd. The mode operators form a restricted $mathcal{N}$-dimensional Clifford algebra.