Splitting of Majorana-Fermion Modes due to Intervortex Tunneling in a px+ipy Superconductor

We consider a two-dimensional (p(x)+ip(y)) superconductor in the presence of multiple vortices, which support zero-energy Majorana-fermion states in their cores. Intervortex tunnelings of the Majorana fermions lift the topological state degeneracy. Using the Bogoliubov-de Gennes equation, we calculate splitting of the zero-energy modes due to these tunneling events. We also discuss superconducting fluctuations and, in particular, their effect on the energy splitting.