Index Theorem for the Zero Modes of Majorana Fermion Vortices in Chiralp-Wave Superconductors

We show that the Majorana fermion zero modes in the cores of odd winding number vortices of a 2D ($p_x+i{p}_y$)-paired superconductor is due to an index theorem. This theorem is analogous to that proven by Jackiw and Rebbi for the existence of localized Dirac fermion zero modes on the mass domain walls of a 1D Dirac theory. The important difference is that, in our case, the theorem is proven for a two component fermion field theory where the first and second components are related by parity reversal and Hermitian conjugation.